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Take a deep breath and check your heart

The physician is often faced with diagnosing causes of dyspnea in its clinical practice. Patients may spontaneously complain from shortness of breath but otherwise, and often, the symptom has to be recognized and extracted from patient's history through questioning [START_REF] Banzett | Dyspnea: Don't Just Look, Ask![END_REF]. In most cases, dyspnea occurs because normal breathing frequency and amplitude does not allow delivering appropriate oxygen supply to tissues and maintaining low blood carbon dioxide or hydrogen ions (pH) concentration, at rest and/or at exercise. This occurs especially in the brain, triggering chemoreceptor stimulation and causing feeling of discomfort. Besides several different conditions pertaining to respiratory, haematological or neurological disorders, coronary insufficiency and heart failure are leading causes of dyspnea. Dyspnea is then due to non-adaptation of cardiac output to peripheral organ metabolism and, in congestive heart failure, to pulmonary hemodynamic alterations. Cardiac causes of dyspnea are frequent and dyspnea is a bad prognosis indicator. In a large cohort study, subjects presenting with dyspnea and otherwise asymptomatic had over a few years an incidence of death of cardiac causes, including sudden death, several fold higher than subjects that were not suffering from the symptom [START_REF] Abidov | Prognostic significance of dyspnea in patients referred for cardiac stress testing[END_REF]. Diabetes (presumably mainly type 2) was more frequent in subjects reporting dyspnea than in nondyspneic subjects [START_REF] Abidov | Prognostic significance of dyspnea in patients referred for cardiac stress testing[END_REF]. In type 1 diabetes, cardiac involvement is frequent and may occur early [START_REF] Boudina | Diabetic cardiomyopathy revisited[END_REF][START_REF] Wai | Prevalence, predictors and evolution of echocardiographically defined cardiac abnormalities in adults with type 1 diabetes: an observational cohort study[END_REF]. Cardiac disease remains a main cause of death [START_REF] Harjutsalo | Time trends in mortality in patients with type 1 diabetes: nationwide population based cohort study[END_REF]. Thus recognizing cardiac dysfunction at its early stage in patients with type 1 diabetes is a clinical need. This should lead to thoroughly checking glycemic control and may trigger use of treatments aimed at preserving ventricular function through lowering of peripheral resistance and/or desobstruction of coronary arteries. Can dyspnea be considered as an early marker of cardiac dysfunction in type 1 diabetes? The study by Jensen et al in the present issue [START_REF] Jensen | Self-Reported dyspnea is associated with impaired global longitudinal strain in ambulatory type 1 diabetes patients with normal ejection fraction and without known heart disease[END_REF] attempts at addressing the question in a well phenotyped population. Cardiac function was evaluated by speckle-tracking echocardiography. This technique is an improvement of two-dimensional cardiac echography and is considered to accurately allow analysis of global and regional myocardial deformation in all spatial directions. It provides information on left ventricular longitudinal, rotational and torsional dynamics, in a simpler way than magnetic resonance imaging [START_REF] Mondillo | Speckle-tracking echocardiography a new technique for assessing myocardial function[END_REF]. The study shows that dyspnea is indeed associated with alterations in ventricular dynamics by this technique in patients with no previously known heart disease and normal ventricular ejection fraction. These alterations are consistent with systolic and diastolic dysfunction. The data document the potential interest of speckle tracking echography over conventional echography for diagnosing incipient diabetic cardiac disease, although confirmation of ventricular dysfunction by hemodynamic study or magnetic resonance imaging was not sought. Patients presenting with these echographic abnormalities could however be further evaluated by monitoring of blood pressure and tests aimed at detecting subclinical coronary atherosclerosis. Interest of the study relies on both its epidemiological and clinical aspects but there is limitation in the practical usefulness of these observations. Firstly, association is mainly due to patients with the most severe stages of dyspnea (severely limiting physical activity, New York Heart Association classification class III-IV) and is weak or absent in those with the more benign and common forms of the symptom. Secondly, association is not causality, which can be difficult documenting here. Accordingly, non-cardiac causes of dyspnea should not be overlooked in otherwise asymptomatic diabetic patients [START_REF] Hsia | Lung involvement in diabetes Does it matter?[END_REF][START_REF] Thomas | Unrecognized anemia in patients with diabetes A cross-sectional survey[END_REF]. In any case, the Jensen et al study addresses, with a new technology, the difficult issue of diagnosing incipient cardiac dysfunction in diabetic patients. Together with other,

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related studies performed in patients with type 2 diabetes and in animals [START_REF] Ernande | Impaired myocardial radial function in asymptomatic patients with type 2 diabetes mellitus: a speckle-tracking imaging study[END_REF][START_REF] Li | Speckle tracking echocardiography in the diagnosis of early left ventricular systolic dysfunction in type II diabetic mice[END_REF] it should provide impetus for further evaluation of speckle-tracking cardiac echography in diabetic patients.


Cécile Vuillermoz
email: cecile.vuillermoz@inserm.fr

Stéphanie Vandentorren

Mathilde Roze

Claire Rondet

Pierre Chauvin

Cervical cancer screening among homeless

Keywords: homelessness, cervical cancer, screening, Behavioral Model of Vulnerable Populations

INTRODUCTION

Since the implementation of cytological screening tests in the 1970s, the incidence of and mortality rates from cervical cancer have declined in most European countries [START_REF] Mathew | Trends in incidence and mortality rates of squamous cell carcinoma and adenocarcinoma of cervix--worldwide[END_REF][START_REF] Vaccarella | Worldwide trends in cervical cancer incidence: impact of screening against changes in disease risk factors[END_REF]. A lack of cervical cancer screening (CCS) is strongly associated with the development of invasive cervical cancer [START_REF] Leyden | Cervical cancer in women with comprehensive health care access: attributable factors in the screening process[END_REF]. Many studies and reports have identified strong disparities in CCS coverage in the general population. In France, there were an estimated 3,000 new cases and 1,000 deaths from cervical cancer in 2012. Although national recommendations have been issued since 1990

(which recommend a CCS test every 3 years after two normal tests one year apart) (Fédération des Gynécologue et Obstétriciens de Langue Française, 1990), only 10% of women in the recommended age range (25-65 years) have a Pap test at the recommended frequency, 50% have delayed screening or have never been screened, and 40% are overscreened, resulting in a national coverage rate that has stagnated at 57% (from 2003 to 2008) (Haute Autorité de Santé (HAS), 2010). In the French-speaking general population in the Greater Paris area 8% of concerned women had never been screened for cervical cancer in 2010 [START_REF] Rondet | Are Immigrants and Nationals Born to Immigrants at Higher Risk for Delayed or No Lifetime Breast and Cervical Cancer Screening? The Results from a Population-Based Survey in Paris Metropolitan Area in[END_REF]. Multiple factors associated with an increased risk of no lifetime screening have been reported, such as socio-economic status and origin [START_REF] Vallée | The combined effects of activity space and neighbourhood of residence on participation in preventive health-care activities: The case of cervical screening in the Paris metropolitan area (France)[END_REF][START_REF] Grillo | Inequalities in cervical cancer screening for women with or without a regular consulting in primary care for gynaecological health, in Paris, France[END_REF][START_REF] Rondet | Are Immigrants and Nationals Born to Immigrants at Higher Risk for Delayed or No Lifetime Breast and Cervical Cancer Screening? The Results from a Population-Based Survey in Paris Metropolitan Area in[END_REF], but it has never been studied among homeless women in France.

Over the last decade, women with children have been the fastest growing segment of the homeless population in France. This is due to the dramatic increase in the number of homeless families [START_REF] Guyavarch | A Paris, de plus en plus de familles sans domicile[END_REF]. Between 2001 [START_REF] Brousse | Enquête sans domicile 2001, 1ère partie : Définition de la population sans-domicile et choix de ma méthode d'enquête[END_REF] and 2012 [START_REF] Yaouancq | L'hébergement des sans-domicile en 2012. Des modes d'hébergement différents selon les situations familiales[END_REF], the absolute number of French-speaking homeless adults increased by almost 50%, 25% of whom had young children living with them. In the Greater Paris Area (a region of 849 km 2 with 7.0 million inhabitants), emergency social services have sheltered more people with families than lone individuals.

Previous studies of health and healthcare in homeless families revealed that women's physical and mental health status was cause for concern [START_REF] Hwang | Interventions to Improve the Health of the Homeless: A Systematic Review[END_REF]. They are particularly more likely to have HIV/AIDS, sexually transmitted infections or gynaecological problems [START_REF] Beijer | Prevalence of tuberculosis, hepatitis C virus, and HIV in homeless people: a systematic review and meta-analysis[END_REF]. Studies of CCS in homeless women in the United States [START_REF] Chau | Cancer Risk Behaviors and Screening Rates Among Homeless Adults in Los Angeles County[END_REF][START_REF] Hogenmiller | Self-efficacy scale for Pap smear screening participation in sheltered women[END_REF][START_REF] Bharel | Disparities in cancer screening: acceptance of Pap smears among homeless women[END_REF] indicate that they are at greater risk for infection by the human papilloma virus (HPV) and for developing an invasive cancer [START_REF] Long | Cancer screening in homeless women: attitudes and behaviors[END_REF]. In addition, homeless women encounter many barriers to accessing health services (such as cost, language, transportation and discrimination) [START_REF] Kushel | Factors associated with the health care utilization of homeless persons[END_REF][START_REF] Stein | Applying the Gelberg-Andersen behavioral model for vulnerable populations to health services utilization in homeless women[END_REF][START_REF] Teruya | Health and health care disparities among homeless women[END_REF]. Compared to homeless men, women face an additional problem: the services targeting the homeless population were designed mainly for men and may not be properly suited to women's needs [START_REF] Lewis | Health care for homeless women[END_REF].

Faced with this population's invisibility, both in the public space and in French routine health statistics and health surveys, the Observatoire du Samusocial de Paris conducted a multipurpose health and social survey among sheltered families in the Greater Paris Area in the winter of 2013 [START_REF] Vandentorren | Characteristics and health of homeless Families: the ENFAMS survey in the Paris region, France 2013[END_REF]. Using those data, we sought to determine the proportion of homeless women who had undergone CCS, the time since their last test, and the factors associated with no lifetime CCS.

METHODS

Study sample

This study was based on data collected during the ENFAMS (a French acronym for "homeless families and children") survey, the first statistical survey of homeless families conducted in France [START_REF] Vandentorren | Characteristics and health of homeless Families: the ENFAMS survey in the Paris region, France 2013[END_REF]. The reference population consisted of adults, accompanied by at least one child under 13 years of age, living in social hotels, emergency centres, centres for asylum-seekers and long-term rehabilitation centres. The sampling design for the ENFAMS survey included three levels of sampling: shelters, families (the single parent or one of the two parents was interviewed, who was a woman in 95.4% of the cases), and one child in every family.

The final sample consisted of 801 families, which were interviewed face-to-face in seventeen languages by an interviewer and a psychologist. The interviewer collected a large array of data on their demographics, socioeconomic status, living conditions, health conditions and health service utilisation.

Subsample analysis and outcomes

Among the total number of women interviewed (N1=764), we performed an analysis of the subsample of those aged 25 to 65 years, the target range in the French CCS recommendations (N2=641). They were asked two questions: "Have you ever had a Pap test?" and, if the answer was 'yes', "When was your most recent one?". For the multivariate analysis, our outcome was never having had a Pap test.

Conceptual model

We used the Behavioral Model of Vulnerable Populations (BMVP) as a conceptual framework to select a set of relevant cofactors [START_REF] Aday | A framework for the study of access to medical care[END_REF][START_REF] Gelberg | The Behavioral Model for Vulnerable Populations: application to medical care use and outcomes for homeless people[END_REF][START_REF] Stein | Applying the Gelberg-Andersen behavioral model for vulnerable populations to health services utilization in homeless women[END_REF]. This model includes traditional factors and specific vulnerabilities relating to homelessness. It hypothesises that health service utilisation is a function of predisposing, enabling and need factors. Predisposing factors are characteristics that predispose an individual to access health services, enabling factors are the factors that enhance or limit the individual's ability use these services, should the need arise, and need factors include the immediate cause of health service utilisation.

Independent variables

Predisposing factors. In this study, the general predisposing factors were demographics, such as age and country of birth (in or outside of France), the level of education (none, primary, secondary or tertiary), occupational status, couple status and the number of children. The specific vulnerable predisposing factors concerned immigration (administrative status and the length of time lived in France), homelessness (the duration of homelessness, the type of housing at the time of the study, and the number of moves per year since the first period of homelessness), victimisation (a history of excision or physical or sexual violence) and substance abuse (smoking and alcohol use).

Enabling factors. The enabling factors were financial resources and healthcare utilisation. Income was divided into two categories: below or above the median value in the study population (i.e., 211 €/CU per month). Social benefits included all types of financial assistance (for the unemployed, the disabled, asylum-seekers and parents). As for the variables pertaining to healthcare utilisation, we used data on health insurance (yes/no), a physician visit during the previous year (yes/no), contraception, and previous breast cancer screening (yes/no). The vulnerable enabling factors concerned language (difficulties understanding, speaking, reading or writing French), transportation (having or not having a car and having or not having difficulties using public transportation), mobility out of the Paris area (had left the area for more than a day at least once during the previous year) and having given birth in France (at least once versus never). We also considered four variables pertaining to social networks: contact with family and friends (contact with family or friends less or more than once by telephone, SMS, Internet or mail), invitations from friends or family members to a party or a family celebration during the previous year (at least once versus never), relatives living in the Paris area, and feelings of trust (towards at least one person versus none).

Need factors. The traditional need factors were perceived general, physical and mental health status and having reported a history of at least one serious health problem. The vulnerable need factors were depression and food insecurity. The presence of depression was determined from the responses to the CIDI (Composite International Diagnostic Interview) questionnaire [START_REF] Kessler | The World Mental Health (WMH) Survey Initiative Version of the World Health Organization (WHO) Composite International Diagnostic Interview (CIDI)[END_REF]. Food insecurity was assessed by the French version of the Household Food Security Module questionnaire [START_REF] Radimer | Measurement of household food security in the USA and other industrialised countries[END_REF].

Statistical analyses

All the descriptive prevalences and proportions were weighted inversely to each participant's inclusion probability in accordance with the sampling design. The comparisons between proportions were performed using the chi-square test with a p-threshold < 0.05. We examined factors associated with no lifetime CCS separately for women with and without a regular gynaecological follow-up (RGF) because of a significant interaction (p<0.001). First, we fitted a robust Poisson regression model to each group of BMVP factors (traditional predisposing, vulnerable predisposing, traditional enabling, vulnerable enabling, traditional need and vulnerable need). We then included all the variables previously selected at p=0.20 in a final model and backward-selected them manually.

RESULTS

Population characteristics

The total number of women in homeless families in the Greater Paris Area was estimated at 9,883 (CI 95% [9,207]). These N1 women were 34 years old on average. Most of them had been born in Africa (66.0%) and had at least a secondary level of education (76.0%). One-third of them were single, and they had an average of two children living with them. Only 21.8% were employed, and their average monthly income was 319 euros per consumption unit. On average, they had been homeless for 3 years (range: 0-19), and they moved three times a year (range: 0-36). The rest of the analysis was performed for N3=508 women with complete data (among the N2=641 in the target age range).

Differences between the women with and without a regular gynaecological follow-up

The characteristics of the women with and without an RGF were different. Those without an RGF were less educated (25.3% had a primary or lower level of education vs. 12.3% of those with an RGF; p=0.007) and were less often living in a couple relationship (45.9% vs. 60.1%; p=0.017) (Table 1). They had been homeless for a shorter period of time (52.4% had been homeless for less than 2 years vs. 36.0%; p=0.0146) and more often were living in social hotels (77.6% vs. 61.4%; p<0.001) and less often in long-term rehabilitation shelters (11.7% vs. 27.3%; p<0.001). They more often had been victims of physical or sexual assault (16.1% vs. 4.1%; p<0.001) and were more likely not to have health insurance (15.8% vs. 8.3%; p=0.049) and not to have had a medical visit (20.1% vs. 9.9%; p=0.015) or a mammogram (85.0% vs. 68.4%; p<0.001) during the previous year (Table 2). Difficulties in French were also more prevalent in this group (62.4% vs. 46.4%; p=0.011).

Screening participation rates

We determined that 56.9% (CI 95% [52.4-61.4]) of the homeless women were never-screeners, with a significant difference between the women who reported having an RGF (33.3% (CI 95% [23.3-43.2]) and those who reported not having an RGF (64.2% (CI 95% [58.0-70.4]). Of the screeners, 11.5% (CI 95% [5.8-17.2]) had their last Pap test more than 3 years before the survey (Figure 1).The proportions were also significantly different according to their RGF status: 4.2% (CI 95% [0.1-8.3]) and 15.5% (CI 95% [7.4-23.5]), respectively (p=0.005).

Factors associated with no lifetime cervical cancer screening

Univariate analysis

In the women without an RGF, no lifetime CCS was significantly associated with somepredisposing factors such as a low level of education, being unemployed and alcohol abuse( see Table 1) and some enabling factors (no physician visit during the previous year, no invitation from friends or family during the previous year, difficulties in French, and not having a car; see Table 2). No need factors were associated with no lifetime cervical cancer screening (Table 3). The factors associated with a p-value < 0.20 for the multivariate analysis were age, the length of time lived in France, the duration of homelessness, social benefits, health insurance, mobility out of the Paris area, and having given birth in France. In the women with an RGF, the predisposing factors significantly associated with no lifetime CCS were age and the country of birth (Table 1). The enabling factors associated with no lifetime CCS were a low monthly income, not having health insurance, no physician visit during the previous year, being a never-screener for breast cancer, and difficulties in French (Table 2). The need factors associated with no lifetime CCS were poor (or very poor) mental health status and food insecurity (Table 3).

Multivariate analysis

After adjustment for age, among the women without an RGF, those who had never been screened for cervical cancer had more often a low level of education (with a dose-response trend, although it was not significant; p=0.597) and were more often unemployed or in one or more of the following situations: had lived in France for less than a quarter of their lives, had been homeless for less than 2 years, or had a history of excessive alcohol consumption (predisposing factors; see Table 4). They more often had not seen a physician during the previous year (but also slightly more often had health insurance), more often had not been invited by friends or family during the previous year and/or had never given birth in France (enabling factors).

In the women with an RGF (Table 4), the predisposing factors associated with no lifetime CCS were age > 45 years, not being a French citizen and a history of excessive alcohol consumption. The enabling factors were not having health insurance, no physician visit during the previous year, never having been screened for breast cancer and having difficulties in French. The only need factor associated with no lifetime CCS was poor mental health status.

DISCUSSION

More than half of the homeless women in the Greater Paris Area who were interviewed in our study had never been screened. Since only sheltered women with children had been sampled, our results cannot be extrapolated to women living on the street and/or who do not have any children with them. Some studies indicate that the absence of screening practices may even be higher in this population (Nyamathi et al., 2000;[START_REF] Boxwala | Factors associated with breast cancer screening in Asian Indian women in metro-Detroit[END_REF].

In comparison, in the French-speaking general population in the same area in 2010, only 8% of women had never been screened for cervical cancer [START_REF] Rondet | Are Immigrants and Nationals Born to Immigrants at Higher Risk for Delayed or No Lifetime Breast and Cervical Cancer Screening? The Results from a Population-Based Survey in Paris Metropolitan Area in[END_REF]. In 2013, a non-governmental medical organisation, Doctors of the World, conducted a survey in France among 203 socially excluded women who visited their free clinics and reported that 70% of them had never been screened (Médecins du Monde, 2013). In the United States, studies on homeless women found that 10 to 50% of them had never been screened [START_REF] Weinreb | Pap smear testing among homeless and very low-income housed mothers[END_REF][START_REF] Chau | Cancer Risk Behaviors and Screening Rates Among Homeless Adults in Los Angeles County[END_REF][START_REF] Lewis | Health care for homeless women[END_REF][START_REF] Bharel | Disparities in cancer screening: acceptance of Pap smears among homeless women[END_REF].

Consistently with previous French studies, having or not having a regular gynaecological health followup in primary care influences the risk of being a never-screener [START_REF] Grillo | Inequalities in cervical cancer screening for women with or without a regular consulting in primary care for gynaecological health, in Paris, France[END_REF]. In our study, the proportion of never-screeners was almost twice as high in women without an RGF. Clearly, although we believe that "gynaecological health" refers to genital health for most women (and even those with the poorest health literacy), we do not know exactly what "regular" means. However, improving access to women's healthcare is probably the best way to increase CCS coverage among these women.

In our study, the characteristics of the women with an RGF differed from those of women without an RGF. A previous French qualitative study among homeless women in the Paris area in 2005 described profiles of gynaecological healthcare [START_REF] Brunet | Féminité, accès aux soins, maternité, et risques vécus par les femmes en grande précarité. Une contribution à l'amélioration de leur santé gynécologique[END_REF]. It found that homeless women who did not avail themselves of gynaecological health services used other health services less in general, that pregnancy was often the only reason they had ever seen a gynaecologist, and that a history of sexual violence was a strong barrier to gynaecological consultations. In this connection, in our study, the women without an RGF reported a history of physical or sexual abuse four times more often than those with an RGF. It is noteworthy that the women without an RGF had been homeless for a shorter period of time than those with an RGF. It can be hypothesised that recently homeless women have other urgent priorities than preventive care and that, over time, some of them re-engage in preventive behaviours.

The barriers to CCS identified in this study among the women without a regular gynaecological follow-up were consistent with the literature on homeless women [START_REF] Weinreb | Health characteristics and medical service use patterns of sheltered homeless and low-income housed mothers[END_REF][START_REF] Long | Cancer screening in homeless women: attitudes and behaviors[END_REF][START_REF] Weinreb | Pap smear testing among homeless and very low-income housed mothers[END_REF][START_REF] Chau | Cancer Risk Behaviors and Screening Rates Among Homeless Adults in Los Angeles County[END_REF][START_REF] Bharel | Disparities in cancer screening: acceptance of Pap smears among homeless women[END_REF] and were mainly associated with socioeconomic conditions (education level and occupational status) [START_REF] Lewis | Health care for homeless women[END_REF]. Interestingly, we observed that the homeless women who had never given birth in France were also more likely to be never-screeners, since a Pap test is part of the first routine, mandatory and free prenatal check-up, if one was not performed recently. Two factors were associated in an unexpected direction: excessive alcohol consumption and not having health insurance seemed to "protect" women from being never-screeners.

We attempted to explain these unexpected findings by testing certain interactions (e.g., with immigration status or the duration of homelessness), but none of them was significant, probably because of the small size (N=383) of this subsample of women without an RGF. We cannot explain these results, but we did note that, inversely, associations were observed in the expected direction in the other stratum (women with an RGF).

Although the screening rate was higher among the women with a RGF, a third of them were neverscreeners. Reporting biases are possible in such declarative data, but the investigators systematically explained the Pap test in lay terms ("A pap is a small sample taken by scraping at the back of the vagina during a gynaecological exam"). The factors associated with never-screening might enable us to understand why these women with a RGF had never been screened for cervical cancer. The barriers were mainly migration origin, exclusion from the healthcare system and health-related behaviours. These barriers are consistent with the literature concerning the general population [START_REF] Akers | Factors underlying disparities in cervical cancer incidence, screening, and treatment in the United States[END_REF][START_REF] Grillo | Inequalities in cervical cancer screening for women with or without a regular consulting in primary care for gynaecological health, in Paris, France[END_REF].

Our study has some limitations apart from the recall and reporting biases mentioned above in connection with self-reported data. First, we did not collect any information about the women's knowledge and attitudes about CCS. Such information would have provided explanations for the never-screening.

Second, because of the small sample size and the vast heterogeneity of the women's origins (more than 60 countries of birth were reported), we were unable to investigate these origins or cultural factors much further. Lastly, the causal ordering between predisposing, enabling and need factors cannot be demonstrated in this study because of its cross-sectional design. On the other hand, the main strengths of the ENFAMS survey were its sampling design, which guaranteed its representativeness, its multilingualism, which made it possible  for the first time in France  to collect data from non-Frenchspeaking homeless women, the large set of data collected, and the use of a conceptual model to help in the modeling strategy.

Our results argue for a more systematic proposal and performance of CCS in primary care. Indeed, 82% of the women in the target age range had visited a physician at least once during the previous year, yet 53% of them were still never-screeners, not to mention, once again, the fact that a third of the women with an RGF were never-screeners as well. This means that there had been many lost opportunities during these women's primary care visits and it reveals the failure of the primary health care system to offer proper medical preventive care to the homeless women population. Since homeless women are regularly relocated from shelter to shelter (depending on the facilities' availability and on homeless flow management in a chronically underresourced region), primary care professionals must be more informed and aware that every contact with health services should be an opportunity to check their screening status and to ensure that those due for one actually have a Pap test.

Of course, providing a Pap test is not the end of the story. Many studies have documented that lowincome women do not understand the results and consequently do not obtain the necessary follow-up and treatment for their abnormal Pap test [START_REF] Engelstad | Abnormal Pap Smear Follow-Up in a High-Risk Population[END_REF][START_REF] Quinlivan | Abnormal pap smears in teenage mothers and the association with domestic violence, homelessness, and Chlamydia[END_REF][START_REF] Coker | Life stressors are an important reason for women discontinuing follow-up care for cervical neoplasia[END_REF]. However, to our knowledge, none of those studies specifically considered homeless women. Further studies on the linkage to care among homeless women with detected abnormalities are needed to ensure that they enjoy equal access to care, even in countries like France, where financial barriers are not an issue (at least theoretically) in cancer healthcare.

Table 1 -Predisposing factors and no lifetime cervical cancer screening among homeless women with or without 299 a regular gynaecological follow-up in the Greater Paris Area, France, 2013.

 1

	300
				Regular Gynaecological Follow-up		p-
		Freq. N=508 (%)	Freq (%)	No (N=383) No CCS (%) PR	95% CI	Freq. (%)	Yes (N=125) No (%) CCS PR	95% CI	value for no RGF versus RGF
	Traditional Predisposing Factors
	Age				0.062				<0.001	0.804
	25-29	27.1 28.2 73.5 1.10	[1.02-1.17]	23.4 59.8 1.21 [1.03-1.42]
	30-34	30.3 29.5 59.2 Ref.		33.0 37.9	Ref.
	35-44	37.5 37.5 61.1 1.02	[0.94-1.11]	37.5 18.1 0.87 [0.75-1.02]
	45 or older	5.1	4.8	65.5 1.03	[0.89-1.20]	6.1	0.0	0.77 [0.66-0.90]
	Country of birth				0.509				<0.001	0.801
	Outside of France	94.6 94.7 65.0 1.03	[0.94-1.14]	94.2 35.3 1.25 [1.10-1.42]
	France	5.4	5.3	50.5 Ref.		5.8	0.0	Ref.
	Level of education				<0.001				0.157	0.014
	None	8.9	10.2 92.0 1.43	[1.29-1.58]	4.6	54.2 1.28 [0.95-1.74]
	Primary	13.4 15.1 79.8 1.33	[1.19-1.48]	7.7	53.5 1.26 [0.97-1.63]
	Secondary	60.4 56.5 64.0 1.20	[1.09-1.33]	73.5 32.6 1.06 [0.90-1.25]
	Tertiary	17.2 18.1 36.2 Ref.		14.2 18.9	Ref.
	Occupational status				0.015				0.710	0.797
	Employed	21.9 22.9 48.4 Ref.		18.7 18.0	Ref.
	Unemployed	32.1 31.5 73.9 1.16	[1.05-1.28]	34.2 30.0 1.07 [0.91-1.26]
	Student or retiree	46.0 45.6 65.5 1.09	[0.99-1.20]	47.1 41.7 1.04 [0.86-1.22]
	Couple status				0.368				0.910	0.049
	Living in a couple relationship	49.1 45.9 67.9 Ref.		60.1 35.8	Ref.
	In a couple relationship but not living together	16.3 17.8 62.1 0.98	[0.90-1.06]	11.4 41.1 1.02 [0.84-1.23]
	Not in a couple relationship	34.6 36.4 60.6 0.95	[0.89-1.02]	28.5 24.8 0.97 [0.85-1.11]
	Number of children
	Fewer than 3	75.8 76.6 62.8 Ref.	0.553	73.2 31.5	Ref.	0.557	0.548
	3 or more	24.2 23.4 69.0 1.03	[0.95-1.12]	26.8 38.0 1.05 [0.89-1.23]
	Vulnerable Predisposing Factors
	Administrative status				0.503				0.107	0.663
	French citizen	8.4	8.5	58.6 Ref.		7.9	0.0	Ref.
	Legal resident status	57.6 58.5 60.3 0.95	[0.81-1.11]	37.9 36.0 1.27	[1-1.61]
	Undocumented	34.0 32.9 72.6 0.99	[0.84-1.17]	54.3 36.3 1.26	[1-1.58]
	Length of time lived in France				0.052				0.692	0.561
	A quarter of life or less	73.7 74.4 69.5 1.10	[1.00-1.22]	71.3 38.6 1.04 [0.85-1.27]
	More than a quarter of life	26.3 25.6 48.8 Ref.		28.7 20.1	Ref.
	Duration of homelessness				0.151				0.922	0.015
	2 years or less	48.6 52.4 71.0 1.06	[0.98-1.15]	36.0 28.0 1.01 [0.83-1.23]
	More than 2 years	51.4 47.6 56.8 Ref.		64.0 36.3	Ref.
	Type of housing				0.939				0.289	<0.001
	Social hotel	73.9 77.6 65.1 1.02	[0.88-1.18]	61.4 39.3 1.13 [0.95-1.34]
	Centre for asylum-seekers	4.7	5.0	65.5 1.03	[0.88-1.21]	3.7	13.5 0.97 [0.75-1.26]
	Emergency housing centre	6.1	5.6	66.5 1.00	[0.84-1.18]	7.7	39.8 1.17 [0.96-1.44]
	Long-term rehabilitation centre	15.3 11.7 56.6 Ref.		27.3 20.7	Ref.
	Number of moves per year				0.493				0.375	0.390
	Less than 4	79.7 78.7 61.2 Ref.		83.2 34.8	Ref.
	4 or more	20.3 21.3 75.6 1.03	[0.95-1.11]	16.8 25.6 0.91 [0.74-1.12]
	History of excision				0.433				0.279	0.052
	Yes	21.5 19.2 66.5 1.03	[0.95-1.13]	29.1 45.9 1.10	[0.93-1.3]
	No	78.5 80.8 63.7 Ref.		70.9 28.1	Ref.
	History of physical or sexual violence				0.747				0.081	<0.001
	Yes	13.4 16.1 63.3 0.99	[0.90-1.08]	4.1	19.5 0.80 [0.63-1.03]
	No	86.6 83.9 64.4 Ref.		95.9 33.9	Ref.
	Smoking status				0.578				0.111	0.405

Table 2 -Enabling factors and no lifetime cervical cancer screening among homeless women with or without a 302 regular gynaecological follow-up in the Greater Paris Area, France, 2013.

 2 Less than 1 contact in a 3-day period 73.6 73.6 66.0 1.00 [0.93-1.07] 73.7 40.2 1.14 [0.98-1.32] More than 1 contact in a 3-day period 26.4 26.4 59.3 Ref. 26.3 13.7 Ref. Invited

	303
				Regular Gynaecological Follow-up		p-
		Freq. N=508 (%)	Freq. (%)	No (N=383) CCS No (%) PR	95% CI	Freq (%)	Yes (N=125) (%) No CCS PR	95% CI	value for no RGF versus RGF
	Traditional Enabling Factors
	Monthly income per consumption unit				0.338			0.042	0.480
	Less than 211 euros	46.6 45.6 72.0 1.05 [0.95-1.15] 49.7 39.5 1.17 [1.01-1.37]
	More than 211 euros	53.4 54.4 57.7 Ref.		50.3 27.1 Ref.
	Social benefits during the previous year				0.059			0.168	0.627
	None	64.0 63.3 75.1 1.08 [1.00-1.18] 66.2 36.0 0.89 [0.76-1.05]
	One or more	36.0 36.7 57.9 Ref.		33.8 31.9 Ref.
	Health insurance				0.081			0.015	0.049
	No	15.8 18.0 67.2 0.93 [0.85-1.01]	8.3	72.1 1.28 [1.05-1.57]
	Yes	84.2 82.0 63.6 Ref.		91.7 29.8 Ref.
	Physician visit during the previous year				<0.001			0.005	0.015
	Yes	82.2 79.9 59.9 Ref.		90.1 30.1 Ref.
	No	17.8 20.1 81.5 1.13 [1.06-1.21]	9.9	61.8 1.31 [1.08-1.57]
	Contraception				0.430			0.550	0.203
	Yes	41.1 60.8 61.3 Ref.		47.7 34.3 Ref.
	No	58.9 39.2 66.1 1.03 [0.96-1.11] 52.3 32.4 0.96 [0.85-1.09]
	Mammogram				0.246			<0.001	<0.001
	Yes	18.8 15.0 54.3 Ref.		31.6 16.6 Ref.
	No	81.2 85.0 66.0 1.06 [0.96-1.16] 68.4 41.0 1.24 [1.09-1.40]
	Vulnerable Enabling Factors
	Difficulties in French				<0.001			0.005	0.011
	Yes	58.8 62.4 72.5 1.11 [1.04-1.19] 46.4 47.5 1.21 [1.06-1.38]
	No	41.2 37.6 50.5 Ref.		53.6 20.9 Ref.
	Had a car				0.050			0.547	0.460
	Yes	11.4 11.9 42.1 Ref.		9.4	19.7 Ref.
	No	88.6 88.1 67.2 1.15 [1.00-1.33] 90.6 34.7 1.06 [0.87-1.29]
	Difficulties with public transportation				0.313			0.113	0.577
	Yes	37.6 36.6 71.2 1.03 [0.97-1.09] 40.7 39.2 1.11 [0.97-1.27]
	No	62.4 63.4 60.2 Ref.		59.3 29.2 Ref.
	Mobility out of the Paris area				0.088			0.082	0.980
	Yes	21.7 21.5 47.2 Ref.		21.7 42.2 Ref.
	No	78.4 78.5 68.9 1.08 [0.99-1.18] 78.3 30.8 0.88 [0.76-1.02]
	History of delivery in France				0.122			0.153	0.985
	At least 1 delivery in France	74.5 74.5 60.2 Ref.		74.4 34.6 Ref.
	No deliveries in France	25.5 25.5 76.0 1.05 [0.99-1.11] 25.6 29.5 0.91 [0.80-1.04]
	Contact with family and friends				0.952			0.089	0.978

by friends or family to a party or a family celebration during the previous year

		0.040	0.493	0.481
	No	40.9 41.9 77.4 1.08 [1.00-1.17] 37.3 35.6 0.96 [0.85-1.08]
	At least once	59.1 58.1 54.7 Ref.	62.7 31.9 Ref.
	Family living in the Paris area	0.454	0.120	0.693
	Yes	45.8 46.3 58.7 Ref.	44.0 21.5 Ref.
	No	54.2 53.7 69.0 1.03 [0.96-1.10] 56.0 42.5 1.10 [0.98-1.24]
	Trust in at least one person	0.294	0.061	0.102
	Yes	69.0 66.7 61.0 Ref.	77.0 30.2 Ref.
	No	31.0 33.3 70.7 1.04 [0.97-1.11] 23.0 43.7 1.15 [0.99-1.34]

Table 3 -Need factors and no lifetime cervical cancer screening among homeless women with or without a 304 regular gynaecological follow-up in the Greater Paris Area, France, 2013.

 3

	305
		Freq. N=508 (%)	Freq (%)	Regular Gynaecological Follow-up No (N=383) Yes (N=125) No CCS (%) PR 95% CI Freq (%) no CCS (%) PR	95% CI	p-value for no RGF versus RGF
	Traditional Need Factors
	History of at least one serious health problem				0.362	0.355	0.268
	Yes	31.6 30.0	61.1	0.96 [0.88-1.05] 36.9 27.2 0.93 [0.79-1.09]
	No	68.4 70.0	65.6	Ref.	63.1 36.8 Ref.
	General health status				0.215	0.416	0.979
	Very good, good or average	88.1 88.1	63.3	Ref.	88.2 30.4 Ref.
	Poor or very Poor	11.9 11.9	71.2	1.08 [0.96-1.23] 11.8 54.9 0.87 [0.63-1.21]
	Physical health status				0.605	0.127	0.608
	Very good, good or average	89.7 90.1	64.3	Ref.	88.3 29.8 Ref.
	Poor or very poor	10.3	9.9	63.5	0.96 [0.82-1.12] 11.7 59.2 1.23 [0.94-1.59]
	Mental health status				0.863	0.006	0.269
	Very good, good or average	76.8 78.1	63.8	Ref.	72.2 24.5 Ref.
	Poor or very poor	23.2 21.9	65.9	1.01 [0.92-1.11] 27.8 56.2 1.25 [1.07-1.47]
	Vulnerable Need Factors
	Food insecurity				0.873	0.012	0.367
	Security or low insecurity	52.4 53.6	64.1	Ref.	51.7 21.1 Ref.
	Medium or severe insecurity	47.6 46.4	64.3	1.01 [0.94-1.07] 48.3 46.3 1.21 [1.04-1.40]
	Depression				0.479	0.698	0.412
	Yes	29.3 30.5	61.2	0.97 [0.90-1.05] 25.4 30.9 0.97 [0.81-1.15]
	No	70.7 69.5	65.5	Ref.	74.6 34.1 Ref.
	306
	307

Time since the last cervical cancer screen as at the day of the survey (among screeners).

	312
	313

Acknowledgements

ENFAMS survey received financial support from the Agence régionale de santé d'Ile-de-France (ARS), Cancéropôle Ile-deFrance, Caisse nationale des allocations familiales (CNAF), Fondation de France, Fondation Macif, Fondation Sanofi Espoir, Institut national de prévention et d'éducation pour la santé (INPES), Institut de recherche en santé publique (IReSP), Institut de veille sanitaire (InVS), Ministère de l'Intérieur, Procter et Gamble, State Street, Observatoire national de l'enfance en danger (ONED) and material support from HemoCue®T. We thank all the families involved in this study. Finally, our thanks to Mark Wickens for the English editing and revision of the manuscript.


Ph.D Leonardo Milan Militano

Milan Erdelj

Antonella Molinaro

Nathalie Mitton

Antonio Iera

Antonella Erdelj

Nathalie Molinaro

Antonio Mitton

Iera

Enrico Natalizio
email: enrico.natalizio@hds.utc.fr

Senior Lecturer, M J Thinus Booysen

Valeria Loscrì
email: valeria.loscri@inria.fr

Recharging vs. Replacing Sensor Nodes Using Mobile Robots for Network Maintenance

Keywords: Telecommunication Systems Recharging vs. Replacing Sensor Nodes Using Mobile Robots Wireless Sensor Networks, Mobile robots, Network maintenance, Energy recharging

published or not. The documents may come   L'archive ouverte pluridisciplinaire

Abstract Wireless sensor networks (WSNs) have been of very high interest for the research community since years, but the quest for deploying a self-sustained network and effectively prolonging its lifetime has not found a satisfactory answer yet. Two main approaches can be identified that target this objective: either "recharging" or "replacing" the sensor nodes that are running out of energy. Of particular interest are solutions where mobile robots are used to execute the above mentioned tasks to automatically and autonomously maintain the WSN, thus reducing human intervention. Recently, the progress in wireless power transfer techniques has boosted research activities in the direction of battery recharging, with high expectations for its application to WSNs. Similarly, also sensor replacement techniques have been widely studied as a means to provide service continuity in the network. Objective of this paper is to investigate the limitations and the advantages of these two research directions. Key decision points must be identified for effectively supporting WSN self-maintenance: (i) which sensor nodes have to be recharged/replaced; (ii) in which order the mobile robot is serving (i.e., recharging/replacing) the nodes and by following which path; (iii) how much energy is delivered to a sensor when recharged. The influence that a set of parameters, relative to both the sensors and the mobile robot, on the decisions will be considered. Centralized and distributed solutions are compared in terms of effectiveness in prolonging the network lifetime and in allowing network self-sustainability. The performance evaluation in a variety

Introduction

Wireless sensor networks (WSNs) are nowadays deployed for a large variety of applications and are still gaining interest in several fields [START_REF] Akyildiz | A survey on sensor networks[END_REF]. The network usually consists of battery-powered wireless devices, with sensing and communication capabilities, that collect data about the environment or an event of interest (e.g., temperature, light, movement) and relay data toward a "sink" in a multi-hop manner [START_REF] Watteyne | From MANET To IETF ROLL Standardization: A Paradigm Shift in WSN Routing Protocols[END_REF]. Research in this field has been active for years, and still several open issues are waiting for valid solutions [START_REF] Yick | Wireless sensor network survey[END_REF]. Besides the constraints in terms of processing power and storage capacity, the most important issue in WSNs is the limited battery duration of sensors and the consequent limited network lifetime.

As a consequence, WSN deployments should cope with the problem of sensor isolation and multiple deaths of nodes over the time. To manage such issues, solutions should either prevent or resolve these anomalous situations. How crucial the death of a single sensor node can be for the network, is related to the definition of network lifetime for a specific application. In this paper, we focus on the restrictive cases when the network lifetime is determined by the first dying node; in this case the objective of a network selfmaintenance solution is to prevent any single node from running out of energy. In order to succeed in this task, sensor nodes should be "refilled" with energy or "replaced" with a new node prior to their battery exhaustion. In particular, sensor recharging is a technique for sensor lifetime pro-longation that implies the process of directly or wirelessly recharging sensors' battery, whereas sensor replacement is the process of physical replacement of the entire sensor device or its battery unit. Noteworthy, when WSNs are being deployed in hardly accessible areas, or where human intervention is costly to carry out recharging/replacement tasks, the use of mobile robots for automatic and autonomous WSN maintenance becomes of high interest; this is the reference scenario for this paper.

The research in the direction of sensor recharging has been fueled by the recent evolution in wireless power transfer techniques [START_REF] Kurs | Wireless power transfer via strongly coupled magnetic resonances[END_REF]- [START_REF] Kurs | Simultaneous mid-range power transfer to multiple devices[END_REF]. The recharging solutions still have some issues to solve, mainly related to the best route the mobile robot has to follow to refill the battery of exhausting sensors. On the other hand, the alternative technique of sensor replacement has additional practical limitations related to the number of sensors a mobile robot can carry around simultaneously. This aspect can be very limiting in applications where the sensing hardware is not dimensionally small.

Solutions will be proposed for answering key questions such as: (i) which sensor nodes are to be recharged/replaced;

(ii) which order the robot is going to follow to serve (i.e., recharge or replace) the nodes and which delivery route is chosen; (iii) how much energy is delivered to a sensor when recharged. Several parameters (such as battery capacity of the mobile robot, time needed to recharge the nodes, number of nodes in the network, battery power consumption, and network topology) influence the effective system design. The most important among them will be duly taken into account in our research.

The remainder of the paper is organized as follows. The next section gives an overview of the related work relevant to node recharging and replacement techniques to prolong the network lifetime. In Section 4 a detailed overview and definition of system settings, parameters of interest, and objectives for the present work is given. Sections 5 and 6 describe the proposed solutions to the raised problem, when either recharging or replacement techniques are adopted. In Section 7 a performance evaluation for the proposed solutions is presented, and final remarks in Section 8.

Related Work

Energy conservation solutions in WSN is a widely investigated topic in the literature [START_REF] Liu | Energy conservation algorithms for maintaining coverage and connectivity in wireless sensor networks[END_REF], [START_REF] Anastasi | Energy conservation in wireless sensor networks: a survey[END_REF], [START_REF] Akyildiz | A survey on wireless multimedia sensor networks[END_REF], [START_REF] Pantazis | A Survey on Power Control Issues in Wireless Sensor Networks[END_REF], [START_REF] Yeh | ipower: an energy conservation system for intelligent buildings by wireless sensor networks[END_REF] as the limited energy storage capacity of sensors requires solutions that either solve or alleviate the impact on the service continuity in a WSN. Besides the two approaches discussed in this paper, also energy harvesting techniques that convert ambient energy (for instance, solar, wind, thermal or vibration energy [START_REF] Sudevalayam | Energy harvesting sensor nodes: Survey and implications[END_REF]) into electrical energy could be applied. However, even if the results seem to be promising, in many cases their success is limited due to the environment dependent technology and the strong requirements for practical deployment.

Node Recharging Solutions

The ability to transfer electric power from one storage device to another one [START_REF] Kurs | Wireless power transfer via strongly coupled magnetic resonances[END_REF] or to multiple devices [START_REF] Kurs | Simultaneous mid-range power transfer to multiple devices[END_REF] without any plug or wire, and in non-line-of-sight conditions, is indeed revolutionary. In fact, these novel techniques pave the way for a plethora of innovative applications and service when recharging of battery-driven devices is of vital importance for the system sustainability (e.g., border surveillance, security monitoring, agents-based patrolling, real-time fire detection).

Particular attention has been devoted to these techniques by the WSN research community, where self-sustainability and network lifetime are topics of utmost importance. This is witnessed, for instance, by recent works in [START_REF] Shi | On renewable sensor networks with wireless energy transfer[END_REF], [START_REF] Xie | Making sensor networks immortal: An energy-renewal approach with wireless power transfer[END_REF] and [START_REF] Xie | On renewable sensor networks with wireless energy transfer: The multinode case[END_REF] where the authors propose very powerful solutions for network self-sustainability based on wireless power transfer between devices. In particular, in [START_REF] Shi | On renewable sensor networks with wireless energy transfer[END_REF] and [START_REF] Xie | Making sensor networks immortal: An energy-renewal approach with wireless power transfer[END_REF] the authors present a system model where a recharging vehicle visits all the nodes in the network to fully recharge them. In the proposed solution, using a vehicle instead of a mobile robot gives some degrees of human intervention in the network. An optimization problem is modeled to maximize the time the vehicle is not active over the time it is driving around the network to recharge the nodes. A key assumption for the proposed model is that the vehicle has infinite energy to recharge the nodes; this assumption guarantees that the vehicle fully recharges the whole network in every visiting cycle. In their contributions the authors show that, under certain conditions and network settings, the network is actually "immortal" in the sense that no sensor is ever running out of battery, which is a very promising result.

In [START_REF] Xie | On renewable sensor networks with wireless energy transfer: The multinode case[END_REF] the problem is extended by considering the possibility to divide the network area into cells and recharge more nodes simultaneously. While this solution clearly improves the network performance, still the scalability remains an issue since for larger number of nodes always a limiting condition exists where a single vehicle is not able to find a solution that guarantees the network immortality.

The wireless power transfer technology has been studied in other contributions as well. In particular, in [START_REF] Peng | Prolonging sensor network lifetime through wireless charging[END_REF] with the objective to prolong the network lifetime, the effects of different configurations and design parameters are studied in a scenario where a robot delivers energy to single sensors. The robot has a limited battery capacity and it has to find the optimal charging sequence, that is the sequence of nodes to visit and recharge. At the same time, the amount of time to recharge sensors is not fixed and needs to be defined. Various traveling and charging algorithms are compared show-ing the beneficial effect of simultaneously considering the robot movement plan and the residual energy of each sensor nodes in every instant of time. Nevertheless, prolonging the network lifetime and immortality is not guaranteed; this result showing that further investigation in this field is strongly needed.

Node Replacement Solutions

Node replacement is a valid alternative to be considered whenever a sensor node fails due to different reasons (e.g., running out of energy, hardware crash, etc.). A viable approach to node replacement is to fill sensing holes by relocating redundant nodes in the network. To implement this solution either sensors mobility is required [START_REF] Wang | Sensor relation in mobile sensor networks[END_REF] or a mobile robot can be used to discover holes and replace out-of-work nodes in the network [START_REF] Magklara | Node Discovery and Replacement Using Mobile Robot[END_REF]. A challenging issue for the latter solutions is to allow mobile robots to precisely navigate toward the interested sensor nodes. This aspect is analyzed in [START_REF] Sheu | Design and implementation of mobile robot for nodes replacement in wireless sensor networks[END_REF], where a solution based on the received signal strength allows to determine the direction taken by the mobile robot. A further alternative to cope with sensing holes is proposed in [START_REF] Mei | Sensor replacement using mobile robots[END_REF], where a small number of mobile robots is used to replace failed sensors with new ones. This is particularly interesting when nodes are static and have no possibility to relocate autonomously. In particular, the authors propose both centralized and distributed algorithms for detecting and reporting sensor failures, and coordinating the movement of robots to minimize the motion energy and the messaging overhead.

A different approach is proposed in [START_REF] Tong | Node reclamation and replacement for long-lived sensor networks[END_REF] and [START_REF] Tong | On-demand node reclamation and replacement for guaranteed area coverage in long-lived sensor networks[END_REF], where a node reclamation and replacement strategy is presented. A mobile repairman (a robot or a human labor) periodically replaces sensors with low or null energy with fully charged ones. The retrieved sensors are then recharged at a base station. In particular, in [START_REF] Tong | Node reclamation and replacement for long-lived sensor networks[END_REF] the reference scenario considers multiple sensors near the same location and several sensing locations in the system. The solution is based on a two-tier scheduling; the global-tier scheduling calculates the travel schedule and the number of sensors to be reclaimed/replaced; the local-tier scheduling regards the local activity scheduling of the sensors in the group. While the two-tier solution is interesting in general, for the scenario studied in the paper, the sensor nodes are allowed to die before being replaced, as long as the sensing quality in the group they belong to meets the system requirements. In [START_REF] Tong | On-demand node reclamation and replacement for guaranteed area coverage in long-lived sensor networks[END_REF] the same research is extended to consider also network area coverage instead of point coverage, where single points of interest are monitored within a network, as studied in [START_REF] Tong | Node reclamation and replacement for long-lived sensor networks[END_REF].

Motivations and Objectives

As described in the previous sections, both node recharging and node replacement techniques seem to be valid approaches to prolong the network lifetime in WSNs. An investigation on the key aspects, on the limitations and the advantages of these two research directions would offer the network designer useful information to deploy and manage a WSN. The focus of this paper is limited to a single mobile robot moving around the network to carry out the task of recharging/replacing energy endangered sensors. The scope of the analysis is oriented on highlighting the different solutions and approaches that can be proposed to model a WSN maintenance based on either of these techniques.

A first classification of the possible solutions discerns between centralized and distributed approaches. This classification refers to the recharge/replace decisions taken by the mobile robot. With a centralized approach decisions are taken at the base station, which then provides the mobile robot with instructions on the best way to visit the nodes that need assistance. This implies some information processing at the base station, as it is supposed to have full-knowledge of the state of the network. This is a reasonable assumption under the hypothesis of sending energy state information from the sensors to the base station through the WSN. A distributed approach, instead, leaves space to the robot to implement its own method to visit the nodes. These choices will be performed step-by-step, based on the information the mobile robot collects from sensors in its sensing range and current energy conditions of nodes and mobile robot.

For any of the approaches to implement, a WSN maintenance solution is required to answer the following questions:

1. Which nodes will be visited by the robot for maintenance purposes? 2. In which order should the nodes be visited by the robot? 3. How much energy should each visited node receive from the robot? Only in case of energy recharging solutions, the amount of energy to be transferred to the sensor nodes to prolong the network lifetime shall be defined.

In particular, the first two questions yield for any of the considered approaches, whereas the third question refers only to recharging techniques. Examples of study cases that can be identified are: (i) the mobile robot has the possibility to reach and fully serve (when recharging this means fully recharge the battery of the sensor) all nodes requiring assistance, (ii) the mobile robot has not the possibility to reach and serve all nodes requiring assistance due to its low energy for movement or long distances between the sensors, (iii) the mobile robot can reach and serve all nodes requiring assistance, but has not the possibility to replace all nodes or recharge the nodes fully due to low energy or low number of sensors for replacement available, (iv) the time available to the mobile robot for recharging the sensors is enough to visit all sensors requiring assistance, but they cannot be fully recharged.

Solutions will be proposed for any of the study cases, and the performance evaluation presented in this paper aims at evaluating the proposals in a variety of scenarios and network settings. In particular, the boundaries for one technique being preferable to the other will be investigated, whereas the choices relevant to robot movement and served node selection will be compared and discussed.

Reference System Overview and Assumptions

In this section, basic notions and background information about the considered WSN are introduced to support and guide the reader through our analysis. An assumption that simplifies the analysis is to consider heterogeneous sensor networks, with static sensors of different types (sensing temperature, luminosity, movement, radiation, etc.) but with equal power consumption law and recharge rate. We assume that all nodes start with the same energy level, while their energy consumption depends on the sensing and message broadcasting activities within the WSN. Furthermore, each sensor piggybacks energy status and consumption information jointly with the data in the messages transmitted to the sink (or base station).

Sensors

We refer to the i th sensor node with notation S i , and to its position in the network by its Euclidean coordinates S i (x i , y i ). Given two sensor nodes S u and S v with positions S u (x u , y u ) and S v (x v , y v ), we say that sensors S u and S v can communicate if their Euclidean distance d(S u , S v ) is less than the sensor communication range r c that is supposed to be the same for all the sensors. Consequently, the WSN can be represented as a graph G(V, E), where V is the set of sensor nodes (including the sink) and E is the set of edges,

E = {(S u , S v ) ∈ V | S u S v ∧ d(S u , S v ) ≤ r c }.
We denote by |V| the number of sensors in V.

In order to have a realistic evaluation of the energy consumption in the network, we consider a WSN where every sensor S i generates a message about the event it has sensed with a frequency F i . After the message is generated, it will be transmitted toward the data sink in a multi-hop manner with a sensor transmitting at instant t at a rate T i (t). In terms of power consumption, sensing and transmitting activities of sensor i are characterized by P s i and P t i , respectively. Any multi-hop transmission in a WSN requires message relaying policies and represents an important source of sensor energy consumption. Battery recharging rate (assumed equal for all sensors) P i (t)

Total power consumption equal to:

P s i F i + P t i T i (t)
During network operations, some of the sensors will inevitably run out of the energy and, thus, possibly jeopardize the whole network functional behavior. The expected sensor lifetime at time t, i.e., L i (t), is defined as the time between the sensor start-up, i.e., its "birth", when its current battery is fully charged, E i (t) = Emax i , until its "death", when its energy level falls below the minimum energy threshold Emin i . Similarly, the network lifetime is defined as the time between the "birth" of the sensor network until the first interruption of the sensing activity of a single sensor in the network [START_REF] Chang | Maximum lifetime routing in wireless sensor networks[END_REF][START_REF] Wang | Extending the lifetime of wireless sensor networks through mobile relays[END_REF].

The Recharging procedure of a generic sensor i is characterized by a recharging duration T ch i that depends on the amount of energy transferred to the sensors. In particular, to fully recharge a sensor with maximum energy capacity Emax i , current battery energy level E i (t) at time t, and a recharging rate R ch of the battery, we have that:

T ch i = Emax i -E i (t) R ch .
Replacement is, instead, characterized by the time T r required by the implemented replacement technique/process of the mobile robot. Table 1 summarizes the further information of interest relevant to a sensor node i.

In the context of this paper, the specific technique adopted to recharge or replace is not very relevant. In fact, the parameter that actually makes the difference between the two techniques is the required time to carry out the task. For the implementation of both types of analysed techniques, we consider the use of a mobile robot (instead of a vehicle or a human) so that human intervention is minimized.

Mobile robots

A mobile robot is a mobile robotic platform capable of moving across the positions of target sensor nodes for maintenance purposes. In this paper a mobile robot is designated by the notation R and it is characterized by its Euclidean position within the network R(x, y) and a sensing range r s . We assume that the base station is the energy source for the mobile robot and the sensors: the robot can be charged directly by visiting the base station, while sensor nodes are charged indirectly via the mobile robot. Moreover, we assume that the time needed for a robot to recharge/replace its own energy sources at the base station T replace is set to zero. This can for instance be implemented by swapping the robot at the base station where a fully charged robot is waiting to take the place of the exhausted incoming robot. The mobile robot is characterized by a movement speed V m and a power consumption for movement P m . When recharging a sensor node, the mobile robot has a power consumption P r . A further contribution to the power consumption of a mobile robot is the operation power consumption, but this is very small and set to zero for simplicity in the analysis. A distinction has to be made between the cases when a robot uses the same or a different energy source for movement and recharging. The choice in this paper is to keep the two energy sources separated, as the energy consumption due to the movement of a mobile robot is not negligible. In particular, a mobile robot will have a distinct amount of energy available for movement and recharging, i.e., Emax m and Emax r respectively. Thus, when modeling any maintenance solution, the energy constraints set by the current remaining energy at time t for recharging and movement should be considered separately, i.e., E r (t) and E m (t) respectively. Instead, when a replacement technique is implemented, the energy dedicated to recharging is not of interest. In particular, this constraint is replaced by a limitation on the number of node replacements nodes Nmax r the mobile robot can perform, whereas T r is the time needed to replace a sensor node. All assumed robot features are summarized in Table 2.

Node Recharging Techniques

In all the solutions presented next, a mobile robot reaches the exact position of a sensor in the network. Moreover, we assume that when the robot stops at a recharging position only the targeted sensor will be recharged. With this assumption we will obtain a lower bound performance for any proposed solution. In fact, in dense scenarios where multiple sensors can simultaneously be recharged by the mobile robot, the performances in terms of network lifetime prolonging potentialities are expected to be higher as discussed in [START_REF] Xie | On renewable sensor networks with wireless energy transfer: The multinode case[END_REF].

Centralized Approach for Node Recharging

According to this approach, a mobile robot collects at the base station all the instructions it has to fulfill in the next maintenance cycle, including the exact path to follow to recharge the nodes in need of assistance. The input information taken into account is: the set of energy-endangered nodes, i.e., the nodes that will die if not recharged in the next maintenance cycle; the amount of energy spent on recharging a sensor; and the energy spent by the robot to move toward the sensor.

Noteworthy, finding an optimal tour where each energy endangered node is visited once per tour and provided with the required energy is an NP-Hard problem, as it can be modeled as a well-known Traveling Salesman Problem (TSP) [START_REF] Padberg | A branch-and-cut algorithm for the resolution of large-scale symmetric traveling salesman problems[END_REF]. Therefore, we propose heuristic algorithms to solve the problem. In view of this, the energy constraints set by the mobile robot for movement and the energy to be transferred to the sensors are mapped onto the corresponding required time. In particular, we will consider the total time available to the robot to move as the fraction of the maximum energy available for movement and the power consumption for movement:

Emax m P m . Similarly, the total time available to recharge the sensor nodes is evaluated as the fraction of the maximum energy available to recharge and the power consumption in recharging:

Emax r P r . Considering the problem in terms of time, we introduce a key parameter for the centralized approaches. In particular, we define a maintenance cycle duration T as the time between two consecutive visits of the robot at the base station. This time is available to the robot to perform the maintenance tasks and it will be split into the time needed for moving operations to reach the sensor nodes, and the time needed fr recharging operations. The proposed solutions are also requested to define how this time T is used by the mobile robot.

To the purpose, any recharging centralized technique operates by answering the three key questions listed in Section 3 as detailed in the following and summarized in Algorithm [START_REF] Akyildiz | A survey on wireless multimedia sensor networks[END_REF].

P n = (E n (t -T ) -E n (t))/T L n (t) R ch
Algorithm 1: Centralized node recharging algorithm.

Data: Set of sensor nodes V at time t Result: Energy maintenance on V in every time cycle

T 1 T ravel Method ← random | closest | T S P 2 Nodes recharged ← FALS E for ∀i ∈ V do 3 if L i (t) < 2T then
if T travel (V * ) ≥ T ∨ T travel (V * ) > Emax m P m ∨ min T -T travel (V * ) , Emax r P r < i∈V * Emin i + 2T P i -E i (t) R ch then 20 V * ← V * \{S k } s.t. L k (t) = max q∈V * L q (t) 21 else 22 if min T -T travel (V * ) , Emax r P r ≥ i∈V * Emax i -E i (t) -T P i R

Nodes visited for maintenance

Based on the collected information, the base station, identifies the set of sensors that need to be recharged in the next time window of duration T . This set of nodes is denoted by V * . In particular, a sensor is considered as endangered, and denoted by S * i , if its energy level in the next two time windows E i (t + 2T ) is expected to drop under the threshold Emin i . This means that a sensor is added to V * if its expected lifetime L i (t) is lower than 2T (please refer to lines 1-7 in Algorithm 1). The information collected by the base station about nodes includes, therefore, also the mean power consumption in the previous time window of duration T , see Table 3. Based on this information, the base station estimates the expected lifetime of each sensor in the network.

Node visiting order

Once the set of endangered nodes is found, the path to visit all the selected sensors within the time frame T must be defined for the mobile robot. We propose three possible path selection policies (please refer to lines 9-19 in Algorithm 1):

random: the order of the sensors to visit is randomly chosen; closest: the order of the sensors to visit is built by iteratively choosing the node with the lowest product of the Euclidean distance from the current position and the expected lifetime of the node; -TSP: the path to cover is defined by an implementation of the well-known Traveling Salesman Problem (TSP)

[10] solution.

As an example, in Fig. 1, an implementation of the three solutions is plotted for a sample study case scenario with eight sensors.

As a consequence of the definition of the mobile robot path, the estimation of the time T travel (V * ) needed to cover the selected path is possible. Moreover, also the required energy for moving along the selected path can estimated:

E visit (V * ) = T travel (V * ) • P m
. These values are useful to answer the third question and identify the possible study cases, as detailed next.

The amount of energy required by each visited node

For a successful energy recharging solution at least the minimum energy should be transferred to all the endangered nodes so that they stay alive during the next time cycle of duration T . When considering the energy constraints of the mobile robot (both for recharging and for movement) and those of the sensor nodes, four different study cases are identified. To best identify them, all parameters are analyzed in terms of time, i.e., time to travel, time to recharge a sensor 1 The robot calculates the path to follow considering only the sensors that need recharging. If sensors S 2 , S 6 and S 8 do not require additional energy, the robot follows a selected path providing the remaining sensors with energy.

with minimum or maximum energy, time corresponding to the energy available at the robot for moving or recharging.

-Case 1: the time T travel (V * ) to visit all sensors in V * is larger then total cycle time T or the required energy is larger than the energy available for movement at the robot:

T travel (V * ) ≥ T ∨ T travel (V * ) > Emax m P m .
In this case, we propose to iteratively remove one of the sensors to be recharged until the feasibility conditions are met and the reduced set of sensors can be recharged, in the hope that the removed nodes will survive (e.g., the lifetime value was a pessimistic estimation of the real value). In particular, the less critical nodes with the highest estimated lifetime L i (t) are removed from the set of nodes to recharge V * (please refer to lines 20-21 in Algorithm 1). -Case 2: the available time to recharge the sensors in V * , is not enough to recharge them all with the minimum required energy 1 . This condition is computed by evaluating whether the sensors will have at time t + 2T at least Emin i energy 2 :

min T -T travel (V * ) , Emax r P r < i∈V * Emin i + 2T P i -E i (t) R ch .
Also in this case, we propose to remove iteratively the node with the highest estimated lifetime L i (t) from the 1 The time available to recharge a sensor is limited by the lower of the values of two parameters: the spared time in cycle T during the robot travel, the energy for recharging (mapped onto a time value) available in the robots battery.

2 A 2T time is considered to cover the case of a sensor recharged at the beginning of one cycle and then at the end of the next cycle. set of nodes to recharge V * until the feasibility conditions are met (lines 20-21 in Algorithm 1). -Case 3: the time available to recharge the sensors in V * , is enough to recharge all the nodes fully 1 :

min T -T travel (V * ) , Emax r P r ≥ i∈V * Emax i -E i (t) -T P i R ch .
In this case the robot will visit all sensors and recharge them completely (please refer to lines 26-28 in Algorithm 1). -Case 4: the time available to recharge the sensors in V * , is enough to recharge them all with minimum required energy 1 , i.e., at time t + 2T the energy in the battery will be at least Emin i , but it is not enough to recharge them all fully:

i∈V * Emin i + 2T P i -E i (t) R ch ≤ min T -T travel (V * ) , Emax r P r ≤ i∈V * Emax i -E i (t) -T P i R ch .
In this case a policy is required to decide how to distribute the remaining energy among the sensors (see lines 23-25 in Algorithm 1). More details on the latter aspect are given in Section 5.1.3.

Energy allocation solutions for Case 4 in centralized recharging solutions: This case is particularly interesting as several possible policies can be adopted. A simple approach is to equally distribute the energy (recharge time) among the sensors. Differently, in the view of maximizing the number of time windows in which they are not endangered, an alternative approach is to recharge some nodes fully, while guaranteeing the minimum energy to the others. Parameters such as the power consumption or the expected lifetime may drive the choice of the nodes to be fully recharged. A further alternative is to adopt a weighted function that guarantees the minimum to all sensors, like in equation ( 1):

T ch i = Emin i + 2T P i -E i (t) R ch + (1) ω i i∈V * ω i         T -T travel (V * ) - i∈V * Emin i + 2T P i -E i (t) R ch         ,
under the constraint that a sensor cannot be recharged with more energy than its maximum capacity and by defining ω i as the weight for a sensor node proportional, e.g., to its importance, power consumption, or lifetime. An analysis on sample random networks has been performed to have some indications on the best policy to implement. We compared solutions where the energy is shared equally, or it is allocated proportionally to the lifetime according to weighted function [START_REF] Akyildiz | A survey on wireless multimedia sensor networks[END_REF], as well as where some nodes are fully recharged while others are not, according to their expected lifetime L i (t). From this analysis we observed that, especially for small number of nodes, the most performing solution is the one we hereinafter call maximize high solution. According to it, the residual energy is used to fully recharge as many sensors as possible , by following an ordering from the highest expected lifetime L i (t) to the lowest expected lifetime of the sensors.

Distributed Approach for Node Recharging

In the distributed approach, adopted solutions are not decided by the base station, and the robot will autonomously decide how to recharge the sensor nodes. This stepwise choice will be based on the information (updated over the time) it collects from the sensors in its sensing range.

Nodes visited for maintenance

A new node is visited if and only if the robot energy available for movement is enough to visit the selected node and reach the base station, if needed, to recharge itself.

Node visiting order

We propose three different algorithms for the selection of the next sensor to recharge. A graphical overview of the proposed solutions is given in Fig. 2, where in a sample network scenario with eight sensors the mobile robot at the base station makes the first node selection. The proposed solutions are listed below:

random: the next sensor the mobile robot will visit is randomly chosen based on the known information; minenergy: the sensor with the current minimum energy level is selected as the next node to visit; minlife: the sensor with the current minimum expected lifetime is selected as the next node to visit.

The amount of energy required by each visited node

In all of the cases listed above, when a sensor is visited the robot will recharge it fully. Moreover, at each time instant it is checked if the energy needed to recharge the selected node is available and if the residual energy for moving in the robot is enough to reach the selected node and then go back to the base station. If both conditions are not met, then the mobile robot will go back to the base station to recharge/replace its own power supplies.

The distributed recharge algorithm is summarized in Algorithm [START_REF] Akyildiz | A survey on sensor networks[END_REF]. In particular, by starting from the base station, the next node to visit derives from the adopted method random, minenergy or minlife (see lines 1-22 in Algorithm 2). Then, the energy the robot requires to move toward the selected node and move back to the base station is computed (see line [START_REF] Xie | On renewable sensor networks with wireless energy transfer: The multinode case[END_REF]. Also the energy to fully recharge the targeted node is computed (see line 24). If the power available at the mobile robot is not enough to satisfy both energy requirements, then the selected node is not served and the mobile robot moves back to the base station to replace its own power supply (see lines [START_REF] Yick | Wireless sensor network survey[END_REF][26][27][28][29][30][31]. Otherwise, the selected node is visited and fully recharged, and the mobile robot is ready to choose the next node to visit (see lines 33-35 in Algorithm 2).

Node replacement techniques

When analyzing the node replacement techniques, two main differences must be considered with respect to the recharging based solutions. The first one is that the time needed to replace a sensor T r is generally much lower than the time needed to fully recharge. The second main difference is in the constraint to be set on the maximum number of sensors a mobile robot can carry Nmax r , which replaces the maximum amount of charging energy a robot can spend Emax r .

Centralized Approach for Node Replacement

Also for sensor nodes replacements, the mobile robot will collect all the instructions about the tasks to fulfil in the next maintenance cycle of duration T at the base station. The analysis on the mobile robot energy needed for movement will, again, be performed based on the corresponding time duration. When replacing techniques are implemented, only the following two issues need to be addressed.

Nodes visited for maintenance

Similarly to the recharge based solutions, the base station collects all the information needed to find the set of sensors V * to substitute in the next time window of duration T . Also Fig. 2 The path to follow for the robot is calculated stepwise based on the knowledge gathered from the coverage range of the robot. in this case, a sensor S i is considered as endangered, denoted by S * i , if its energy level in the next two time windows E i (t + 2T ) is expected to drop under the threshold Emin i .

Node visiting order

Also for the replacement case, three different solutions discussed in section 5.1 are considered for the traveling path of the mobile robot, namely random, closest and TSP.

In Algorithm (3) all the steps of the replacement algorithm are illustrated. Note that the occurring cases for replacement solutions differ from those of the recharging solution and are listed below:

-Case 1: either the time to visit all nodes in V * is larger than total cycle time T or the energy required to cover the complete distance is more than that available in the robot (the condition is also here expressed in terms of time needed):

T travel (V * ) ≥ T ∨ T travel (V * ) > Emax m P m .
Similar to recharge based solutions, in these cases we propose to iteratively remove from V * one of the sensors to be replaced until the feasibility conditions are met.

In particular, the node with the highest estimated lifetime L i (t) is removed from the set of nodes to recharge V * (see lines 19-20 in Algorithm 3). Obviously, this is an emergency situation where the proposed solution is implemented in the hope that the removed sensors will somehow survive (e.g. the lifetime value was a pessimistic estimation of the real value). -Case 2: the robot has not sufficient nodes to replace all endangered senors:

Nmax r < |V * |.
Also in this case we propose to iteratively remove one of the sensors to be replaced until the feasibility conditions are met (we fall again in the condition stated in lines 19-20 in Algorithm 3). -Case 3: the time available to replace the sensors is not enough to replace them all:

T -T travel (V * ) < (|V * | • T r
) . As for the other problematic cases one or more nodes will be removed from V * until the feasibility conditions are met (same condition stated in lines 19-20 in Algorithm 3). -Case 4: the time available to replace the sensors is enough to replace them all and the number of available replacement sensors is sufficient:

T -T travel (V * ) ≥ (|V * | • T r ) ∧ (Nmax r ≥ |V * |) .
In this case, all nodes in V * are replaced and the mobile robot moves back to the base station for the next maintenance cycle (see lines 21-23 in Algorithm 3).

Distributed Approach for Node Replacement

Nodes visited for maintenance

A mobile robot makes stepwise decisions based on the information gathered from the nodes in its sensing range. A difference from the recharge based approach is that now a threshold value is set on the residual energy to consider a node "in need of replacement". This avoids the inefficient behavior of a robot replacing sensors with almost full battery. The threshold value we consider in this analysis is two times the minimum energy for sensing 2 • Emin i (see Algorithm (4)). However, this value could be tuned according to the operational scenario, to improve the efficiency of the replacement algorithm.

E recharge = Emax i -E i (t) + P r × Emax i -E i (t) R ch 25 if (E m (t) < E travel ) ∨ (E r (t) < E recharge

Node visiting order

Also in this case, three algorithms, which drive the decisions taken by the mobile robot, are proposed: the so-called random, minenergy, and minlife approaches already presented in section 5.2 (see lines 1-22 in Algorithm 4). The remainder of the algorithm is the same as the one in the recharging case, but for the condition set on the number of replacing sensors available at the mobile robot (see line 24 in Algorithm 4.

Performance Evaluation

In this section we present simulation results relevant to the proposed node recharging and replacement policies for WSN Algorithm 3: Centralized node replacement algorithm.

Data: Set of sensor nodes V at time t Result: Energy maintenance on V in every time cycle T maintenance. The key performance parameters in our analysis are:

1 T ravel Method ← random | closest | T S P 2 Nodes recharged ← FALS E for ∀i ∈ V do 3 if L i (t) < 2T
if T travel (V * ) ≥ T ∨ T travel (V * ) > Emax m P m ∨ T -T travel (V * ) < (|V * | • T r ) ∨ (Nmax r < |V * |) then 20 V * ← V * \{S k } s.t. L k (t) = max q∈V * L q (t)
-Sustainability ratio: given a number of simulation runs, this parameter shows the number of times the objective of maintaining all sensors alive is reached; -Network lifetime: that is the average value expressed in hours, between the network start-up and the first death of a sensor in the network; -Percentage of dead nodes: this gives a quantitative value of the number of dead nodes, in those case where the network maintenance algorithm did not succeed to keep the network alive; -Movement energy: expressed in kilojoule (kJ), it captures the amount of energy spent by the mobile robot in moving around the network. This parameter will highlight how efficient, in terms of energy consumption, the adopted movement path selection is for the mobile robot.

All scenarios are tested under realistic WSN implementations modeled with the WSNet simulator [START_REF] Wsnet | An event-driven simulator for large scale wireless sensor networks[END_REF]. A variable number of sensors in the range 20 -80 is considered, randomly deployed within a simulated area of 100m × 100m. Each simulation run covers 24 hours and the average results for each of the proposed solutions are reported. Further pa- Before showing the behavior of the performance figures of interest, a preliminary analysis is first presented to determine the best time cycle T duration to be adopted for the centralized approaches.

Definition of time cycle in centralized approaches

A set of simulations has been run to experimentally find the optimal value of time period T for the node recharging solution described in section 5. The analysis has been performed for values of T ∈ {0.5, 1, 1.5, 2, 2.5, 3} h in a sample scenario with a random movement technique assumed for the mobile robot and 80 nodes (similar results are obtained for other tested solutions). Fig. 3 shows the results in terms of the four main performance figures, namely the percentage of sustainability ratio, dead nodes percentage, network lifetime, and average energy consumed by the mobile robot for movement. Observing the plotted results, we can conclude that a good value to be adopted is T = 1.5h. This value will be used for the remaining simulations for the assessment of the centralized approaches performance.

WSN sustainability ratio analysis

In this analysis all the proposed solutions are compared in terms of WSN sustainability. The obtained results are plotted in Fig. 4. What emerges is that, for the adopted simulations settings, the replacement techniques perform better than the recharging ones. The motivation for this is that the time needed for node replacement is much lower than the time needed to recharge the sensor nodes, which is a reasonable assumption. In particular, from subplot (b) we observe that in a centralized approach the replacement techniques always succeed to maintain the network alive. In particular, this is true independently from the path selection algorithm for the mobile robot. When looking at subplot (d) instead, we observe that the distributed approach for node replacement is adversely affected by a random choice of the next node to replace. In fact, the percentage of sustainability dramatically decreases with the number of nodes in the network.

When focusing on the recharging techniques in subplots (a) and (c), we notice that the network sustainability is always guaranteed with small networks of 20 sensors. When increasing the number of nodes this value decreases. The Fig. 3 Evaluation metrics for centralized approach to node recharging with random technique, 80 nodes and period T ∈ {30min, 1h, 1.5h, 2h, 2.5h, 3h}. distributed approach, for any movement solution of the mobile robot, with 40 nodes and above never succeeds in keeping the network alive, see subplot (c). For the centralized approach reported in subplot (a), we observe that the movement of the mobile robot has some influence with 40 nodes. In particular, the path selection based on the T S P solution performs the best with about 45% of network sustainability while the so-called closest algorithm guarantees about 20% of network sustainability.

Noteworthy, for node replacement techniques, increasing the number of sensors will at some point provoke the non-sustainability of the network.

Network lifetime analysis

Let us now further investigate on the average lifetime of the WSN in the simulated scenarios. For those cases where the network sustainability is always guaranteed the network lifetime is obviously equal to the whole simulation time. This happens: for all centralized replacement techniques in subplot (b) in Fig. 5, for the distributed replacement techniques in subplot (d) with minenergy and minlife robot movement solutions, and for all the recharging solutions with 20 nodes. For the random robot movement solution instead, the network lifetime is reduced to about 4,5 hours already for 40 nodes.

Besides, for the centralized recharging approach with 40 nodes, in subplot (a) we can observe that the T S P guarantees longer network lifetime on average, followed by the closest and the random solutions. A clearer distinction among the movement solutions for the mobile robot, can be observed in subplot (c) for the distributed recharging solution. In fact, for all values of the number of nodes in the network larger than 20, the minenergy solution guarantees longer network lifetime than the minlife and the random solutions. The observed differences are related to how efficient the robot movement selection is for the considered solutions. The more the robot movement is efficient, the longer the network can be kept alive.

Percentage of dead nodes analysis

As plotted in Fig. 6, in those cases where the network sustainability is always guaranteed, the percentage of dead nodes is obviously equal to zero (refer to replacement techniques in subplots (b) and (d)). For the replacement technique, only a distributed approach with random movement of the mobile robot makes the percentage of dead nodes increasing with the total number of nodes in the WSN. This happens because the choices of the mobile robot become less effective as the network size increases. More interesting is the analysis of the recharging approaches in subplot (a) and (c). For the centralized approach in subplot (a), we observe that, as expected, the TSP is performing the best, followed by the closest solution based on local distances between nodes and the random solutions. For the distributed approach instead (subplot (c)) we observe that starting from 40 nodes the minenergy and minlife algorithms seem to introduce more dead nodes than the random solution. In particular, the plots show that a local distributed decision based on local information on the energy-related constraints of single nodes does not actually improve the global performance and the network is not kept alive (please refer to the plots in Fig. 4).

Movement energy for the mobile robot analysis

In this last analysis, we investigate on how the proposed movement path selection algorithms influence the energy consumption for the mobile robot. Focusing the attention on the centralized approaches, subplots (a) and (b) in Fig. 7, the average movement energy for the mobile robot is always the highest for the random algorithm. It has the lowest value for the TSP, while the closest algorithm shows values in between the other two solutions. For the distributed approaches, see subplots (c) and (d), again the random algorithm is the worst performing solution. Concerning the other two solutions, the differences between minenergy and the minlife solutions are more evident with node replacement, with the minenergy solution showing higher movement energy consumption for the mobile robot. Finally, looking at the recharging based solution, subplots (a) and (c) in Fig. 7, we underline that for more than 40 nodes the energy for movement is much lower because we do not succeed in keeping the network alive (see analysis in Fig. 4).

From a comparative analysis of the performance figures reported in this section, we can summarize the most important findings in Table 5.

Conclusions

In this paper we proposed solutions for wireless sensor networks maintenance based on the use of mobile robots visiting the nodes requiring assistance. A careful analysis on the constraints set by the network has been performed to classify the possible solutions based on recharging and re- Further issues addressed in the paper are (i) the definition of parameters to be considered for successful network maintenance, (ii) the identification of possible cases for each solutions as determined by the energy constraints for the nodes and the mobile robot, and (iii) a comparative analysis of movement patterns and maintenance solutions implemented by the mobile robot. The presented performance evaluation gives a preliminary understanding on how and to what extent the proposed solutions succeed in guaranteeing the selfsustainability of a WSN. We believe that the proposed comparative analysis will be very helpful for future research activities in this field.

  Noname manuscript No. (will be inserted by the editor) Recharging vs. Replacing Sensor Nodes Using Mobile Robots for Network Maintenance Leonardo Militano • Milan Erdelj • Antonella Molinaro • Nathalie Mitton • Antonio Iera the date of receipt and acceptance should be inserted later

4 Add 8 switch 13 T 16 T

 481316 Nodes recharged = FALS E do Travel Method do 9 case random 10 T travel (V * ) ← random algorithm on V * travel (V * ) ← closest algorithm on V * travel (V * ) ← TSP algorithm on V *

ch then 23 maximize high sensor recharge policy on V * 24 Nodes

 2324

  Fig.1The robot calculates the path to follow considering only the sensors that need recharging. If sensors S 2 , S 6 and S 8 do not require additional energy, the robot follows a selected path providing the remaining sensors with energy.

Algorithm 2 : 5 9 Chosen

 259 Distributed node recharging algorithm. Data: Nodes V sensed by mobile robot Result: WSN maintenance 1 Method ← random | minenergy | minli f e 2 S 0 ← Base station 3 Last ← S 0 4 Chosen ← S 0 ← random(S 1 , S 2 , . . . , S |V | ) ||Last(x, y), Chosen(x, y)|| + ||Chosen(x, y), S 0 (x, y)|| V m 24

  then

4 Add 10 T 13 T 16 T

 4101316 travel (V * ) ← random algorithm on V * travel (V * ) ← closest algorithm on V * travel (V * ) ← TSP algorithm on V *

Algorithm 4 : 5 9 Chosen 25 Chosen

 45925 Distributed node replacement algorithm.Data: Nodes V sensed by mobile robot withE i (t) < 2 • Emin i Result: WSN maintenance 1 Method ← random | minenergy | minli f e 2 S 0 ← Base station 3 Last ← S 0 4 Chosen ← S 0 ← random(S 1 , S 2 , . . . , S |V | ) ||Last(x, y), Chosen(x, y)|| + ||Chosen(x, y), S 0 (x, y)|| V m 24 if (E m (t) < E travel ) ∨ (N s (t) = 0) then Chosen 35 endrameter settings for the sensor nodes and the mobile robot are reported in 4.

Fig. 4 Fig. 5 Fig. 6

 456 Fig. 4 Percent of successful maintenance.

Fig. 7

 7 Fig. 7 Average movement energy during the maintenance.

Table 1

 1 Notations for sensor node S i .

	Notation Explanation
	S i (x i , y i )	Position in Euclidean coordinates
	r c	Communication range
	F i	Information sampling rate
	T i (t)	Transmission rate in instant t
	P s i P t i L i (t)	Sensing power consumption Transmission power consumption Expected lifetime at instant t
	E i (t)	Residual energy at time t
	Emax i	Maximum energy that can be stored in the battery
	Emin i	Minimum energy threshold for being active
	R ch

Table 2

 2 Notations for mobile robot R.

	Notation Explanation
	R(x, y)	Position in Euclidean coordinates
	Emax m	Total energy available for movement
	E m (t)	Remaining energy for movement at time t
	Emax r	Total energy available for recharging
	E r (t)	Remaining energy for recharging at time t
	Nmax r	Maximum number of sensor nodes for replacement
	T r	Time needed to replace a sensor node
	P m	Power consumption for movement
	V m	Movement speed
	P r	Power consumption for recharging
	T replace	Time for own battery recharge/replacement
	r s	Sensing range

Table 3

 3 Sensor node list provided to the robot by the data sink at time t

	Sensor	Euclidean coordinates	Minimum Maximum Residual energy energy energy	Mean power consumption	Expected lifetime	Battery recharge rate
	1 2 ...	S 1 (x 1 , y 1 ) S 2 (x 2 , y 2 ) ...	Emin 1 Emin 2 ...	Emax 1 Emax 2 ...	E 1 (t) E 2 (t) ...	P 1 = (E 1 (t -T ) -E 1 (t))/T P 2 = (E 2 (t -T ) -E 2 (t))/T ...	L 1 (t) L 2 (t) ...	R ch R ch ...
	n	S n (x n , y n )	Emin n	Emax n	E n (t)

Table 4

 4 Simulation parameters.

		Parameter	Value
	Robot	Movement energy Emax m Recharging energy Emax r Movement power consumption P m Recharging power consumption P r Movement velocity V m Energy sources refill T replace Sensing range r s Time needed to replace a sensor node T r Number of sensor replacements Nmax r	5000 kJ 2000 kJ 50 W 3 W 1 m/s 0 s 30 m 20 s 50
	Sensor i	Information sampling rate F i Sensing power consumption P s i Transmission power consumption P t i Maximal energy Emax i Minimal energy for sensing Emin i Battery recharging rate R ch Communication range r c	1 Hz 0.1 J/packet 0.1 J/packet 9 kJ 0.05Emax i [22] 25 J/min 30 m
	Simulation duration Simulation Simulated area Number of sensors	24 h 100m × 100m 20 . . . 80

Table 5

 5 Summary of main findings. Both centralized and distributed approaches have been presented, with a cautious view on the possible movement pattern selection for the mobile robot.

		Centralized	Distributed
		Recharging	Replacing	Recharging	Replacing
	Successful main-	20-40 nodes	20-80 nodes	20 nodes	20-80 nodes
	tenance
	Most energy effi-	TSP	TSP	minenergy	minlife
	cient path
	placement techniques.

Supplementary Material

Click here to download Manuscript: Recharging vs Replacing Sensor Nodes Using Mobile Robots for Network Maintenance.tex