Lorna J Sutcliffe

Katharine E Sadler

Nicola Low

Jacqueline A Cassell
email: j.cassell@bsms.ac.uk.

Jackie Cassell

Comparing expectations and experiences of care for sexually transmitted infections in general practice: a qualitative study

Keywords: family practice, sexually transmitted infections, general practice, qualitative research

Comparing expectations and experiences of care for sexually transmitted infections in general practice: a qualitative study.

• Where patients attending general practice reported disappointment with care, this usually related to lack of formal referral, lack of information or perceived avoidance of the subject by practitioners.

• Commissioning of general practice based care should focus on ensuring that all patients have access to comprehensive care in practice, or through supported referral.

INTRODUCTION

Diagnosed rates of bacterial sexually transmitted infections (STI) in the United Kingdom (UK) have more than doubled since 1995. [START_REF](STIs) including HIV, and to reduce the rate of under 18 conceptions, especially among vulnerable and at risk groups[END_REF] The National Strategy for Sexual Health and HIV lifted sexual health up the political and health care agenda in England 2 ; it encouraged improved access, patient information, and choice in sexual health services, particularly in primary care.

More recently, the National Institute for Health and Clinical Excellence (NICE) recommended that health professionals in a variety of settings, including primary care, provide a one-to-one counselling session about preventing sexually transmitted infections (STI) and under 18 conceptions for individuals at high risk. 3 General practice is already an important provider of STI care in the UK, providing an increasing proportion of STI diagnosis and treatment, [START_REF] Hughes | Use of a primary care database to determine trends in genital chlamydia testing, diagnostic episodes and management in UK general practice[END_REF] reaching up to 30% for chlamydia and genital warts. [START_REF] Cassell | Trends in sexually transmitted infections in general practice 1990-2000: population based study using data from the UK general practice research database[END_REF] About a third of new patients seen in genitourinary medicine (GUM) clinics have initially gone to their general practitioner. [START_REF] Mercer | How much do delayed healthcare seeking, delayed care provision, and diversion from primary care contribute to the transmission of STIs?[END_REF] Many of these patients report that they had not been examined or had any tests done. 7;8 Little is known however about the experiences of patients who remain in general practice, or are referred to GUM clinics but do not subsequently attend. We aimed to describe the expectations and experiences of patients presenting to general practice with STI-related problems.

METHODS

Population and sampling strategy.

The study took place in the contrasting populations of Brent, in North West London and Avon, in the South West of England. The population of Brent is ethnically diverse; 55% are from non-white ethnic groups by contrast with under 10% in Avon.

Recruitment of healthcare settings

We started by identifying practices serving populations likely to have high levels of sexual health care needs, as indicated by teenage conception rates and deprivation scores above the median for the locality. Within this group of practices we then used district laboratory data (up to 2005 for Brent and up to 2004 in Avon) to calculate rates of testing for chlamydia and HIV. We used these measures as proxy indicators of the level of involvement in providing sexual health care. In Brent we were also able to identify practices with high referral rates to GUM accompanied by low testing in the practice, using data from a previous study. [START_REF] Mercer | How much do delayed healthcare seeking, delayed care provision, and diversion from primary care contribute to the transmission of STIs?[END_REF] We initially approached practices in each area known to have either high or low rates of testing (above and below the median for the area) to take part in the study, in order to recruit patients with diverse experiences within our resource We also enrolled participants from the main GUM clinic serving each area so that patients who had presented in primary care but gone on to attend a GUM clinic could be included.

Recruitment of patients

General practice: Patients aged 16 years and over with a diagnosed or suspected STI whose first presentation was at a participating general practice were eligible, with a planned maximum of 30 interviews. We explained the purpose of the study to staff in each general practice and agreed on a method for enrolling participants. Due to the unpredictable timing of potentially eligible consultations a researcher could not be present at all times, so GPs and practice nurses invited patients to participate during the consultation, obtained written consent and sent a copy of this to the researchers with a contact telephone number. Practices were asked to approach all eligible patients. However we were not able to monitor the number of eligibles or refusals, as no suitable register of cases could be made available. Researchers made up to three attempts to arrange a suitable time for a telephone interview.

Participants were sent a £15 postal order thank you gift after the interview.

GUM clinics:

In each GUM clinic, a researcher recruited at a range of clinic session types (walk-in, young persons and booked appointments). Reception staff identified patients aged over 16 years who had already seen their GP for their current problem.

The researcher approached all eligible patients, obtained written informed consent and undertook interviews during the clinic visit. Initially 30 interviews were planned, but this was increased to 38 since practice based interviews proved difficult to arrange.

Interviews. The interviews were semi-structured, based on a topic guide which explored basic demographic information and relationship status, reasons for initially attending, experience of accessing care, consultation, referral and treatment, views about the service received, and preferences for future care. Both telephone and face to face interviews lasted between 25 and 30 minutes, were audio-taped with permission, labelled with an identity number to protect confidentiality and transcribed verbatim. Data analysis followed the 'framework' approach, which involves a structured process of 'sifting, charting and sorting' material according to key issues. [START_REF] Ritchie | Qualitative data analysis for applied policy research[END_REF] Recurring themes and concepts were identified to make up a thematic framework, or index, which was then applied systematically to the transcripts. LS and KS undertook the analysis. Reliability was enhanced by double coding and comparing a subset of transcripts. Few discrepancies emerged and, where they did, consensus was negotiated.

The study was approved by South West Multicentre Research Ethics Committee.

RESULTS

Recruitment: Six of 16 general practices approached agreed to participate, split equally between Brent (3/71) and Avon (3/143), along with both local GUM clinics. However, we were unable to enroll any practice in Brent with chlamydia testing rates below the median for the area. Forty-nine interviews were conducted between July 2005 and March 2006. In general practice we interviewed 11 (9 women, 2 men) of 22 patients who agreed to be contacted; the other 11 could not be contacted on the telephone number provided. In the GUM clinics all 38 (20 women, 18 men) patients approached agreed to be interviewed. We could not determine overall participation rates in either setting because we did not know the total numbers of eligible patients.

Characteristics of the sample:

The characteristics of participants are summarised in Table 1. The median age of general practice patients in Bristol was lower than in other settings because most of them were enrolled from a more specialised "locally enhanced" sexual health service that had links with local schools. While most participants in Bristol (26/27) were of White British ethnicity, 11/16 from Brent who reported their ethnic group were from Black or Asian minority ethnic groups. About a quarter of all participants from GUM clinics but none from general practice were married or cohabiting. Most participants reported one sex partner during the last three months; the two men interviewed in general practice reported "three to four" and 2 partners. Of 11 patients enrolled from primary care, 9 had been wholly managed in that setting.

In all settings, participants presented variously with genital tract symptoms, reported symptoms in a partner, and requesting a check-up following risky behaviour or between relationships.

Three main themes emerged from the thematic analysis.

Theme 1: Accessing general practice

Most respondents had chosen to go to their GP first because of perceived speed and ease of access, particularly those who had used GUM services before and had had difficulty getting an appointment.

"The reason why I hadn't got checked out earlier is just trying to get an appointment in an STI clinic is very, very hard, especially when you're working full time. And even though they sometimes have a drop in time to go there, but sometimes it's not actually convenient times when you're working."

[Female, 27 years, GP practice] "Because it's difficult, it's like a rat race here [GUM clinic] at 9 o'clock in the morning and when I've just arrived at work, you know, spending all the time on the phone it just really didn't go down too well".

[Female, 26 years, GUM clinic] One general practice in Bristol provided a locally enhanced service for sexual health care.

Participants enrolled from this practice said that they chose this service because the practice nurse also ran school drop-in sessions and sex education lessons and they perceived her as a "specialist."

"I'd always choose to go to the Locality Centre because it is kind of… I feel it's more suitable like youth-based and I feel like they've got more time kind of thing if I need it. Because I know that GP clinics are busy and trying to get an appointment… you know it can be hard work… and also I know the nurse as well. She used to come to my school when I was at school and she used to give sort of, well she'd, she'd do a No Worries session then."

[Female, 18 years, GP specialist clinic] "Because it's the same lady that does the swabs, the testing as the one in the [GUM] clinic, she does it in the hospital as well."

[Female, 16 years, GP specialist clinic] All respondents reported that it had been easy to book an appointment at their general practice and many were seen within 48 hours of first contact. While some women waited longer because they preferred to see a female doctor, men did not seem to mind about the sex of the doctor.

Theme 2: Patients' expectations and experiences

Many of the young patients enrolled from the in house "enhanced" sexual health service in Bristol reported initial nervousness but all were happy with the outcome.

"Well I went in there, she asked me why I wanted to go, when was the last time I slept with someone and everything. And then I had to lie down on the couch and then I had to take my trousers and boxers down then they just took a swab and like felt around the area to see if there's any pain or whatever or any unusual lumps or something. At first I was a bit uncomfortable with it but then I just got used to it…….really there ain't really nothing to be embarrassed about, at least they know that you're actually checking up to be sure."

[Male, 20 years, GP specialist clinic] Patients enrolled from all other settings reported mixed expectations and experiences at their general practice. Participants reported that they expected to receive information about their condition or symptoms verbally or in a patient information leaflet, yet many received none. This emerged as an important influence on their satisfaction with the service received. Many patients also felt that the GP avoided discussing sexual health matters with them.

"They just don't look at you, they just look at the computer….she should tell me because she is my GP and I don't know about these diseases, she knows. She got an education for that and she is therefore our service".

[Male, 30 years, GUM clinic] Participants often expressed surprise that they weren't questioned about their sex partners, use of condoms or previous STI at the general practice consultation. Many men and women had a physical examination but few had tests or swabs taken, usually for chlamydia and occasionally for gonorrhoea. For the majority of participants this was a disappointment as they had thought they would be able to be tested for all STIs. Often they referred themselves to the GUM clinic after the GP consultation because of this.

"I think that's the perception people get that when you go to see your GP you expect to maybe have all your treatment there".

[Male, 32 years, GUM clinic] "I thought they'd give me more advice or -I don't know I went there and they just, she was so well you need to go to the GUM clinic we can't do it here, which I thought was like -because my friend had been to the same doctor's as me and she had it done there".

[Female, 23 years, GUM clinic] Several participants spontaneously mentioned having requested an HIV test, or being surprised that this was not offered. One of these had requested an HIV test but had been refused for incorrect, outdated reasons.

"She [the doctor] said that it would be better if I didn't have it [HIV test] done at the doctor's surgery because if I wanted to apply for a mortgage or some sort of house insurance policy it would obviously all be logged and I would be better off going to like a hospital where you're slightly more anonymous. If I could have just done the whole thing together in one fell swoop I

would have just done all of the tests altogether… but now you know the chances of me going down and queuing up one morning at hospital before work or whenever I probably won't do it, I won't I know I won't. I mean I haven't done it and that was a couple of months ago that I had the other things done at the doctor's surgery".

[Female, 35 years, GP practice] Several participants (n=7) had attended with an expectation of referral to a GUM clinic by letter. Generally these patients were given a telephone number to call themselves, and they often said they would have felt more confident turning up at the GUM clinic with a referral letter in their hand. Those who were given a referral letter or for whom the GP made a GUM clinic appointment described attending the GUM clinic more quickly than those who had only been told to attend or were given a phone number to call the GUM clinic themselves.

Patient: "She just give me the number for ……. (GUM clinic) and said you have to go to a special clinic."

Interviewer: How did that make you feel then?

Patient: I thought, 'Oh I'm scared', and I don't know, I just felt you know obviously she don't know what she's talking about so I have to go into one of these places.

Interviewer: So how did you feel after you'd come out of that appointment?

Patient: I wanted to cry, someone, what's going on?

Interviewer: Why did it make you feel you wanted to cry? Patient: Because she was no help at all. You know being a doctor you should be more caring.

These things happen she should be more caring; she could have booked the appointment or given me a letter or something, then I'm thinking, 'Oh I'm going to come here [GUM clinic] and it's going to be like this again.

[Female, 23years, GUM clinic] Theme 3: Expectations and preferences for future STI related care

Participants were asked where they would prefer to seek treatment in future if they experienced a sexual health problem. All saw primary care as their preferred source of help, including those who had been referred on to the GUM clinic. Their reasons included convenience, ease of access, having a good relationship with their GP and satisfaction with past consultations. Most participants did not want a designated clinic time, preferring to be treated during normal surgery.

"In an ideal world the general practitioner would be an expert in everything [laughs] which I think you know isn't possible, but that would be my ideal, for me personally, although the awkwardness is still there it kind of takes away the stigma, which is probably really old fashioned, but yeah it's just that thing you know it's embarrassing to you know -I don't know anybody in the area but there's always that thing in the back of your mind what if somebody sees me going in".

[Female, 29 years, GUM clinic] "You sit here and everyone knows why you're here. At least at the doctor it could be a case of you've got a bad back or something".

[Male, 25years, GUM clinic] However, when asked where they would in fact go to get treatment for a suspected STI again, most participants said they would choose the GUM clinic, perceiving its staff to be 'specialists' and expressing high levels of satisfaction about the information, tests and advice received before, during and after their consultation.

"I would suggest you go there first then everything, you get everything sorted out on the same day, don't have to wait for your results, wait a week for your results and wait a week for your prescription".

[Female, 22 years, GUM clinic]

DISCUSSION

This study showed that patients who approach their general practice seeking care for a possible STI typically anticipate either written referral or in-house care, but an absence of formal referral, and lack of information, were often cited as unmet expectations. Informal referral to GUM, without a letter or appointment, was experienced as stressful and disappointing, and often led to avoidable delay in care. A lack of detailed sexual history taking in general practice in this context was surprising to these patients, who often felt that practitioners were avoiding the subject.

Few studies to date have addressed patient experiences of sexual health care received in general practice in detail. 7;10 Structured questionnaire surveys of patients in GUM clinics have found, however, that a substantial proportion would have preferred to have had their problem managed in primary care. [START_REF] Doherty | New approaches to sexual health services in a rural health board area: involving service users and primary care professionals[END_REF] We also found that patients expected their GP to examine them and ask questions about their sexual history. This finding makes more surprising other surveys which report that up to three quarters of primary care staff refer patients with a suspected STI to GUM clinics without a consultation, [START_REF] Doherty | New approaches to sexual health services in a rural health board area: involving service users and primary care professionals[END_REF] and that of those receiving a consultation most do not have tests for STI or are not examined. [START_REF] Neale | Who attends primary care services prior to attendance at genitourinary services and what level of care have they received?[END_REF] The perception by many study participants of a lack of confidence in primary care staff concurs with other studies reporting reluctance by practitioners to engage with sexual health issues, with less experienced practitioners only considering an STI as a last resort. 11;12 Primary care practitioners taking part in focus groups to discuss chlamydia screening have suggested that it is patients who are reluctant to have tests taken or to have sexual health problems recorded in their notes. [START_REF] Mcnulty | Barriers to opportunistic chlamydia testing in primary care[END_REF] Our study seems to contradict this since patients reported that they expected details of sexual histories to be recorded, investigations to be done and referrals to be made formally.

A major strength of this study was that we obtained "consumer" data about expectations and experiences of accessing sexual health care relevant to a range of settings and populations.

Our recruitment of practices was based on demographic and laboratory data, focussing on high sexual health need. In doing so we reduced the "enthusiast" effect as far as possible.

However we were not able to recruit a low-testing practice in London. We were disappointed at how difficult it was to recruit patients, particularly men, in the non-"enhanced" general practice setting, despite extensive efforts. There are a number of reasons for this, which reflect wider difficulties in studying single-episode conditions in primary care. [START_REF] Cassell | The potential of primary care for reducing the transmission of sexually transmitted infections[END_REF] Unless the practice has some kind of enhanced sexual health service -and even if it has -eligible patients form a small group presenting at unpredictable times, in busy practices. They are therefore hard to recruit without a dedicated researcher who would be unoccupied for much of the working week. Our general practice patients cannot be considered fully representative of the eligible population, due to these difficulties in recruiting patients with a single episode, stigmatised condition in a practice without some kind of special provision for sexual health.

A possible mode effect in the interviews must also be taken into account in assessing our results.

Since general practice patients were geographically dispersed, they were interviewed by telephone. It is hard to predict how this might affect the findings or patterns of recruitment.

Our findings suggest that there is often a substantial mismatch between patient expectations and experiences when attending general practice with a possible STI. While patients did not necessarily expect comprehensive management in primary care, dissatisfaction focussed on a few key issues -lack of formal supported referral, lack of information, and lack of engagement with the patient on sexual health. Yet the experiences of the subset of patients drawn from a specialist service within general practice confirm in a non-experimental setting the feasibility of acceptable STI management in this setting. In a qualitative study of patients diagnosed with chlamydia on home-taken specimens but treated in primary care, high levels of satisfaction with the management provided by practice nurses were also reported. [START_REF] Low | Epidemiological, social, diagnostic and economic evaluation of population screening for genital chlamydial infection[END_REF] Our study shows mismatches between the expectation of patients and the care they actually received, and between patient expectations and the different concerns of general practitioners reported elsewhere in the literature. These divergences should now guide service provision. Study participants often reported "informal" referrals to GUM clinics, in which they were told to approach a second service without a letter or telephone call. GPs may still perceive GUM clinics as being embarrassing places to go, and think that "anonymous" referrals are preferred. This would be consonant with the occasional persistence of outdated beliefs that patients will not be able to get life insurance if they have been tested for HIV, which are still sometimes offered as explanations by GPs for not managing sexual health problems in primary care. This suggests that recent modernisation of sexual health services [START_REF] Bailey | Are primary care-based sexually transmitted infection services in the UK delivering public health benefit?[END_REF] needs to be better publicised among professionals. This would be helped if purchasers of primary care explicitly commissioned services specifying pathways from primary to secondary care. It could help to achieve the timely evaluation and treatment of symptomatic patients that are important contributors to STI control. [START_REF] Catchpole | Sexually transmitted infections: control strategies[END_REF] While highlighting scope for improvement, our results also question a recent emphasis on the establishment of "locally enhanced services" in some practices. [START_REF] Sohal | The impact of establishing a local-enhanced service for treating sexually transmitted infections in primary care[END_REF] Without establishing effective and formal referral from the many practices which do not provide testing, many patients may continue to fall between services, resulting in persistent infection and onward transmission.

Our findings have been used to inform the development and piloting of a low-cost intervention aimed at helping GPs improve the care and experiences of patients attending general practice with a suspected STI. The intervention includes a web-based portal that GPs can use to print out information leaflets for patients and referral letters. This kind of approach might provide an opportunity to ensuring effective management for STI within primary care or successful supported referral to specialist services.

Table 1 : Patient Characteristics by geographic area and setting of enrollment

 1 At the population level, one or other must be universally offered if each patient is to be directed quickly into curative treatment and STI control enhanced. Standardised training packages are now available for training general practice staff in the UK, which should now emphasise these findings and incorporate them into training. The incorporation of these findings into low-cost structural interventions -for example by commissioning services that are required either to formally refer on or provide a full package of care -could have an important impact both on patient experience and on outcomes.identification of eligible patients. We thank Lynn Myers for help in designing the topic guide. The Corresponding Author has the right to grant on behalf of all authors and does grant on behalf of all authors, an exclusive licence (or non exclusive for government employees) on a worldwide basis to the BMJ Publishing Group Ltd to permit this article (if accepted) to be published in STI and any other BMJPGL products and sublicences such use and exploit all subsidiary rights, as set out in our licence http://group.bmj.com/products/journals/instructions-for-authors/licence-forms."

	Copyright statement
	"

Acknowledgements:

The authors wish to thank all health professionals in the general practices for consenting eligible patients to the interviews. We thank the GUM clinic staff for their support throughout the study period, in particular the receptionists for assisting in the

Funding: This work was funded by the Medical Research Council, with funding allocated from the Health Departments, under the aegis of the MRC/UK Health Departments Sexual Health and HIV Research Strategy Committee. Statement of independence from funders: The Medical Research Council has had no role in the collection, analysis, and interpretation of data; in the writing of the report; or in the decision to submit the paper publication. The views expressed are those of the authors and not necessarily those of the MRC or the Health Departments. Ethical approval: The CaPSTI study was approved by the South-West Multi-Research

Ethics Committee (reference number 05/MRE06/9)

Competing interests: None


Sylvain Kubler

Éric Rondeau

Jean-Philippe Georges

Dependability of switched network architectures for Networked Control Systems

The switched Ethernet networks are more and more deployed in industry. The Spanning Tree Protocol implemented in the switches enables to manage the link connectivity. But the reconfiguration time of Spanning Tree Protocol (STP) when link failure occurred is not adapted in regard to the industrial constraints. The objective of this paper is to propose a method based only on standard mitigating the probability of disconnection between nodes having hard real-time properties. The approach developed in this paper consists in duplicating frames and in forwarding them on different paths. These paths are optimized and specified by using genetic algorithms. OPNET simulations show the interest of this proposal on a particular Networked Control System.

I. INTRODUCTION

The modern plant architectures implement communication networks to control and to monitor their remote and distributed applications. The major interest facing the point to point architectures is to mitigate the wire costs and to make easier the information sharing. In the context of embedded systems and industrial systems, the communication requirements are both to guarantee bounded end-to-end delays and to maintain the connectivity between all the network nodes. In the 1980's, many networks named fieldbuses were developed to respect these strong constraints. More recently, the trend in fieldbuses consisted in using Ethernet protocol (IEC 61784 gathers the different fieldbuses standards). The advantages are Ethernet is a well known protocol, widely implemented (ensuring its permanence), and its performance are continually increasing with the technologies evolutions (especially its bandwidth). But, Ethernet is not a determinist network since it uses the CSMA/CD protocol to access to the medium. However, the full switched architectures (IEEE 802.1d) allow inhibiting the collisions and are able to manage redundant links. The Spanning Tree Protocol (STP) enables to reconfigure the physical network architecture when a link is in failure in using redundancies. Nevertheless, the standard STP reconfiguration time period is too long and is not compatible with the industry requirements. The objective of this paper is to propose a method based on STP standards for reducing the probability of disconnection between nodes with critical application constraints. The practical approach defended in this paper, is to duplicate the messages with real-time properties and to send them to the remote nodes by using several paths. If one path fails, messages will still arrive at destination by another path in hiding the STP reconfiguration time period on the trouble path.

This article is organized in the following way: the section II describes the Spanning Tree Protocol standards and the related works. The section III formalizes the objective function to be optimized. The section IV presents the approach based on genetic algorithm to increase the dependability of switched network architectures. Finally, the section V illustrates the interest of this study in the Networked Control Systems framework.

II. SPANNING TREE

A. Introduction

Basically, the dependability on network wire is achieved by implementing redundant links and/or network devices. In Ethernet, the redundancy may generate loops in the physical architecture which can lead to infinite retransmissions consuming needlessly bandwidth. The Spanning Tree Protocol (STP) implementing in the switches, aims at breaking the loops in order to form a tree by disabling some links. STP has also to maintain the network connectivity. Then, STP continually monitors the physical link, and dynamically adjusts their states (enable, disable) according to the failure occurrences. Moreover, MSTP (Multiple STP, IEEE 802.1s) or PVST (Per-Vlan STP, Cisco proprietary protocol) are protocols offering the possibility to define as many trees as Virtual Networks (VLAN, IEEE 802.1q).

B. Reconfiguration time

As described previously, the problem of STP is the reconfiguration time period to propose a new fit tree which is around 30 s. This time period corresponds to the addition of failure detection time, spanning tree computation time and link state change time. The new Rapid STP (RSTP, IEEE 802.1w) mitigates this reconfiguration time and enables to propose new physical architecture is less than 5 s. However, these times may still not be adapted to real-time environments. The MOXA Company has then designed a new mechanism named Turbo-ring, which ensures an Ethernet reconfiguration time period around 20 ms. But this solution is not standardized, and it is usable only on a particular topology (a ring), and finally it still generates a breaking time. The objective of this paper is to define a method avoiding this discontinuity of service by even leading it to zero.

C. Related works

In [START_REF] Jayavelu | Maintaining colored trees for disjoint multipath routing under node failures[END_REF], an on-line method which implements a new disjoint multipath routing algorithm (SimCT) is defined in packetswitched networks. This work is based on the colored graph trees theory and takes into account the nodes failures, in order to maintain the communication continuity between a node and a sink. The interest of [START_REF] Jayavelu | Maintaining colored trees for disjoint multipath routing under node failures[END_REF] is to mitigate the long path compared with others proposals and to reduce the number of protocol frame exchanges. Another approach consists in anticipating off-line the path failure. [START_REF] Limal | Formal verification of redundant media extension of Ethernet PowerLink[END_REF] works on Ethernet solutions without switches (hub architecture) and proposes to duplicate the medium and to send the messages twice respectively on the two mediums. A mechanism named link selector is implemented inside each node to ensure the incoming information consistency and to duplicate the sent messages. [START_REF] Jayavelu | Maintaining colored trees for disjoint multipath routing under node failures[END_REF] and [START_REF] Limal | Formal verification of redundant media extension of Ethernet PowerLink[END_REF] are related works, but our approach differs relatively to the network technology. First, we study switched Ethernet architectures not considered in [START_REF] Jayavelu | Maintaining colored trees for disjoint multipath routing under node failures[END_REF] [START_REF] Limal | Formal verification of redundant media extension of Ethernet PowerLink[END_REF]. Secondly, our main objective is to maintain the continuity of service in respecting the standards defined for switched Ethernet. Especially, the MSTP protocol is used to define several trees for interconnecting Networked Control System (NCS) equipment. Also, the strategy consists in implementing a static procedure which consists in forwarding as many frames as defined trees. Thus, if a path is down, the sink node receives the information by at least one of the others paths.

III. FORMALIZATION

A. Introduction

The first work is to define an expression formalizing the problem of the redundant paths between a source generating traffic and its destination node. A path consists of a series of network components. A network component represents either a network node (switch) or a link. The failure probability of a path depends on the number of network components constituting the path. More the network components are used, more the path failure probability is high. Moreover, the failure probability of the redundant paths can be cumulated when a same network component is used in several paths. Indeed, while this network component fails, it may affect the behavior of not only one path but of several paths. Thus, the network dependability evaluation depends on the path length (section III-B) and on the number of common network components implemented in several paths (section III-C). In the present paper, each network component is assumed to have the same failure probability.

B. Network dependability with independent paths

We define α i as being the number network components composing the path i. Let λ be the failure probability per hour of any network component and µ = 1λ as being the nonfailure probability. The failure probability of a path i (P P athi ) is given by [START_REF] Jayavelu | Maintaining colored trees for disjoint multipath routing under node failures[END_REF]. The failure probability of the network (P N etj ) composed of j independent paths is given then by [START_REF] Limal | Formal verification of redundant media extension of Ethernet PowerLink[END_REF].

P P athi = 1 -(1 -λ) αi = 1 -µ αi (1)
P N etj = j i=1 P P athi = j i=1 (1 -µ αi ) (2)
The assessment of ( 2) is studied according to the SIL specifications (Safety Integrity Level, IEC 61508 standard). The Table I provides the values used in the continuous mode. Our research focuses on Networked Control Systems where the SIL 3 and SIL 4 are the levels generally required, especially in avionic, nuclear power plant,. . . The analysis is then based on the choice of network components with SIL 4 (with λ = 10 -8 ). The aim is to observe whether the whole network (constituted of SIL 4 network components) respects the SIL 4 constraint according to both the number of paths and the number of network components used inside a path.

-9 < λ < 10 -8 3 10 -8 < λ < 10 -7 2 10 -7 < λ < 10 -6 1 10 -6 < λ < 10 -5
The results are given in Fig. 1. The first observation is the network with one path is quickly degraded and the scores are upper SIL 4. The second comment is that a network with two independent paths gives a good result since the SIL 4 is guaranteed up to 10 000 network components. Finally, the multiplication of paths considerably increases the cost of the network in terms of price, maintenance, complexity,. . . without necessarily improving the solution relatively to SIL constraints. In conclusion, a network architecture implementing two paths is a good arrangement between dependability and cost. Thereby, the study only analysis redundancy with two paths in the next section.

C. Paths with overlapping

In this section, a network consists of two paths with overlapping. Let α i be the number of exclusive network components composing the path i. An exclusive network component belongs only to one path. Let β be the number of common network components used in both paths. Thus, the total length of a path i is equivalent to α i + β. By relying on the equation (2), the whole network failure probability (P N et ) can be determined by [START_REF] Dréo | Metaheuristics for hard optimization : methods and case studies[END_REF].

P N et = 1 -1 -(1 -µ α1 ) (1 -µ α2 ) µ β (3)
Fig. 2 gives the failure probabilities defined in (3) according to the path length and the rate of common network components used in the two paths : β/(α i + β). Fig. 2 shows that when at

D. Conclusion

The expression (3) is a general expression of (2) with two paths. (3) is then used as objective function to find optimized pair of trees. The network consists of many links, many nodes such that the search of pair of trees quickly meets an explosion combinatory problem. This issue is a subclass of problem studied in [START_REF] Jayavelu | Maintaining colored trees for disjoint multipath routing under node failures[END_REF] described with complexity order O(|L||N |), with |L| the number of links and |N | the number of nodes. Thereby, we propose as suggested in [START_REF] Jayavelu | Maintaining colored trees for disjoint multipath routing under node failures[END_REF] to use heuristic algorithms.

IV. OPTIMIZATION ALGORITHMS

A. Choice of heuristic

There are three main classes of heuristics: the constructive methods (greedy algorithm, pilot method), the local research methods (simulated annealing, taboo search) and the evolutionary methods (Genetic Algorithm, ant colony optimization). It is difficult to compare these methods. But, an analysis in [START_REF] Dréo | Metaheuristics for hard optimization : methods and case studies[END_REF] between the simulated annealing, the taboo search, the ant colony optimization and the genetic algorithms (GA) provides diagrams giving the probability that a method is better than another one. In these works, we notice for a similar problem, the GA give the best results to this type of study.

B. Coding of the component networks

The network architecture is defined by a graph G = (S, M) (digraph or undirected graph) where S is the set of nodes, i.e. the vertices of the graph and where M is the incident matrix and defines the network links. As a matter of fact, the matrix M stands for the "incident-vertexedge matrix" of dimension m × n where m is the number of vertices and n is the number of edges. Each edge of the graph is numbered such that considering an edge i interconnecting two vertices k and l, we have M (j, i) = 1∀j = k, l and M (j, i) = 0 otherwise. As shown in Fig. 3, this matrix can be summarized in a vector where each row corresponds to one edge of G and where columns give the edges of a given vertex. (a)

             
0 1 2 3 4 5 6 7 8 9 10 11 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 1 1 3 1 0 0 1 0 0 0 0 1 0 0 1 4 0 0 1 1 1 0 0 0 0 0 0 0 5 0 0 0 0 1 1 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 1 1 0 7 0 0 0 0 0 0 0 1 1 1 0 0 8 0 0 0 0 0 0 1 1 0 0 0 0 9 0 0 0 0 0 1 1 0 0 0 0 0 According to this definition, it is possible to propose two algorithms aiming at checking if the graph is connected and identifying the nodes along a path. There are two types of algorithms for going through a graph, the Depth First Search (DF S) and the Breadth First Search (BF S). The difference is related to the analysis sequence of the vertices. The DF S explores "deeply" the paths one by one, whereas the BF S generates a research tree achieving layer by layer. However, the BF S requires a lot of memory to store all the alternatives for each layer. Therefore, the DF S algorithm is implemented in our work.

                                0
                  (b) (c)
Firstly, an algorithm is defined in order to check that a vertex s of the graph G is able to access any vertices of S. Running Accessible_Nodes(G, s, {∅}) from Algorithm 1 returns the list V of the accessible vertices from s. Hence if V = S, it means that a graph is connected. This algorithm will then use to check that the proposed trees are respectful according to the spanning tree definition.

Algorithm 1: Accessible_Nodes(G, i, V) output: the list V of the accessible nodes from i begin V ←-V ∪ {i}; forall the j ∈ S\V do if ∃k | M i,k = M j,k = 1 then Accessible_Nodes(G,j,V);
Secondly, the function Path(G, i, e, V, P) of Algorithm 2 is proposed in order to compute the path length. Indeed running Path(G ′ , s, e, {∅} , {∅}) returns a list P containing the vertices of the graph G ′ = (S, M ′ ) along the path between s and e ∈ S. Hence, the path length is given by the size of P. This function will be used in the following to compute the objective function of a spanning tree solution G ′ . Finally, the last step deals with the coding of one spanning tree. There are several methods of spanning tree representation of graph [START_REF] Enacheanu | Flexible Electric Infrastructures for Advanced Distribution Automation[END_REF], [START_REF] Nara | Implementation of genetic algorithm for distribution systems loss minimum reconfiguration[END_REF], [START_REF] Zhu | Adaptive power flow method for distribution systems with dispersed generation[END_REF], [START_REF] Radha | A modified genetic algorithm for optimal electrical distribution network reconfiguration[END_REF], [START_REF] Ramos | Pathbased distribution network modeling: application to reconfiguration for loss reduction[END_REF], [START_REF] Lin | Distribution feeder reconfiguration with refined genetic algorithm[END_REF], [START_REF] Hong | Determination of network configuration considering multiobjective in distribution systems using genetic algorithms[END_REF]. [START_REF] Enacheanu | Radial network reconfiguration using genetic algorithm based on the matroid theory[END_REF] explains by taking the method of coding based on the representation in co-tree (Digital coding of open branches), it avoids the determination of the fundamental loops allowing to test the validity of the resultant topologies after crossover and mutation processes in the genetic algorithms. In conclusion, the "digital coding of open branches" method [START_REF] Radha | A modified genetic algorithm for optimal electrical distribution network reconfiguration[END_REF] is implemented. For instance, considering the graph Fig. 3, a possible spanning tree could be modeled by the sequence 1, 8, 6 in which each number represents the opened branch as shown in Fig. 4 C. Genetic Algorithm According to observations based on the evolution of species, C. Darwin introduces the theory of evolution.

In this paper, individual represents the spanning tree. According to the type of coding previously cited, the crossover and mutation operators might generate invalid individuals compared to the topological constraints. [START_REF] Enacheanu | Radial network reconfiguration using genetic algorithm based on the matroid theory[END_REF] developed a crossover and mutation strategy based on the graphs theory approaches. The mutation technique consists in randomly picking a gene from a chromosome (representative of an opened branch), and then to determine the formed loop resulting of the closure of this branch. Finally GA randomly selects within this loop a branch to open. This principle is illustrated Fig. 4. Step 1 : Random choice of one gene (branch) to mute

Step 2 : Random choice of one branch resulting from the formed loop next the closure of the branch 6. Loop : [ The crossover technique illustrated on Fig. 5, consists in randomly picking a reference point in the chromosome of the individual I1, and then to determine the loop formed after the closure of this branch. GA looks for branches which might be swapped between the 2 co-trees. Moreover, it is necessary to analyze the chromosome of the individual I2. If there are genes belonging to the loop, GA has to make the crossing with one of them. It is necessary to repeat this step until reaching the last gene.

D. Adjustments of GA parameters

[12] defined conventional GA parameters such as population size t pop , crossover p c and mutation p m probabilities. These parameters have an influence on the GA performance. It is then necessary to study the impact of each probability on GA behavior to determine their optimal value. [START_REF] Georges | A design process of switched Ethernet architectures according to realtime application constraints[END_REF] proposes an approach allowing to achieve these adjustments. This method is used in this research and the optimal values obtained are: t pop = 10, p c = 70% and p m = 40% [START_REF] Kubler | Continuité de service sur Ethernet Industriel[END_REF].

V. CASE OF STUDY

A. Introduction

Firstly, specific nodes were developed in the OPNET network simulation tool, to implement the behavior of NCS device. The NCS implemented in our simulations is depicted in Fig. 6. To give numerical results, the approach presented in this paper will be applied on a sample system described by its following system equations: Secondly, a particular switched Ethernet architecture consists of 31 switches and 56 links is defined Fig. 7. The NCS devices (controller, sensor, actuator) are respectively connected to switches 20, 5 and 11. The cycle time is 2 ms, the devices periodically send packets of 64 bytes every 1 ms.

P (s) = 2 (s + 5) (s + 0.
Thirdly, the study is divided in two steps. The first one uses the classic solution with the Spanning Tree Protocol (STP). According to the values of switches and ports priorities, the STP algorithm will defined one spanning tree for the whole network. Fig. 7 depicts the default spanning tree observed in our network. The second one applies the method proposed in this paper, in implementing two paths obtained from GA. Rapid STP is activated on the simulation tool for defining the two trees. To improve the understanding of the figures, only the links belonging to the paths between the NCS devices are highlighted (bold lines) and not the global tree.

B. NCS analysis with RSTP

Fig. 7 shows the path used by the controller to communicate both with its sensor and actuator. This path is a part of one tree that can be defined by RSTP for a particular set of switches and ports identifiers. During the simulation, the link 8 belonging to this path fails at t = 115 s. Fig. 9(a) provides the behavior of the process output according to the reference.

Before the link failure, the process reaches the reference with an acceptable overshot. When the link 8 fails, the actuator is disconnected to the controller during 5 s corresponding to the RSTP reconfiguration time period. Thus, between t = 115 s and t = 120 s, the new references are not taken into account by the process. After t = 120 s, the controller is able to send to the actuator the new control, but a period of instability is observed before reaching again the reference. This instability step may be due to the reception of old messages (by the actuator) buffered in the network.

C. NCS analysis with two redundant paths determined by GA

Fig. 8 shows the two independent paths obtained by GA for interconnecting the controller and the process. Two VLANs are defined and two trees are created respectively for each VLAN by using MSTP. In technical way, the network designer has only to set the switch ports belonging to the path with a high priority, and the root switch is located at the middle switch of the path. Consequently, MSTP determines its tree in overlapping the path. In this approach, the controller duplicates the control messages on the two trees and it receives twice the sensor state. second path associated to the VLAN 1. Next, when both links 6 and 33 fail at t = 170 s, the system becomes unstable. However, this occurrence appears with a probability at SIL 4 if all the network components are SIL 4 as it is explained in the section III.

D. Temporal validity of messages

The classical problem due to the message duplication is the consistency control of information system. The duplication generates desynchronizations since the messages duplicated do not arrived at the same time on the destination nodes. Fig. 9(c) illustrates this problem by adding load traffic at t = 130 s on the link 42 (path VLAN 2). This overload generates a congestion and some delays on messages which are sent on the path VLAN 2. Thus, the messages sent on path VLAN 1 arrive before the ones using the path VLAN 2. Fig. 9(c) shows instabilities since the controller processes the received messages in FIFO order, without managing their temporal validity. This trouble can be suppressed either by numbering or timing the messages. The numbering of messages is implemented in our OPNET simulations and thereby, the reception nodes discard all the messages containing "old" number. This method is applied to eliminate the instabilities issues. The results are similar to the Fig. 9(b).

VI. CONCLUSION

The paper presents both a strategy to face with high dependability constraints and an off-line method to define in practise the pair of paths for each traffic based on a local configuration (without modifying Ethernet standards). This method is based on the definition of two redundant paths determined by GA and relies on message duplication thankfully the MSTP technique. The main interest is to reduce the probability of communication disconnection in particular in a NCS framework. However, this method has to be applied only for specific nodes strongly timed constrained. It cannot be generalized for all the nodes of the network, since the duplication of messages induced overload.

Fig. 1 .Fig. 2 .

 12 Fig. 1. Analysis of dependability for independent paths

Fig. 3 .

 3 Fig. 3. Network modeling, (a) graph G = (S, M), (b) incident matrix M and (c) its equivalent vector

Algorithm 2 :

 2 Path(G, i, e, V, P) output: the list P of the nodes along the path from e to i begin V ←-V ∪ {i}; if i = e then P ←-P ∪ {e}; else forall the j ∈ S\V do if ∃k | M i,k = M j,k = 1 then Path(G,j,e,V,P); if P = {∅} then P ←-P ∪ {i}; return P;

Fig. 4 .

 4 Fig. 4. Mutation technique

Fig. 5 .

 5 Fig. 5. Crossover technique

Fig. 6 .

 6 Fig. 6. NCS feedback control loop

Fig. 7 .

 7 Fig. 7. Classic STP solution

Fig. 8 .Fig. 9 .

 89 Fig. 8. Duplication of messages on a Multi-VLAN architecture

TABLE I DEFINITION

 I

OF SIL IN THE CONTINUOUS MODE (IEC 61508) SIL Range of λ (Failures by hour) 4 10

ACKNOWLEDGEMENT

This work was supported by OPNET Technologies, Inc. thanks to "Teaching with OPNET" program.