Charles Raux
email: charles.raux@let.ish-lyon.cnrs.fr

Tai-Yu Ma

Eric Cornelis

Variability versus stability in daily travel and activity behaviour. The case of a one week travel diary

published or not. The documents may come

Variability versus stability in daily travel and activity behaviour. The case of a one week travel diary

Introduction

Various travel demand management policy measures which are at stake today, such as flexible or staggering work hours, incentive to use enhanced bus or light-rail services, integration of various transport modes as alternatives to the car (e.g. bike and public transport), car pooling and car sharing or even congestion pricing, all need accurate prediction of their effectiveness in changing behaviour. Obviously these old and new policy measures will demonstrate their effectiveness only if they match with day-to-day behaviour of transport users at which theses measures are aimed.

Conventional four-step models are the main tool to produce this kind of prediction, however they are generally based on household travel surveys which measure individual travel (and sometimes diary) on one day only (as in France, Switzerland and Belgium; see [START_REF] Raux | Travel and activity time allocation: An empirical comparison between eight cities in Europe[END_REF]. There are abundant examples of errors when comparing ex-ante prediction with expost realisations, such as with the London Congestion Charging Scheme which endured an unpredicted level of traffic decrease in the charging zone after implementation. Unsuspected levels of flexibility or rigidity in travel behaviour may be revealed in response to travel demand policy measures. This is why the search for regularity, variability, flexibility or "anchor points" in activitytravel behaviour is of crucial interest for modelling.

The literature upon individual day-to-day activity-travel behaviour has delivered, at least since the eighties, a definite picture of large variability in various dimensions of this behaviour. Hanson andHuff (1982, 1988) analyses day-to-day variability of travel patterns on a 35 consecutive days (Uppsala Household Travel Survey) and conclude that while a seven-day record of travel does not capture all the variability of behaviour, it does capture a good sampling of individual's typical daily travel patterns. However, conclusions on variability depend on the way "behaviour" is measured. [START_REF] Hanson | Classification issues in the analysis of complex travel behaviour[END_REF] takes the working hypothesis that individual behaviour is neither completely habitual, neither completely random. They conduct classification analysis on time allocation and travel indicators on a five-week observation period. They identify travel-behaviour groups but considerable intragroup variability remains. [START_REF] Pas | An examination of the determinants of day-to-day variability in individuals' urban travel behavior[END_REF], using a five-day record of travel, show that employed people have much lower levels of intrapersonal variability in trip frequency when compared with people who are not employed outside the home. Social class and the availability of travel and related resources are important factors of intrapersonal variability. Household role related variables (such as gender related effect of children) are also important. [START_REF] Jones | The significance and measurement of variability in travel behaviour[END_REF] develop different measures of variability on multiday data and raise the issue of which variability is at stake and hence the way in which behaviour is measured.

Using a three-day travel data set, [START_REF] Pas | Intrapersonal variability in daily urban travel behavior : Some additional evidence[END_REF] conclude that there is a considerable level of intrapersonal variability in daily trip frequency, trip chaining and travel time.

When discussing the Mobidrive six-week travel diary [START_REF] Axhausen | Observing the rhythms of daily life: a six-week travel diary[END_REF] stress the need to focus on the dynamic processes in travel behaviour, which requires observation on long durations. [START_REF] Schlich | Habitual travel behaviour: evidence from a six-week travel diary[END_REF] use the Mobidrive dataset and use different methods to measure similarity of travel behaviour. Travel day-to-day behaviour is more stable on work days. They argue that two weeks are required at minimum in order to measure variability. Schlich et al (2004) also provide measures of repetition on leisure travel. [START_REF] Ettema | Weekly rhythms in task and time allocation of households[END_REF] analyse a one-week time use survey held over couples in The Netherlands. They explore day-to-day variability and the influence of role expectations, of role in the household on time allocation, and specialisation of tasks within the household (linked to time constraints, e.g. the presence of young children or the level of accessibility to jobs or stores). They conclude that spatial factors play a limited role in task allocation, compared to personal and household characteristics (presence of young children, work status, age, gender). This last result is also in line with [START_REF] Raux | Travel and activity time allocation: An empirical comparison between eight cities in Europe[END_REF]. [START_REF] Kang | Exploring day-to-day variability in time use for household members[END_REF] describe day-to-day variability in activity time-use patterns within households, taking account of interactions between household members, and develop structural equation models of these patterns.

However most of these studies do not take account of scheduling of activities and trips. Sequential alignment method (SAM) was introduced by [START_REF] Wilson | Activity pattern analysis by means of sequence alignment methods[END_REF] for comparing sequence of activities in activity patterns. This method has been extended to multidimensional SAM taking into account the dependencies between different attributes of activity patterns (activity type, location and duration, beginning and ending time, travel mode; see [START_REF] Joh | Activity pattern similarity: a multidimensional sequence alignment method[END_REF]. However this extension raises some critical issues of choosing the various attributes and categorisation of interval-scaled variables such as activity duration or trip distance, which lack of theoretical justification.

Multiday data sets are rare (even if originating in the 70's as referred to in the literature), and this paper takes the opportunity of availability of a new 7-day data set to explore again the issue of day-to-day activity-travel behaviour.

Beyond the expected day-to-day variability, another issue is also to find some empirical indications of stability or regularity in individual activity patterns along the week. A seminal idea is that of "core stops" developed by [START_REF] Hanson | Systematic variability in repetitious travel[END_REF]: these are elaborated as combinations of activity, mode, arrival time and location, repeated a certain number of times within a period of several days, that serve to "anchor" the rest of the individual's travel.

The questions which guide our analysis are the following:

• What are the relative levels of interpersonal and intrapersonal variability, according to various attributes of activity-travel patterns? • What are the days which are the most similar along the week from the point of view of activity-travel behaviour? • Do individual characteristics influence this variability and to what extent?

• Can we find stability (i.e. "core stops") in activity-travel patterns, according to travel modes, activity performed, arrival times and places visited?

Our analysis confirms the large level of intrapersonal variability whether for daily trips, tours, time use and activity sequence. However our analysis goes further by studying this variability along various time periods within the week. Moreover, we show that the systematic day-today variability has an extremely low share in intrapersonal variability. Another perspective is then taken by searching for repetitive activity-travel behaviour, through attributes of activity at trip destination, travel mode, trip arrival time and destination location. Our results on core stops are somewhat encouraging by showing some kind of concentration of activity patterns on a few "anchor" points.

The organization of the paper is as follows. First the data, a one-week travel diary in Ghent (Belgium), are introduced. Then the overall methodology for measuring variability is presented. This method is applied in the next section successively to travel indicators (trips and home-based tours), time use over various activities, and daily activity sequence. Influence of socioeconomic characteristics on intrapersonal variability is also tested. In the following section a search for potential "core stops" in the week is performed. Finally, we discuss the results and draw some conclusions.

The data

The data for the analysis is based on a seven-day travel diary collected in the city of Ghent in Belgium. The objective of this survey was to investigate individual's weekly activity patterns and their impact on day-to-day variation of travel behaviour.

The surveyed households are randomly drawn from the population in the city of Ghent based on the stratification of household size, gender and age of household head (12 to 75). The surveyed individuals are based on randomly selected individuals in the household because sampling whole household members over a week may reduce the response rate. The survey methodology is based on paper and web survey followed by phone support. Although this survey cannot collect the activity patterns of all members in the household, it still allows us to investigate individual's daily activity patterns and the determinants related to individual's socio-demographic characteristics.

The collected information contains continuous trip chain information over a week (trip purposes of 12 categories, approximate address of destination, departure and arrival time of trip, travel cost, used modes and travel time) and its potential influence factors (sociodemographic characteristics and mobility practices). The survey was conducted from September to November 2008 and 717 individual 7-day mobility diaries were collected (starting from any day within a week).

The initial 12 activity types are classified into six categories in our empirical analysis: 1 home (home), 2 work and school (work, school), 3 shopping (daily and long-term shopping), 4 personal business (personal business (bank, doctor etc.)), 5 social-recreation (eating, visit to family or friends, walking, riding, leisure, sport, culture etc.), 6 others (drop off/pick up someone and others).

Methodology for measuring variability

Multidimensional statistical techniques could be applied (e.g. factor analysis), however the travel-activity pattern is so complex in its multiple dimensions that a cautious approach is adopted by analysing separately the various indicators. These are number of trips and number of home-based tours per day, time allocation to activities per day (i.e. daily time-budget), activity sequence each day, all of them computed at the individual level.

Variability in day-to-day behaviour can be attributed either to interpersonal differences or to intrapersonal differences. Basic theoretical results regarding the splitting up of variance may be applied, along with the ideas of [START_REF] Pas | Intrapersonal variability and model goodness-of-fit[END_REF] who originally developed these measures for analysing day-to-day variability in individuals' travel behaviour.

The total variability of any daily travel/activity indicator (total sum of squares TSS) can be split up into interpersonal variability (between person sum of squares BPSS) and intrapersonal variability (within person sum of squares WPSS).

Indeed considering some indicator of daily activity-travel behaviour ij n (e.g. number of trips made by the individual i on day j), we have

∑∑ = = = - I i J j i ij n n 1 1 0 ) (
where I is the number of persons in the sample J is the number of days in the observation period and i n the mean daily travel/activity indicator for individual i over period J,

∑ = j ij i n J n 1 It follows that ( ) ( ) ( ) BPSS WPSS n n n n n n TSS i j i i j i ij i j ij + = - + - = - = ∑∑ ∑∑ ∑∑ 2 2 2
with n the mean daily travel/activity indicator over all individuals I and period J,

∑∑ = i j ij n IJ n 1 ∑∑ = = - = I i J j i ij n n WPSS 1 1 2 ) (
, the within-person sum of squares,

∑ = - = I i i n n J BPSS 1 2 ) (
, the between-person sum of squares, When it comes to socio-economic analysis or modelling, the interpersonal variability BPSS is generally explained by between-person differences in socio-demographic or place-based attributes.

The intrapersonal variability WPSS can be further split up into a systematic day-of-week variability (between-day sum of squares BDSS) and a residual variability (within-day sum of squares WDSS).

( ) ( ) [ ] ∑∑ ∑∑ + = - - - - + = - = = = i j j i j ij I i J j i ij BDSS WDSS n n n n n n n n WPSS 2 1 1 2 ) ( ) (
∑ = i ij j n I n 1 ) ( n n n j ij - +
is the travel/activity indicator for person i on day j adjusted for the systematic effect of day j

( ) 2 ) ( ∑∑ - - + = i j i j ij n n n n WDSS ∑ - = j j n n I BDSS 2 ) (

Variability on various dimensions of activity-travel behaviour in the week

Variability in the number of trips and home-based tours per day

Table 1 gives an overview of the mean number of trips per person over the week for various activities. The 717 people surveyed all perform at least one outside activity (at least 1 return trip to home) and on average perform 10.3 return trips to home over the seven days with a standard deviation of 3.8. Other activities are practiced at various levels, e.g. 57% for work, 26% for school, 87% for shopping and 95% for social recreation. However the variability in trip numbers is large (compare "mean" and "S.D.") when compared with that for home return trips. Moreover, as shown in Table 2, the variability in trip numbers (over all activities) remains high whatever the period considered in the week. First, the total variability of daily trip number (TSS, divided by the number of days on which this statistics is computed) is roughly the same whatever the five periods considered (from Monday-Friday to Saturday-Sunday). This indicates that the number and the type of days on which the variability is computed have no incidence on its level.

The between person variability (BPSS) is in general less than the within person variability (WPSS): the share of BPSS in total variability is minimum (35.8%) when considering the whole week (Monday to Sunday); it increases to make up 45% of total variability when considering Monday to Friday period (working days); and it is maximum (60.6%) when narrowing the period to the week-end (Saturday and Sunday). It is only over the week-end that the between person variability is above the within person variability.

These results suggest that socio-demographic characteristics attached to the person, which are generally used to explain differences in travel behaviour, should perform better on week-end days and less on working days period (Monday-Friday). The impact of these sociodemographic characteristics is explored later in this paper. When it comes to further breakdown of within person variability (WPSS) into between-day (systematic day-to-day) and within-day variability, the results show that the systematic dayto-day variability (BDSS) has an extremely low share of WPSS (about 5% on Monday-Sunday period). This is again in line with [START_REF] Pas | Intrapersonal variability and model goodness-of-fit[END_REF] but one can analyse the variations of this share along the various periods.

First, if we consider the first four lines of the table, which include the working days (Mon-Fri) and Saturday or Sunday, the level of within-day variability (WDSS) remains approximately the same (from about 2.3 to 2.5). However, the share of BDSS changes significantly when Sunday is included (from about 1% to 5%), and peaks up to 12.5% when the period is narrowed to Saturday-Sunday (BDSS increases while WDSS decreases sharply). Somewhat expected, regarding variability in trip numbers, Sunday appears definitely as a different day from other days of the week, including not only the traditional working days but also Saturday.

Overall this indicates that the within person variability has to be explained by factors other than systematic day-to-day variability.

Table 5 shows the same structure as Table 4 but now for the number of daily home-based tours. However the view offered by home-based tours is rather different from that regarding trips.

The total variability of daily trip number (TSS) is roughly the same for the first four periods considered (less than 0.7, from Monday-Friday to Monday-Saturday) but different regarding the period Saturday-Sunday (1.61, with BPSS tripling and WPSS roughly doubling).

The between person variability (BPSS) is always less than the within person variability (WPSS) whatever the period considered, and goes from about 30% to 39%.

Regarding breakdown of within person variability (WPSS), the systematic day-to-day variability (BDSS) has an extremely low share of WPSS, as for trips, while WDSS remains approximately the same for the first four periods. However while WDSS doubles for the Saturday-Sunday period, BDSS stays at the same level.

Variability in the individuals' daily time use

The daily travel/activity indicator under study here is the duration of activity a on day j for individual i (in minutes) ija d . Only out-of-home activities are distinguished while in-home activities are not available in detail. Table 6 shows mean duration (and standard deviation) of activities for various periods in the week. Hence ia d refers to the mean duration of activity a for individual i over period J,

∑ = j ija ia d J d 1 ja d
is the mean duration of activity a over individuals on day j,

∑ = i ija ja d I d 1
and a d is the mean duration of activity a over all individuals I and period J,

∑ = i ia a d I d 1 ∑∑ = = - = I i K a a ia d d J BPSS 1 1 2 ) ( ∑∑∑ = = = - = I i J j K a ia ija d d WPSS 1 1 1 2 ) ( ∑∑ - = j a a ja d d I BDSS 2 ) (
Table 7 shows the various figures of variability for time allocation to activities per day. TSS is remarkably stable across the various periods of observation, except for a decrease in variability on Saturday-Sunday period. Within this variability the share of between-person variability (BPSS) is in the majority only when considering working days (Monday-Friday, 58%) or the week-end (Saturday-Sunday, 59%). On the opposite the share of BPSS is minimal (and less than half) when considering the whole week (Monday-Sunday): the intrapersonal variability in time allocation over the whole week takes the lead.

Regarding the breakdown of intrapersonal variability (WPSS), the share of systematic day-today variability is again in the minority (BDSS, less than 20%), however with significant differences when considering various periods in the week. This share is almost null (0.6%) on the working days period (Monday-Friday) and about 1% on the week-end period.

This indicates that within whether the working days or week-end period intrapersonal variability is not driven by alternation of days but by other kinds of variability. The opposition of working days on the one hand and week-end days on the other hand, when compared to the whole week indicates a probable effect of socio-demographic individual status which makes the allocation of time more heterogeneous between people during the working days and during the week-end. Thus the same table is computed by restricting to workers only, with figures shown in Table 8. With this subsample, compared to the previous table, the total variability (TSS) is divided by two, reflecting the homogenization of time allocation across individuals (and probably the impact of work activity on daily time use).

There is only a slight decrease of intra-personal variability (WPSS) and thus the share of inter-personal variability (BPSS) decreases significantly. BPSS is in the majority only when considering week-end (Saturday-Sunday) and it is minimal when considering the whole week (Monday-Sunday), as previously. Finally the share of systematic day-to-day variability (BDSS) increases but remains in the minority.

Overall, when restricting to the subsample of workers, there is more homogeneity in time allocation across the sample and the days, but the intra-personal variability increases its share.

Variability for individuals' daily activity sequence

The similarity of activity chains (patterns) has been a widely studied research issue in activity-based travel demand analysis. The comparison of activity patterns is the basis for longitudinal analysis of travel behaviour. The question concerns how different activity patterns vary over a week. In the past, most similarity indicators compare the corresponding elements between a pair of activity patterns. The distance is measured by summation of 0-1 scores resulting from pairwise comparison of sequences. The sequential (order) information between elements is neglected. As the sequential relationships reveal the dependency of travel/activity participations of individual's activity chaining behaviour, it is important to take it into account.

For this issue, [START_REF] Wilson | Activity pattern analysis by means of sequence alignment methods[END_REF] firstly introduced a Sequential Alignment Method (SAM) for activity pattern analysis. The SAM allows comparing the similarity between a pair of sequences by incorporating its ordering information. The method is originated from molecular biology, aiming to identifying segments of similarity reflecting some functional relationship between sequences of DNA or protein. The sequence is defined as a set of ordered elements arranged as a string. The difference (dissimilarity) between sequences is evaluated as the efforts to equalize them, which allows one takes into account the sequential information in the measurement of similarity between sequences. The SAM has gained its popularity in comparing the similarity between activity patterns recently (Schlich and Axhausen, 2004;[START_REF] Shimamoto | An effective algorithm to detect the similarities of activity-travel patterns[END_REF]. Some methodological advancement in the SAM for activity pattern analysis has also been reported [START_REF] Joh | Activity pattern similarity: a multidimensional sequence alignment method[END_REF][START_REF] Wilson | Activity patterns in space and time: Calculating representative Hagerstrand trajectories[END_REF].

The similarity of activity patterns can be measured based on a variety of attributes of each activities between two activity chains, such as activity type, transport mode, destination and activity duration etc. If we consider only one attribute, the ordered attribute values represent corresponding travel/activity characteristics in the activity chain. To measure the similarity, a distance function needs to be defined. The SAM utilizes a process for which a set of operations, i.e., deletions, insertions and substitutions, are utilized to equalize the sequences. Each type of operations is associated with a cost (score) for which substitutions are generally assigned as two times of deletion/insertion costs. This is because one substitution needs to implement one deletion and one insertion. For example, to equalize the sequence where d w , i w and r w is the costs (weighting coefficients) of deletion, insertion and replacement, respectively. The distance (Levenshtein distance) between two sequences can be calculated by applying a dynamic programming algorithm, computing the least number of operations necessary to equalize two sequences.

As activity patterns are generally characterized by different attributes, the similarity between these patterns should take into account all important attributes, which make the calculation of similarity more complex. As mentioned by Schlich and Axhausen (2004), different attributes may depend on each others, i.e. trip duration, transport mode and destination choice are correlated. Hence, the similarity between activity chains with multiple attributes cannot be obtained by simply summing uni-dimensional alignment costs for all attributes. For this issue, [START_REF] Joh | Activity pattern similarity: a multidimensional sequence alignment method[END_REF] propose a multidimensional alignment method by taking into account the interdependence information among the attributes in activity patterns. The idea is that first a multidimensional sequence is constructed with each line representing corresponding attribute. The operation set for each attribute is identified based on the calculation of Levenshtein distance. If the operations for attributes are identical, the costs are counted once as one simultaneously aligns a bundle of elements. They further proved that the minimum cost of multidimensional alignment can be obtained efficiently by searching the combination of onedimensional alignment results for each attribute. [START_REF] Joh | Measuring and predicting adaptation in multidimensional activity-travel patterns[END_REF] proposed a heuristic method to calculate the multidimensional alignment costs. However, some issues concern the choice of attributes and the categorisation of interval-scaled variable such as activity duration or trip distance still lack theoretical justification. Because different ways of selecting, weighting and categorizing attributes may generate trivial results, we applied one-dimensional alignment method to compare activity type sequences.

In the general formulations ij n is replaced by ij s the SAM distance for individual i, between day j and the other days of the week, defined as

∑ = = J k ik ij ij q q d s 1 ) , (
with ij q being the activity sequence on day j performed by individual i.

Thus i s is the mean SAM distance for individual i of all days j of period J to all other days in the same period J,

∑∑ ∑ = = = = J j J k ik ij j ij i q q d J s J s 1 1
) , ( 1 1 j s is the mean SAM distance over all the individuals of day j to all other days in period J, defined as

∑∑ ∑ = = = i J k ik ij i ij j q q d I s I s 1 ) , ( 1 1
s is the mean SAM distance over all the individuals and all days of period J,

∑ = i i s I s 1
Other statistics are straightforward:

∑ - = i i s s J BPSS 2 ) ( ∑∑ - = i j i ij s s I WPSS 2 ) ( ∑ - = j j s s I BDSS 2 ) (
Table 9 shows the overall mean SAM distance for different periods in the week. The SAM distance is minimal in the week-end period (Saturday-Sunday), at a significantly lower level than on other days, and maximal when considering the whole week (Monday-Sunday). This indicates a specificity of Saturday and Sunday in activity sequences, when compared with the remainder of the week, and also a significant degree of homogeneity of these two days in the nature of activities when compared with the working days. Remark: s is divided by 10 9

Table 10 shows the inter-and intrapersonal variability of SAM distances for various periods in the week. The total variability (TSS) is minimal on week-end and maximal when considering the whole week. The main difference with previous indicators is the high level of between-person variability, always over intrapersonal variability (with a share of more than 70%). This share is maximal on the working days period (Monday to Friday). Thus the heterogeneity of individuals would explain a large part of variability in the sequencing of activities.

Hence the intrapersonal variability (WPSS) is small and within it, the systematic day-to-day variability (BDSS) is even smaller (roughly between 1% and 9%). Because of this high level of between person variability on working days, the impact of individual socio-demographic status on daily activity sequence is explored further with Table 11 relative to workers subsample.

Compared to Table 10 the workers subsample shows no significant change in structure. There is a slight decrease of total variability (TSS), which is expected as the subsample is more homogeneous, and no change in the share ranking of BPSS. There is a slight increase in the share of day-to-day systematic variability (BDSS) but it is still in the minority.

Does socio-demographic status explain intrapersonal variability?

Since we suspect that socio-demographic status might explain the level of intrapersonal variability, linear regression models are employed to investigate the effects of sociodemographic variables on individual intrapersonal variability.

Referring to the general notation the endogenous variable is

∑ = - = J j i ij i n n WPSS 1 2 ) (
More than twenty socio-demographic and lifecycle variables are included as explanatory variables for intrapersonal variability analysis. They are listed in Table 12 and include gender, age (in groups), household type (couple or single), the presence of young children (under 12) in the household, work status, holding of a driving license, work duration (in groups) and a combination of variables describing the role of the individual (head, spouse or child) and the household structure (single, couple; child, no child; zero, one or two workers).

Holding a driving license is retained as a proxy for car availability. Indeed we know by the survey the number of cars available in the household but not the number of driving licenses within the household. Previous studies indicate that the possession of driving license influences individual's travel and activity participation [START_REF] Bhat | A multidimensional mixed ordered-response model for analyzing weekend activity participation[END_REF][START_REF] Lee | A latent class accelerated hazard model of activity episode durations[END_REF]. separate models for these four categories is tested with likelihood ratio tests and this breakdown of model is significant in all cases (see Table 18, Table 21, Table 24 andTable 27 in appendices).

Overall the models show that the influence of socio-demographic status on intrapersonal variability is weak, whether for daily trips, tours, time use and daily activity sequence.

However some variables have a systematic effect.

Gender is always significant in nearly all categories of the sample and men have in general lower intrapersonal variability than women.

Adults living single without young children (H_Sing_NChild) have also in general lower variability in all intrapersonal variability dimensions, although depending on the category (students, etc.). However they are only 1% in the sample.

Sometimes age appear significant but without definite meaning.

Holding a license has a positive significant effect on intrapersonal variability for students only. Potential access to car driving is associated with more intrapersonal variability in activity-travel pattern.

Searching for core stops in the week

The search for core stops starts with the measure of repetition of travel behaviour based on trip characteristics. Each trip can be classified based on one-or multi-dimensional trip attributes. These four attributes are activity type, transport mode, arrival time at destination and activity location. Activity is classified as 6 categories: 1. work; 2. school; 3. shopping; 4. personal business; 5. social recreation; 6. others; 7. home. Mode is classified as: 1. walk; 2. bicycle; 3. car; 4. public transportation. Arrival time is classified as: 1. 0:00-8:30; 2. 8:31-10:30; 3. 10:31-12:30; 4. 12:31-16:00; 5. 16:01-18:30; 6. 18:31-23:59. Location of activity is based on the 45 zones actually visited by the overall sample.

Table 13 gives an overview of the frequency of trip attributes according to activity, mode, arrival time and location. On average, individuals perform almost five activities among the seven potential, they use three of the four potential modes, arrival times of their trips fall within five intervals of the six possible and they visit only six locations (with a maximum of 14) among the 45 visited overall by the sample. This first overview indicates at the same time diversity and specificity in activity-travel across the week. People seems to perform the whole range of activities (except work for non-workers and school for adults and non-students), they use various transport modes and at any time. However, they visit only a few places among the infinity of potentials. As in [START_REF] Hanson | Assessing day-to-day variability in complex travel patterns[END_REF] measures of repetition of individual's trips on various combinations of two to four attributes are given in Table 14. On average, 12 combinations of four attributes (activity x mode x arrival time x location) are enough to describe all the types of trips performed in the week, compared to the 6480 theoretical possibilities. However, standard deviation is high since it amounts to almost half the mean.

Looking at the number of cells with more than one trip, the combination of four attributes shows that on average about 3 types of trips are repeated, which on average concentrate each more than 10% of trips.

Moreover, looking at the last columns, on average 40% of trips may be described by one combination of travel mode and location among the 24 potential, 30% by a combination of one activity, travel mode and location among the 1080 potential. Promising, about 20% of trips may be described by only one combination of activity, travel mode, arrival time and location (see last line, 23.3%), among the 6480 potential. However dispersion around these mean values is large.

Definition of "core stops" has somewhat to do in the arbitrary. [START_REF] Hanson | Systematic variability in repetitious travel[END_REF] define them as stops which occur at least half the "representative days" they have elaborated on a 35day recording period. Here only a 7-day recording period is available. In our application core stops are defined for each individual as the trips, classified by four-attribute characteristics (activity, mode, arrival time, location), occurring at least three different days in the week. Since, as analysed above, Saturday and Sunday are very different compared to the five remaining working days, a frequency of three times in a week is somewhat large.

Table 15 shows the distribution of core stops based on four-attribute characteristics of trips (activity, mode, location, arrival time), overall (last line of the table) and broken down over activity type. With the definition above, for almost everybody there is no core stops for activities like shopping, personal business, social recreation and "others" (see column "% of zero" in the first section of the table, which goes from the 80% to the 100%). For school less than half of people concerned have core stops (100-55.4 = 44.6%), while they are in the majority for work (100-35.8 = 64.2%) and return to home (100-21.8 = 78.2%). This definitely separates mandatory activities (i.e., work, school) and home as anchors while other activities are far more flexible in location, time and mode used.

When it comes to the distribution in percentage, for half of the sample (see column "Q2" in the "percentage of trips" section of the table) at least 30% of all trips are core stops. This percentage of core stops rises to more than 40% for home trips (they occur with the same combination of mode x arrival time) and to more than 60% of work trips (they occur with the same combination of mode x arrival time x location).

However we suspect that the "arrival time" attribute blurs the concentration of trips in core stops. This can be detected in Thus core stops based on three attributes (excluding the "arrival time" attribute, leaving only activity, mode and location) are analysed in Table 16. With this restriction to three attributes, nearly everybody has home return trips as core stops (3% in the column "% of zero" in the first section of the table): this is somewhat expected in this specific case since as place and activity ("home") are fixed, the only attribute remaining is mode. The percentage of zero trips in core stops for individuals engaging in mandatory activities is decreasing, or in other words, three-quarter of workers have work trips in core stops (100-23.9 = 76.1%) and more than half of schoolgirls(boys) and students have school trips in core stops (100-46.2 = 54.8%). Flexibility of shopping, personal business, social recreation and "other" activities is confirmed since the percentages of individuals having no trips as core stops for these activities are still high (from 71% to 97%).

The distribution in percentage shows a significant increase of core stops shares. Over all activities the minimum percentage of trips being core stops for half of the individuals goes from 30% with four attributes to 56% now with the three attributes activity x mode x location (more than 43% for three-quarter of the sample). Breaking down by activity, and thus having only two attributes (mode x location), at least 86% of home return trips are core stops for half of individuals (and at least 75% of trips for three-quarter of the sample). These figures are respectively 83% and 43% for work trips for the sample of workers. 57% of school trips are core stops for half of the sample of schoolgirls(boys) and students.

Finally, the linkage of core stops with individual socio-demographic characteristics is tested with regression analysis. The endogenous variable is the percentage of core stops in the week, with two models, one for workers (N=389) and one for non-workers (N=307), and two series of tables, respectively for core stops based on four-attribute characteristics of trips (see Table 44 in appendices) and core stops based on three-attribute characteristics of trips (see Table 45).

As shown by these tables, the influence of socio-demographic characteristics on percentage of core stops is weak. For workers the only significant variable is work duration where duration shorter than 21 hours induces a lower percentage of core stops, and duration longer than 41 hours induces a higher percentage of core stops.

For non-workers, gender is significant as men have a higher percentage of core stops and the same positive effect is observed when young children are present, for those living in couple or those under 25. On the opposite, holding a driving license is associated with a lower percentage of core stops. Remarks: 1. Number in the parenthesis means total number of cells in the contingency table 2. Return trips to home are excluded. Out-of-home activity is classified as 6 categories : 1.work, 2.school, 3.shopping, 4.personal business, 5.social recreation and 6.others 3. Mode is classified as: 1 walk, 2 bicycle, 3 car 4 public transport 4. Arrival time is classified as: 1 0:00-8:30, 2 8:31-10:30, 3 10:31-12:30, 4 12:31-16:00, 5 16:01-1830, 6 18:31-23:59 5. Location of activity is based on 45 zones. Remark: Core stops are defined for each individual as the trips, classified by three-attribute characteristics (activity, mode, location), occurring at least three different days of a week

Discussion and conclusion

The large level of intrapersonal variability in daily trip numbers (or home-based tours) already demonstrated in the literature is confirmed. However our analysis goes further by studying this variability along various time periods within the week.

First of all overall variability in daily trip numbers is roughly constant whatever the periods considered within the week (number and type of days). Then within this overall variability, intrapersonal variability is generally greater than interpersonal variability, except in the weekend period. And finally the systematic day-to-day variability has an extremely low share in intrapersonal variability. Overall this indicates that intrapersonal variability has to be explained by factors other than systematic day-to-day variability.

When it comes to daily time allocation to activities a slightly different picture appears.

Overall variability in time allocation is roughly constant whatever the periods considered within the week except on week-end (where it decreases). Unlike the case of trips, intrapersonal variability is lower than interpersonal variability either on working days or on week-end. However intrapersonal variability is still greater when considering the whole 7-day week. Moreover, as for trips, intrapersonal variability is not driven by alternation of days (systematic day-to-day variability) but by other sources of variability. Even when focusing the analysis to workers, the intra-personal variability gets a greater share, although there is more homogeneity in time allocation across the sample and the days.

The differences in activity sequence between days are minimal in the week-end period, at a significantly lower level than on other days, and maximal when considering the whole 7-day week. This indicates a significant degree of homogeneity of these two days in the nature of activities when compared with the working days. There is also a great difference with previous activity-travel indicators, since interpersonal variability in activity sequences is always over intrapersonal variability. However, even when focusing the analysis on workers, there is a decrease of overall variability but interpersonal variability keeps the major share.

The influence of socio-demographic characteristics on intrapersonal variability is weak, whether for daily trips, tours, time use and activity sequence. Men have in general lower intrapersonal variability than women which would mean either more flexibility or more irregular constraints (e.g. linked to maintenance, childcare, shopping) for women. Access to car for students (through holding a driving license) is also linked to greater intrapersonal variability. If socio-demographic characteristics explain weakly intrapersonal variability, what is left as explanatory factors?

Another perspective is then taken by searching for repetitive activity-travel behaviour, summed up through attributes of activity type at trip destination, travel mode, trip arrival time and destination location. The picture is at the same time one of diversity and of specificity in activity-travel across the week. People perform the whole range of activities (except for work or school depending on the individual status), they use the various transport modes, at any time. However, they visit only a few places among the infinity of potentials. This is a story of limited location choice set.

The picture is also one of concentration of activity-travel patterns on few combinations, despite a large dispersion. On average, 12 combinations of four attributes (activity x mode x arrival time x location) are enough to describe all the types of trips performed in the week. On average 40% of trips may be described by one combination of travel mode and location, 30% by a combination of one activity, travel mode and location, and about 20% of trips by only one combination of activity, travel mode, arrival time and location.

Core stops are defined for each individual as the trips, classified by four-attribute characteristics (activity, mode, arrival time, location), occurring at least three different days in the week. Core stops concern essentially mandatory activities (i.e., work, school) and home as anchors while other activities (like shopping, personal business, social recreation) are far more flexible in location, time and mode used. For half of the sample at least 30% of all trips are core stops. This percentage rises to more than 40% for home trips and to more than 60% for work trips.

Most of the percentage dispersion comes from the "arrival time" attribute. If we exclude this attribute, leaving only activity, mode and location, of course the percentage of trips which are core stops increases. Flexibility of shopping, personal business, social recreation and "other" activities is confirmed, opposite to mandatory activities. Over all activities the minimum percentage of trips being core stops for half of the individuals rises to 56% with the three attributes, and to 83% for work trips for the sample of workers, to 57% of school trips for half of the sample of schoolgirls(boys) and students.

As for variability of previous activity-travel indicators, the influence of socio-demographic characteristics on percentage of core stops is weak. Men (non-workers) have a higher percentage of core stops, while holding a driving license is associated with a lower percentage of core stops. As the percentage of trips which are core stops may be considered as an indicator of stability, there is an obvious convergence with intrapersonal variability.

Overall this analysis of variability of activity-travel behaviour over a 7-day period shows that individual behaviour is neither completely habitual (or routine), neither completely random, in agreement to what was initially a working hypothesis of [START_REF] Hanson | Classification issues in the analysis of complex travel behaviour[END_REF]. However, a limitation of our analysis is the reference to the day as the basis for computing the activity-travel indicators, while the rhythm of repetition could be every other day or on three days, or so on.

The global picture is both that intrapersonal variability is large, and the role of systematic day-to-day variability is marginal. Moreover, a striking result is that socio-demographic characteristics are mostly unable to explain the level of intrapersonal variability.

However results on core stops are somewhat encouraging by showing some kind of concentration of activity patterns on a few "anchor" points. This is a stimulating perspective for modelling behavioural adaptations to changes in transport context.

jn

  is the mean daily travel/activity indicator over individuals on day j,

Table 1 : Number of trips per person per week

 1

	Activity		Number of trips per person per week
		N*	% of N Mean	S.D. Min Q1	Q2 Q3 Max
	Home	717	100	10.3	3.8	1	8 10 12	25
	Work	406	57	4.9	2.5	1	3	5	6	17
	School	186	26	3.8	2.4	1	1	4	5	11
	Shopping	627	87	4.0	2.7	1	2	3	5	17
	Personal business	368	51	1.9	1.3	1	1	1	3	8
	Social recreation	684	95	5.3	3.6	1	3	4	7	27
	Others	528	74	4.8	4.0	1	2	4	7	32
	Total (N=717)	717	100	27.0	10.2	2	20 26 33	58
		N*: Number of individuals with number of trips >0

Table 2 : Mean number of trips per day for different types of day (minutes, N=5019)

 2

	Period	Monday-	Monday-	Monday-	Monday-	Saturday,
		Friday	Saturday	Friday,	Sunday	Sunday
						Sunday
		Mean	Std Mean	Std Mean	Std Mean	Std Mean	Std
	Number of trip	4.0	2.4	4.0	2.4	3.8	2.4	3.9	2.4	3.5	2.4
	per day

Table 3 : Mean number of home-based tour per day for different types of day (minutes, N=5019)

 3

	Type of day	Monday-	Monday-	Monday-	Monday-	Saturday,
		Friday	Saturday	Friday,	Sunday	Sunday
						Sunday
		Mean Std Mean Std Mean Std Mean Std Mean Std
	Number of home-	1.5	0.9	1.5	1.0	1.5	1.0	1.5	1.0	1.3	1.0
	based tours per
	day

Table 4

 4

	shows the inter-and intrapersonal variability in number of trips per day. One finds
	again the large level of intrapersonal variability in daily trip numbers denoted in the literature
	like in Pas (1987, with a seven-day data set) and Pas and Sundar (1995, with a three-day data
	set). However one can go further by analysing this variability along various time periods
	within the week.

Table 4 : Inter and intrapersonal variability in number of trips per day

 4

	Period	TSS	BPSS	WPSS	BPSS	BDSS WDSS	BDSS
					/TSS (%)			/WPSS (%)
	Mon-Fri	4.16	1.88	2.29	45.1%	0.03	2.26	1.2%
	Mon-Sat	4.23	1.72	2.52	40.6%	0.02	2.49	0.9%
	Mon-Fri, Sun	4.15	1.58	2.57	38.0%	0.15	2.43	5.7%
	Mon-Sun	4.22	1.51	2.71	35.8%	0.13	2.58	4.7%
	Sat, Sun	4.18	2.53	1.65	60.6%	0.21	1.44	12.5%

Remark: BPSS, WPSS, BDSS, WDSS and TSS is divided by 10 3 and by the number of days considered

Table 5 : Inter and intrapersonal variability in number of home-based tours per day

 5

	Period	TSS	BPSS	WPSS	BPSS	BDSS WDSS	BDSS
					/TSS(%)			/WPSS(%)
	Mon-Fri	0.65	0.25	0.40	38.5%	0.00	0.39	0.9%
	Mon-Sat	0.67	0.23	0.44	34.3%	0.00	0.44	0.7%
	Mon-Fri, Sun	0.65	0.21	0.44	32.4%	0.01	0.43	3.0%
	Mon-Sun	0.68	0.21	0.47	30.4%	0.01	0.46	2.4%
	Sat, Sun	1.61	0.62	0.99	38.5%	0.01	0.98	0.9%

Remark: BPSS, WPSS, BDSS, WDSS and TSS is divided by 10 3 and by the number of days considered

Table 6 : Mean daily duration of activity for different types of day (minutes, N=5019)

 6

	Type of day	Monday-	Monday-	Monday-	Monday-	Saturday,
		Friday		Saturday	Friday,		Sunday		Sunday
						Sunday
		Mean Std Mean Std Mean Std Mean Std Mean Std
	Home	1013 262	1035 261	1040 265	1055 263	1162 233
	Work/School	247 247	210 243	208 243	182 238	21	96
	Shopping	17	43	20	46	16	42	18	45	21	51
	Personal business	7	26	6	24	6	25	6	24	3	18
	Social-recreation	54 103	65 116	68 123	76 130	130 168
	Others	24	78	25	79	24	77	24	79	24	81

Table 7 : Inter and intrapersonal variability in time allocation to activities per day

 7

	Period	TSS BPSS	WPSS	BPSS	BDSS WDSS	BDSS
					/TSS(%)			/WPSS(%)
	Mon-Fri	0.11	0.06	0.04	58.0%	0.00	0.04	0.6%
	Mon-Sat	0.11	0.05	0.06	44.0%	0.01	0.05	12.0%
	Mon-Fri, Sun	0.11	0.05	0.06	43.3%	0.01	0.05	14.6%
	Mon-Sun	0.11	0.04	0.07	35.8%	0.01	0.06	17.0%
	Sat, Sun	0.07	0.04	0.03	59.2%	0.00	0.03	1.4%

Remark: BPSS, WPSS, BDSS, WDSS and TSS is divided by 10 9 and by the number of days considered

Table 8 : Inter and intrapersonal variability in time allocation to activities per day (workers, N = 389)

 8

	Type of day	TSS BPSS	WPSS	BPSS	BDSS WDSS	BDSS
					/TSS(%)			/WPSS(%)
	Mon-Fri	0.05	0.02	0.03	39.6%	0.00	0.03	0.8%
	Mon-Sat	0.06	0.02	0.04	27.1%	0.01	0.03	19.1%
	Mon-Fri, Sun	0.06	0.02	0.04	26.8%	0.01	0.03	23.3%
	Mon-Sun	0.06	0.01	0.05	21.3%	0.01	0.03	27.2%
	Sat, Sun	0.04	0.03	0.02	57.2%	0.00	0.02	1.8%
	Remark: BPSS, WPSS, BDSS, WDSS and TSS is divided by 10 9 and by the number of days considered

Table 9 : Overall mean SAM distance for different periods

 9

	Period	Monday-	Monday-	Monday-	Monday-	Saturday,
		Friday	Saturday	Friday,	Sunday	Sunday
				Sunday
	s	14.1	19.3	18.6	23.4	3.6

Table 10 : Inter and intrapersonal variability in individuals' daily activity sequence

 10

	Period	TSS	BPSS	WPSS	BPSS	BDSS WDSS	BDSS
					/TSS(%)			/WPSS(%)
	Mon-Fri	0.05	0.04	0.01	78.7%	0.00	0.01	1.3%
	Mon-Sat	0.07	0.05	0.02	72.5%	0.00	0.02	8.4%
	Mon-Fri, Sun	0.07	0.05	0.02	73.6%	0.00	0.02	3.7%
	Mon-Sun	0.10	0.07	0.03	71.3%	0.00	0.03	4.5%
	Sat, Sun	0.00	0.00	-	100.0%	-	0.00	NA

Remark: BPSS, WPSS, BDSS, WDSS and TSS is divided by 10 9 and by the number of days considered

Table 11 : Inter and intrapersonal variability in individuals' daily activity sequence (workers, number of individuals = 389)

 11

	Type of day	TSS	BPSS	WPSS	BPSS	BDSS WDSS	BDSS
					/TSS(%)			/WPSS(%)
	Mon-Fri	0.03	0.02	0.01	76.4%	0.00	0.01	1.8%
	Mon-Sat	0.05	0.03	0.01	69.4%	0.00	0.01	12.7%
	Mon-Fri, Sun	0.04	0.03	0.01	71.2%	0.00	0.01	6.4%
	Mon-Sun	0.06	0.04	0.02	68.5%	0.00	0.02	8.0%
	Sat, Sun	0.00	0.00	-	100.0%	-	0.00	NA

Remark: BPSS, WPSS, BDSS, WDSS and TSS is divided by 10 9 and by the number of days considered

Table 13 : Number of trip types performed by individuals, according to activity, mode, arrival time and location (over the week, N=717)

 13

		Mean	S.D. Minimum	Maximum
	Activity (7)	4.9	1.0	2.0	7.0
	Mode (4)	2.6	0.9	1.0	4.0
	Arrival time (6)	5.3	0.9	1.0	6.0
	Location (45)	5.5	2.1	1.0	14.0
	Remark : number in the parenthesis means total number of classes

  Table 14 when arrival time combines to two attributes, which decreases significantly the percentage in the cell with largest value (last column): compare

	Activity * Mode * Arrival time (26%) to Activity * Mode (39%), Activity * Arrival time *
	Location (25%) to Activity * Location (35%) and Mode * Arrival time * Location (26%) to
	Mode * Location (40%).

Table 14 : Some measures of repetition of individual's out-of-home trips (based on two, three and four attributes)

 14

	Contingency table	Number of cells with at		Number of	Number of	Cell with the
			least one trip		cells with	cells with	largest
						more than one	more than	percent of
						trip		10% of trips	trips (%)
		Mean S.D. Max Min Mean S.D.	Mean S.D. Mean S.D.
	Activity*Mode (24)	6.2	2.3	29	1	3.7	1.7	3.4	1.0	38.9 14.3
	Activity*Arrival time (36)	8.8	3.4	21	1	4.0	2.2	3.1	1.3	28.9 13.4
	Activity*Location (270)	8.0	3.3	21	1	3.4	1.7	3.1	1.2	35.4 14.4
	Mode*Arrival time (24)	7.3	2.7	19	1	4.0	1.9	3.6	1.2	32.9 13.4
	Mode*Location (180)	7.1	2.9	18	1	3.3	1.6	3.1	1.2	40.2 16.4
	Arrival time*Location (270)	9.6	4.0	25	1	3.5	2.0	3.1	1.5	28.4 13.0
	Activity*Mode*Arrival time (144)	10.4	4.4	33	1	3.5	2.1	3.0	1.5	26.0 13.4
	Activity*Mode*Location (1080)	9.5	4.1	24	1	3.2	1.9	2.9	1.4	31.3 14.8
	Activity*Arrival time*Location (1620)	11.5	5.1	31	1	2.9	1.9	2.6	1.7	24.9 13.5
	Mode*Arrival time*Location (1080)	10.9	4.7	33	1	3.2	2.0	2.8	1.6	25.6 13.4
	Activity*Mode*Arrival time*Location (6480)	12.3	5.6	38	1	2.6	1.8	2.4	1.8	23.3 13.6

Table 15 : Core stops distribution per activity type, based on four-attribute (activity, mode, location, arrival time) characteristics of trips

 15

		Number of trips which are core stops, per person per week	Percentage of trips which are core stops, per person (%)
	Activity at destination N* Mean S.D.	% of	Min Q1 Q2 Q3 Max N* Mean S.D. Min Q1	Q2	Q3	Max
					zero
	Home	717	4.4	3.4 21.8%	0	3	4	7	19 717	41.2	27.1	0 25.0 43.8 61.5 100.0
	Work	406	2.7	2.4 35.8%	0	0	3	4	14 406	50.2	40.9	0	0.0 60.0 83.3 100.0
	School	186	2.0	2.4 55.4%	0	0	0	4		9 186	37.5	43.7	0	0.0	0.0 83.3 100.0
	Shopping	627	0.4	1.3 91.2%	0	0	0	0	10 627	4.7	16.0	0	0.0	0.0	0.0	85.7
	Personal business	368	0.0	0.2 99.5%	0	0	0	0		3 368	0.4	5.8	0	0.0	0.0	0.0 100.0
	Social recreation	684	0.6	1.9 88.2%	0	0	0	0	20 684	6.0	17.5	0	0.0	0.0	0.0 100.0
	Others	528	1.0	2.5 81.6%	0	0	0	0	16 528	10.6	24.2	0	0.0	0.0	0.0 100.0
	Total (N=717)	717	8.1	5.9		0	3	7 12	34 717	29.8	19.4	0 15.2 30.0 42.9	85.7
	N*: Number of individuals with number of trips >0

Remark: Core stops are defined for each individual as the trips, classified by four-attribute characteristics (activity, mode, arrival time, location), occurring at least three different days of a week

Table 16 : Core stops distribution per activity type, based on three-attribute (activity, mode, location) characteristics of trips

 16

		Number of trips which are core stops per person per week	Percentage of trips which are core stops per person (%)
	Activity at destination N* Mean S.D.	% of	Min Q1 Q2 Q3 Max N* Mean S.D. Min Q1	Q2	Q3	Max
				zero
	Home	8.6	4.0	3%	0	6	8 11	23 717	81.5	21.0	0.0 75.0 85.7 100.0 100.0
	Work	3.7	2.6 23.9%	0	3	4	5	17 406	67.2	40.3	0.0 42.9 83.3 100.0 100.0
	School	2.6	2.6 46.2%	0	0	3	5	11 186	47.4	45.8	0.0	0.0 57.1 100.0 100.0
	Shopping	1.0	2.2 79.7%	0	0	0	0	16 627	13.8	28.7	0.0	0.0	0.0	0.0 100.0
	Personal business	0.1	0.6 96.5%	0	0	0	0	4 368	2.5	13.9	0.0	0.0	0.0	0.0 100.0
	Social recreation	1.3	2.8 75.0%	0	0	0 1.5	21 684	15.3	28.4	0.0	0.0	0.0	10.0 100.0
	Others	1.8	3.5 71.2%	0	0	0	3	22 528	20.8	34.7	0.0	0.0	0.0	48.3 100.0
	Total (N=717)	14.9	7.7		0 10 13 19	40 717	54.0	18.2	0.0 42.9 55.6	66.7 100.0
	N*: Number of individuals with number of trips >0

Table 17 : Regression analysis for intrapersonal variability (WPSS) of the number of trips per day (Monday-Friday)

 17

		Students etc.		House-wife etc.	Pensioner			Worker
		Coef.	S.E.	Pr>F	Coef.	S.E.	Pr>F	Coef.	S.E.	Pr>F	Coef.	S.E.	Pr>F
	Intercept	55.9	1.4 <.0001	81.9	3.5 <.0001	95.2	2.7 <.0001	79.8	2.2 <.0001
	Gender	-41.3	2.0 <.0001	-46.2	5.2 <.0001	-47.4	3.3 <.0001	-44.4	2.9 <.0001
	Age55_65				12.7	5.3	0.019
	H_Sing_NChild				-40.9	7.1 <.0001	-53.7	4.7 <.0001	-14.7	3.7 <.0001
	H_Coup_Child_1	36.0	5.6 <.0001
	W
	License	7.8	2.4	0.002
	N	113			90			104			389
	F value	174.4			44.4			145.0			121.8
	DF	112			89			103			388
	Model Fit statistics (Pr>F)	<.0001			<.0001			<.0001			<.0001

Table 21 : Model comparison for the regression analysis of the number of home-based tour per day (Monday-Friday)

 21

	Models	All	Students	House-	Pensioner	Worker
			etc. (1)	wife etc.	(3)	(4)
				(2)
	Number of variable	23	18	18	18	23
	LnL	-1973.2	-217.0	-244.4	-249.7	-1158.9
	Likelihood ratio test	model 1+ model 2+model 3+model 4 -model all
	LR			103.05
	df			54
	p-value			<0.0001

Table 24 : Model comparison for the regression analysis of individuals' daily time use allocation (Monday-Friday)

 24

	Models<	All	Students	House-	Pensioner	Worker
			etc. (1)	wife etc.	(3)	(4)
				(2)
	Number of variable	23	18	18	18	23
	LnL	-2040.6	-233.0	-252.3	-256.2	-1197.1
	Likelihood ratio test	model 1+ model 2+model 3+model 4 -model all
	LR			101.74
	df			54
	p-value<			<0.0001

Table 27 : Model comparison for the regression analysis of individuals' daily activity sequence (Monday-Friday)

 27

	Models<	All	Students	House-	Pensioner	Worker (4)
			etc. (1)	wife etc.	(3)
				(2)
	Number of variable	23	18	18	18	23
	LnL	-2633.3	-328.3	-329.91	-344.2	-1529.0
	Likelihood ratio test	model 1+ model 2+model 3+model 4 -model all
	LR			101.79
	df			54
	p-value<			<0.0001

Core stops analysis based on four-attribute characteristics of trips

Table 29 : The quantiles of arrival time at activity destination (by hour from midnight)

 29

	Home		Work	School	Shopping	Personal	Social-
						business	recreation
	Quantile	Estimate	Estimate	Estimate	Estimate	Estimate	Estimate
	100% Max	24.0	22.9	22.8	23.8	23.5	23.8
	99%	23.6	20.8	18.9	19.6	20.5	23.1
	95%	22.3	16.6	18.0	18.3	19.3	21.1
	90%	21.0	14.1	16.0	17.7	18.3	20.2
	75% Q3	18.5	11.8	12.9	15.9	16.1	18.7
	50%	16.7	8.6	8.4	12.9	13.4	15.7
	Median
	25% Q1	12.4	7.9	8.2	10.3	10.2	12.5
	10%	9.8	7.3	8.0	9.2	9.0	10.4
	5%	8.3	6.4	7.8	8.6	8.6	9.2
	1%	0.5	4.6	7.5	7.5	8.1	2.0
	0% Min	0.0	0.8	7.0	0.4	6.0	0.0

Table 30 : Frequency table of number of trips which are core stops (4 attributes) per person per week: Home

 30

	number of trips which are	Frequency	Percent	Cumulative	Cumulative
	core stops			Frequency	Percent
	0	156	21.76	156	21.76
	3	144	20.08	300	41.84
	4	119	16.6	419	58.44
	5	63	8.79	482	67.22
	6	51	7.11	533	74.34
	7	65	9.07	598	83.4
	8	33	4.6	631	88.01
	9	32	4.46	663	92.47
	10	25	3.49	688	95.96
	11	9	1.26	697	97.21
	12	7	0.98	704	98.19
	13	5	0.7	709	98.88
	14	1	0.14	710	99.02
	15	3	0.42	713	99.44
	16	1	0.14	714	99.58
	17	1	0.14	715	99.72
	18	1	0.14	716	99.86
	19	1	0.14	717	100

Table 31 : Frequency table of number of trips which are core stops (4 attributes) per person per week: Work

 31

	number of trips which are	Frequency	Percent	Cumulative	Cumulative
	core stops			Frequency	Percent
	0	145	35.71	145	35.71
	3	92	22.66	237	58.37
	4	83	20.44	320	78.82
	5	63	15.52	383	94.33
	6	7	1.72	390	96.06
	7	3	0.74	393	96.8
	8	7	1.72	400	98.52
	9	2	0.49	402	99.01
	10	2	0.49	404	99.51
	11	1	0.25	405	99.75
	14	1	0.25	406	100

Table 32 : Frequency table of number of trips which are core stops (4 attributes) per person per week: School

 32

	Cumulative	Cumulative

Table 33 : Frequency table of number of trips which are core stops (4 attributes) per person per week: Shopping

 33

	number of trips which are	Frequency	Percent	Cumulative	Cumulative
	core stops			Frequency	Percent
		572	91.23	572	91.23
		31	4.94	603	96.17
		11	1.75	614	97.93
		3	0.48	617	98.41
		5	0.8	622	99.2
		2	0.32	624	99.52
		1	0.16	625	99.68
	10	2	0.32	627	100

Table 34 : Frequency table of number of trips which are core stops (4 attributes) per person per week: Personal business

 34

	number of trips which are	Frequency	Percent	Cumulative	Cumulative
	core stops			Frequency	Percent
		366	99.46	366	99.46
		2	0.54	368	100

Table 35 : Frequency table of number of trips which are core stops (4 attributes) per person per week: Social-recreation

 35

	number of trips which are	Frequency	Percent	Cumulative	Cumulative
	core stops			Frequency	Percent
	0	603	88.16	603	88.16
	3	43	6.29	646	94.44
	4	17	2.49	663	96.93
	5	7	1.02	670	97.95
	6	2	0.29	672	98.25
	7	2	0.29	674	98.54
	8	3	0.44	677	98.98
	11	1	0.15	678	99.12
	12	2	0.29	680	99.42
	13	1	0.15	681	99.56
	14	1	0.15	682	99.71
	15	1	0.15	683	99.85
	20	1	0.15	684	100

Table 36 : Frequency table of number of trips which are core stops (4 attributes) per person per week: Other activities

 36

	number of trips which are	Frequency	Percent	Cumulative	Cumulative
	core stops			Frequency	Percent
	0	431	81.63	431	81.63
	3	35	6.63	466	88.26
	4	14	2.65	480	90.91
	5	16	3.03	496	93.94
	6	5	0.95	501	94.89
	7	2	0.38	503	95.27
	8	9	1.7	512	96.97
	9	1	0.19	513	97.16
	10	7	1.33	520	98.48
	11	2	0.38	522	98.86
	12	1	0.19	523	99.05
	13	3	0.57	526	99.62
	15	1	0.19	527	99.81
	16	1	0.19	528	100

Core stops analysis based on three-attribute characteristics of trips Table 37: Frequency table of number of trips which are core stops (3 attributes) per person per week: Home

	number of trips which are	Frequency	Percent	Cumulative	Cumulative
	core stops			Frequency	Percent
	0	22	3.07	22	3.07
	3	19	2.65	41	5.72
	4	52	7.25	93	12.97
	5	60	8.37	153	21.34
	6	78	10.88	231	32.22
	7	78	10.88	309	43.1
	8	68	9.48	377	52.58
	9	71	9.9	448	62.48
	10	63	8.79	511	71.27
	11	59	8.23	570	79.5
	12	47	6.56	617	86.05
	13	16	2.23	633	88.28
	14	27	3.77	660	92.05
	15	14	1.95	674	94
	16	14	1.95	688	95.96
	17	7	0.98	695	96.93
	18	8	1.12	703	98.05
	19	6	0.84	709	98.88
	20	4	0.56	713	99.44
	21	1	0.14	714	99.58
	22	2	0.28	716	99.86
	23	1	0.14	717	100

Table 42 : Frequency table of number of trips which are core stops (3 attributes) per person per week: Social recreation

 42

	number of trips which are	Frequency	Percent	Cumulative	Cumulative
	core stops			Frequency	Percent
	0	513	75	513	75
	3	59	8.63	572	83.63
	4	41	5.99	613	89.62
	5	25	3.65	638	93.27
	6	9	1.32	647	94.59
	7	12	1.75	659	96.35
	8	6	0.88	665	97.22
	9	4	0.58	669	97.81
	10	3	0.44	672	98.25
	11	2	0.29	674	98.54
	12	1	0.15	675	98.68
	13	1	0.15	676	98.83
	14	1	0.15	677	98.98
	15	2	0.29	679	99.27
	16	1	0.15	680	99.42
	17	2	0.29	682	99.71
	18	1	0.15	683	99.85
	21	1	0.15	684	100

Table 43 : Frequency table of number of trips which are core stops (3 attributes) per person per week: Other activities

 43

	number of trips which are	Frequency	Percent	Cumulative	Cumulative
	core stops			Frequency	Percent
	0	376	71.21	376	71.21
	3	35	6.63	411	77.84
	4	29	5.49	440	83.33
	5	21	3.98	461	87.31
	6	14	2.65	475	89.96
	7	6	1.14	481	91.1
	8	10	1.89	491	92.99
	9	9	1.7	500	94.7
	10	8	1.52	508	96.21
	11	4	0.76	512	96.97
	12	3	0.57	515	97.54
	13	6	1.14	521	98.67
	14	3	0.57	524	99.24
	16	1	0.19	525	99.43
	18	2	0.38	527	99.81
	22	1	0.19	528	100

Table 44 : Regression analysis of average percentage of core stops of a week for workers and non-workers (four-attribute characteristics of trips)

 44

			Workers			Non-workers
		Coef.	S.E.	Pr>F	Coef.	S.E.	Pr>F
	Intercept	33.1	1.2	<.0001	22.3	3.2	<.0001
	Gender				5.6	2.2	0.011
	Children_12				8.7	3.0	0.004
	Couple				7.6	3.0	0.011
	License				-10.9	2.3	<.0001
	Dur_work_21h	-11.0	2.0	<.0001	NA	NA	NA
	Dur_work_41h	10.2	2.0	<.0001	NA	NA	NA
	N of individuals	389			307
	F value	42.12			11.72
	DF	388			306
	Model Fit statistics (Pr>F)	<.0001			<.0001

Acknowledgements

This research has benefited from a grant of ANR (the French Agency for Research, Project EuroCities-DATTA n° ANR-07-BLAN-0032-01). We thank the Groupe de Recherche sur les Transports (FUNDP, Namur) for providing the Belgian Mobility Week database.

The previous analysis suggests that the intrapersonal variability of individuals' daily travel, time use and activity sequence might depends on individuals' socio-professional status. Hence we distinguish four categories as: 1. students, schoolboys(girls); 2. house-wife/husband, unemployed, invalid; 3. pensioners; 4 workers. A regression analysis is performed for each category in order to examine the effects of explanatory variables. Linear regression models are estimated based on stepwise regression method. Moreover, the validity of calibrating

Appendixes

Annex 1


Nanxing Chen
email: nanxing.chen@irisa.fr

Dealing with Asynchronous Observation Issues in Passive Interoperability Testing

Keywords: interoperability testing, time stamps, passive testing test d'interoperabilité, test passif, estampillage logique

The purpose of interoperability testing is to ensure that interconnected protocol implementations communicate correctly while providing the expected services. To perform interoperability testing, conventional approaches rely on the active testing method, which stimulates the system under test to accomplish a diagnose. However, the arbitrary stimuli injected by using active testing method disturb inevitably the normal operation of the system under test. On the contrary, passive testing is a technique for the verication of behavioral properties of systems by only observing their external behavior. However, passive testing method often encounters observation problems due to the asynchronous test environment. In fact, the delay in such environment may inuence the observation of the real order of the outputs produced by the implementations under test. Consequently, the verdict emitted by the test system maybe permissive or bias. As passive testing depends only on observation, issues here are then to keep a high level of observation in the testing activity, ensuring that no biased or permissive verdict is introduced. To solve the observation problems in passive interoperability testing, this report proposes a method based on logical clocks. Each output produced by the implementations under test is associated with a time stamp, which is carried on the y during its transmission. By analyzing the time stamps, the tester is able to recreate the true sequence of the observed events so as to give a correct verdict. Key-words:

Introduction

Modern networks are becoming heterogeneous and complex. As they are composed of equipments based on new technologies from a variety of vendors, it is frequent that errors would be introduced by dierences in protocol implementations. Correct coordination and communication of dierent protocol implementations is essential to guarantee customer expectations.

To increase the condence that network products conform to international standards, conformance testing methodologies have been standardized and deployed. Conformance testing [START_REF] Iso | Information Technology-open system interconnection Conformance Testing methodology and framework-Parts 1-7[END_REF] veries whether a network component conforms to its specication. Although ISO-9646 standard mentions that conformance testing increases the probability of interoperability, it cannot be guaranteed. Conforming products may not interoperate due to several reasons: ambiguity in protocol standards, poorly specied protocol options, incompleteness of specications, etc. Therefore, interoperability testing is indispensable to guarantee the correct operation of network products from dierent product lines and provide expected services.

To perform interoperability testing, the conventional method is the active testing approach [START_REF] Desmoulin | Test d'interopérabilité de protocoles: la formalisation des critères d'interopérabilité la génération des tests[END_REF][START_REF] Seol | Fully automated interoperability test suite derivation for communication protocols[END_REF][START_REF] Hao | Intergated system interoperability testing with applications to VoIP[END_REF]. Active testing is done by building a test system (TS) that is able to stimulate the implementations under test (IUT) and verify whether the outputs obtained for each stimulus are as expected. Generally, the test system tests the IUTs in a specic test environment. It sends carefully designed messages to the IUTs, receives what it responds and makes a conclusion. Although widely used, active testing has some limitations: Test can be dicult or even impossible to perform if the tester is not provided with a direct interface to stimulate the IUTs, or in operational environment where the normal operation of IUTs cannot be shutdown or interrupted for a long period of time.

Current trend in network components deployment is to shorten time-to-market and test their interoperability in operational environment. In this sense, active testing is not a suitable testing method especially for operational networks, where arbitrary inputs inuences networks environment, sometimes may even provoke the crash of services.

The drawbacks of active testing lead to passive testing [START_REF] Zaidi | NetworkProtocol Interoperability Testing based on Contextual Signatures[END_REF][START_REF] Lee | Passive testing and applications to network management[END_REF]. Passive testing is a technique based on a high level of observation in order to establish a diagnostic regarding the implementations' behavior. Compared with active approach, one of the remarkable features of passive approach is that the test system does not interfere with the normal operation of the IUTs. Therefore, passive approach can be applied in operational networks, where it is usually dicult to insert an arbitrary input. Besides, passive approach makes it possible to carry out tests when the test system does not have direct access to stimulate the IUTs. In fact, the test can be done by only observing the trace produced by the IUTs with the help of network protocol analyzing tools such as Wireshark1 .

However, when passive interoperability testing is performed in operational environment, observation problems are often encountered due to the uncontrollable delay introduced by the asynchronous nature of the test environment. In fact, the observation order of the outputs produced by the implementations may be inuenced. As a result, passive interoperability testing in such environment is error-prone: The verdict might be permissive uncooperative IUTs are determined to be interoperable, or biased the IUTs are determined non-interoperable but they are actually interoperable.

In this report, we propose a time-stamp-enabled mechanism that aims at solving the permissiveness and bias problems. The considered testing context is the passive One-to-One interoperability testing where there are two IUTs in interaction. The principle of the mechanism is to associate each event on IUTs with a logical time, which is piggybacked by the outputs sent by the IUTs. An algorithm is proposed to analyze the logical time and to recover the real occurrence order of the events that happened on each IUT. We prove that both bias and permissiveness of asynchronous interoperability testing can be suppressed by using this method. Interoperability verdicts remain the same in asynchronous test environment as in synchronous test environment.

The report is organized as follows: Section 2 represents the preliminaries. Section 3 presents the observation problems in asynchronous passive interoperability testing. Section 4 denes the time-stamp-enabled mechanism to solve the observation problems. The report is nished by a conclusion in section 5.

Preliminaries

2.1

General Interoperability Testing Architecture

The purpose of interoperability testing (iop for short in the sequel) is to verify n (n 2) products from dierent product lines interoperate correctly and provide expected services. General interoperability testing architecture involves a Test System (TS) and a System Under Test (SUT) composed of n (n 2) interconnected Implementations Under Test (IUT) from dierent product lines. According to the quantity of the IUTs, interoperability testing can be in either of the following context: (i) Multi-Component context where SUT has n (n > 2) IUTs. (ii) One-to-One context where SUT is composed of two IUTs. In practice, One-to-One iop is the most common context, either by testing the interoperability of IUTs in a pairwise way, or by testing the interoperability between one protocol implementation and a system already in operation (which may be composed of n IUTs).

In interoperability testing, testing entities communicate with each other through a variety of interfaces:

• Upper Implementation Access Point (U IAP i , i = {1, 2, ...n}) is the interface through which IU T i communicates with its upper layer. U I i is observable and controllable. Test system connected to U IAP i via Upper Point of Control and Observation (U P CO i ) interface can send test messages to the corresponding IU I i and observe its output responses.

• Lower Implementation Access Point (LIAP i ) is the interface through which IU T i communicates with its peer IUT. Contrary to U IAP i , LIAP i is only observable. Test system connected to LIAP i via Lower Point of Observation (LP O i ) interface can only observe the interaction of IU T i with its peer IUT but must not send any message to it.

Passive Interoperability Testing

In this report, we focus our work on One-to-One passive interoperability testing (cf. Fig. 1): The test between two IUTs is based only on observing their interaction (at LIAP i interfaces). No test message is allowed to be injected. The testing procedure consists of the following stages:

1. Interoperability test purpose (ITP) selection. The goal of testing is to nd errors in SUT. However proving correctness is elusive as it is generally impossible to validate all possible behavior described in specications. From the methodological point of view, most tests are carried on by setting test purposes. A test purpose is in general informal, in the form of an incomplete sequence of actions representing a critical property to be veried. It can be designed by experts or provided by standards guidelines for test selection [START_REF] Schulz | TPLan -A notation for expressing test purposes[END_REF].

2. Trace recording. Observable events (trace) produced by SUT are collected during the test execution.

3. Trace verication. The obtained trace is then analyzed against the interaction of IUTs' specications to see whether the interoperability relation between the IUTs is satised. The execution trace verication returns a verdict : where verdict ∈ {P ass, F ail, Inconclusive}. P ass means the test purpose is satised with no error detected. F ail means at least an error is detected. Inconclusive means the behavior of IUTs is correct w.r.t their specications, however does not correspond to the test purpose.

In this report, we consider the asynchronous communication between testing entities: (i) The communication between two IUTs are asynchronous. In fact, protocol implementations interact by traversing several protocol layers. As delay is not controllable, it leads to asynchronous communications. (ii) The environment between the test system and the SUT is asynchronous too. In practice, passive interoperability testing is often done in a remote way, i.e., the test system reaches the SUT through a network. Accorindg to [START_REF] Verhaard | On asynchronous testing[END_REF], asynchronous interaction can be modeled by two FIFO reliable queues, one for each direction between two testing entities and is denoted A .(The environment between the TS and the SUT is modeled by two unidirectional FIFO queues as LIAP i interfaces are only observable). Moreover, we assume the black box testing context: The system has no knowledge of the IUTs inner structure. Only the external behavior of IUTs can be evaluated. In this report, the formal model used to describe specications, implementations, etc is the IOLTS (Input-Output Labeled Transition System) model [START_REF] Verhaard | On asynchronous testing[END_REF], which allows dierentiating input, output and internal events while precisely indicating the interfaces specied for each event.

N. Chen Denition 1 An IOLTS is a tuple M = (Q M , Σ M , ∆ M , q M 0 ) where Q M is the set of states of the system M with q M 0 its initial state. Σ M is the set of observable events at the interfaces of M . Σ M can be partitioned into:

Σ M =Σ M U Σ M L , where Σ M U (resp. Σ M L )
is the set of events at the upper (resp. lower) interfaces. Σ M can also be partitioned to distinguish input (Σ M I ) and output events (Σ M O ). In IOLTS model, input and output actions are dierentiated: We note p?a (resp. p!a) for an input (resp. output) a at interface p.

∆ M ⊆ Q M × (Σ M ∪ τ ) × Q M is
the transition relation, where τ / ∈ Σ M stands for an internal action. Transition (q, α, q ) ∈ ∆ M can be equally noted q α -→ M q .

Other notations Let us consider an IOLTS M , and let an observable event α ∈ Σ M with α = p • {?, !} • m, an executable event of the system µ i ∈ Σ M ∪ τ , a succession of events σ ∈ (Σ M ) * , and q, q , q i ∈ Q M . We dene the following notations:

• q µ1...µn -→ M q = def ∃q 0 = q, q 1 , . . . , q n = q .∀i ∈ [1, n], q i-1 µi -→ M q i . • q ⇒ M q = def q = q or q τ ...τ -→ M q . • Out(q) = def {α ∈ Σ M O |∃q , q α -→ M q } is
the set of possible outputs at state q. Similarly,

In(q) = def {α ∈ Σ M I |∃q , q α -→ M q } is the set of possible inputs and Γ(q) = def {α ∈ Σ M |∃q , q α -→ M q } is
the set of all possible events at the state q.

• q after σ = def {q ∈ Q M |q σ ⇒ M q } is the set of states which can be reached from q by the sequence of actions σ. By extension, all the states reached from the initial state of the IOLTS M are (q M 0 after σ) and will be noted by(M after σ).

• μ = p!a if µ = p?a and μ = p?a if µ = p!a. For internal events, τ = τ .

Passive Interoperability Criteria

Passive One-to-One interoperability criteria are dened in [START_REF] Desmoulin | Test d'interopérabilité de protocoles: la formalisation des critères d'interopérabilité la génération des tests[END_REF] as follows:

Denition 2 In passive One-to-One interoperability testing, two IUTs are considered interoperable I 1 iop I 2 = def 1. After a trace during the asynchronous interaction of IUTs, all the outputs observed at the interfaces of IUTs must be foreseen in the interaction of their specications.

∀ σ ∈ T race(S 1 || A S 2 ) ⇒ Out((I 1 || A I 2 ),σ)⊆Out((S 1 || A S 2 ), σ).
2. And, all messages sent by one IUT to the other IUT must be received by the latter. It should be mentioned that interoperability testing is a black box testing. The TS is able to observe a message which has been sent by an IUT to the other IUT via its interface, but not whether the latter has actually processed the message or not. Therefore, the verication of an input is in fact done by verifying its causal-dependent observable outputs. To conrm that an input has been received involves having veried its related outputs that cannot be observed unless the input has been executed. ∀{i, j} ={1,

2} ,i = j; ∀σ ∈ T race(S i || A S j ), σ i ∈ T races(S i ), σ j ∈ T races(S j ), ∀µ ∈ Out(I i ,σ i ), ∀σ ∈((Σ Si ∪ Σ Sj )\µ) * , σ.µ.σ .µ∈T races(S i || A S j )⇒ Out(I j ,σ j .σ .µ.σ k )⊆Out(S j , σ j. σ , µ) where σ k ∈ (Σ Sj I ) * .

Observation Issues in Remote Passive Interoperability Testing

As mentioned in Section 2, passive interoperability testing is done by building a test system that observes the interaction between two IUTs. Within sight of the observations, a verdict (Fail, Pass or Inconclusive) is emitted w.r.t the passive interoperability criteria (cf. Denition 2). In fact, the passive interoperability cirteria considers only the asynchronous interaction of IUTs. In practice however, one cannot always neglect the test environment intercalated between the test system and the SUT. The most common situation is that the TS reaches the SUT through a network connection (remote testing). In such case, the delay in network causes asynchronism and should be taken into account as well.

In remote interoperability testing, the asynchronous nature of the environment often results in observation problems: The delay in environment inuences the observation order of the events produced by IUTs. There are generally two kinds of problems: (i) the problem of permissiveness that happens when uncooperative IUTs are judged to be interoperable. (ii) the problem of bias occurs when network components are determined uncooperative but they are actually interoperable. The verdict of asynchronous interoperability testing is error-prone.

Example 1 Let us consider the specications S 1 and S 2 in Fig. 2, which represent a connection protocol: Initially, S 1 sends a request (1!cnr) for connection. After S 2 receives the request (2?cnr), it can either accept the connection (2!ack -cnr) or decline it (2!nack -cnr). If S 2 accepts the connection, the connection will be established by an acknowlegement of S 1 (1!ACK). Then, both S 1 and S 2 can terminate the connection by sending F in request, which should be followed by an ack -F in acknowlegement. Fig. 3 illustrates three implementations based on the specications: I 1 =S 1 , I 2 and I 3 are two implementations based on S 2 . This example shows that passive interoperability testing carried out in asynchronous test environment introduces permissiveness and bias observation issues and causes biased verdicts.

We use I i iop A I j to denote the interoperability relation of IU T i and IU T j in asynchronous test environment. We show that I i iop I j I i iop A I j . • Permissiveness: passive interoperability testing in remote asynchronous environment is more permissive. The problem is brought to light by the interaction between I 1 and I 3 (cf. Fig. 4). According to the passive interoperability criteria (cf. Denition 2), I 1 and I 3 do not satisfy interoperability relation.

We have ¬(I 1 iop I 3 ) due to the output 2!ack -F in produced by I 3 after the input 2?Ack specied in S 2 . However, as mentioned before, the verication of an input in a black box testing context is based on verifying its causal dependent observable outputs. Here, the input 2?Ack is done by verifying its causal dependent events 1!Ack→2!F in. Therefore, as illustrated in Fig. In fact, the observation of TS does not reveal the real order of the events that happened on each IUT.

N. Chen

Figure 4: Permissive verdict

• Bias: This problem can be illustrated by the interaction of I 1 and I 2 (cf. Fig. 5). According to the passive interoperability criterion, I 1 iopI 2 . However, the delay in asynchronous testing environment intercalated between the TS and SUT can cause the disorder of the output observation. As a result, the trace 1!F in, 2!ack -F in can be observed as 2!ack -F in, 1!F in from the point of view of the TS. According to the specications, Out(S To sum up, in remote passive interoperability testing, observation problems maybe encountered due to the delay in asynchronous testing environment [START_REF] Doldi | Assessment of automatic generation methods of conformance test suites in an industrial context[END_REF], [START_REF] Jard | Remote testing can be as powerful as local testing[END_REF]. In the next section, we show that these problems can be avoided by an appropriate time stamp enabled mechanism.

1 || A S 2 , 2!ack -F in)= 1!cnr but we have here Out(I 1 || A I 2 , 2!ack -F in)= 1!F in Out(S 1 || A S 2 , 2!ack -F in). Thus ¬(I 1 iop A I 2 ).

Dealing with Observation Problems in Passive Interoperability Testing

In this section, the main issue is to keep a high level of observation in passive interoperability testing activity, ensuring that no biased verdict is introduced while executing the test in an asynchronous environment. The principle is to instrument each IUT by using a logical time enabled mechanism [START_REF] Baldoni | Fundamentals of Distributed Computing[END_REF], [START_REF] Lamport | Time, clocks, and the ordering of events in a distributed system[END_REF] so that each output from IUTs brings additional information about the order in which each event is produced.

The method is illustrated in Fig. 6. The idea is to implement a counting mechanism ST on the synchronous parallel composition of each IUT. The role of the ST is to code the occurrence of the events that happen on each IUT by time stamps. Then, each time an output is produced, its corresponding time stamp is piggybacked. A log le is used to store all the observed outputs from each IUT as well as their time stamps. At the side of the tester, another system ST is implemented. The role of ST is to reorder all the events in log by analyzing their associated time stamps. We will show that ST is able to reconstruct all the events that happen on each IUT with the help of time stamps. Finally, these well ordered traces will be analyzed by the TS against the specications to give a diagnose. • Initially at instant t, ∀{i, j} ={1, 2} ,i = j; CT i = CT j = 0.

• From t to t+δ each time IU T i sends a message α to IU T j , ST i increments CT i by 1. Message α and its time stamp, denoted by a tuple (α, CT i ) are then sent to IU T j (cf. Fig. 7). During message transmission, (α, CT i ) is observed by P O i and put into log.

Each time ST i receives a tuple (α, CT j ) from IU T j , ST i increments CT i by 1. Then CT j is removed, only message α will be sent to IU T i .

In fact, CT i is a counter that associates the occurrence of each event on IU T i with a time stamp. Thus, CT i reveals the sequence number of an event that happens on IU T i .

Time Stamp Analysis

All the observed outputs from both IUTs as well as their associated time stamps are stored in log. The time stamp information is then analyzed by the TS. At the side of TS, an algorithm ST is implemented. We call it ST , the opposition transformation of ST since an output of IU T i corresponds to an input of P O i . The role of ST is to analyze the logical stamps associated to each message recorded in log when trace registration is nished, and recovers the occurrence order of the events that happened on each IUT. ST involves two stages:

1. The construction of M Q (Mirror Event Queue, cf. Denition 3), which aims at nding the non-directly observable inputs on each IUT and helps reconstructing the occurrence order of the events that happened on each IUT.

2. The construction of OQ (Ordering Queue cf. Denition 4), which intends to recover the occurrence order of the events that happened on each IUT. :

M Q i ( )= , M Q i (σ.α)= M Q i (σ), M Q i (σ.β) = M Q i (σ).i?β.
In fact, for all the observed outputs α produced by IU T i taken in order from log, their mirror events α will be put into the mirror event queue M Q j of IU T j with respect to their observation order. As the channel between each testing entity is FIFO reliable, the sequence in M Q j will be received in this order by IU T j . For example, for a trace σ∈log: (1!cnr, 1), (2!ack -cnr, 2), (1!ACK, 3), (1!F in, 4), (2!ack -F in). The corresponding Mirror Event Queues are such that M Q 1 = 1?ack -cnr, 1?ack -F in; M Q 2 = 2?cnr, 2?ACK, 2?F in.

Proposition 3: For a trace σ produced on IU T i in asynchronous environment, the application of algorithm ST reconstructs σ.

Proof: First, the proposed time-stamp-enabled mechanism associates each event that happens on IU T i with a time stamp. This time stamp information is carried on-the-y with the outputs and is analyzed by ST . Although asynchronous environment disturbs the observation order, it preserves the relative order of inputs and outputs on each IUT. Therefore, logical time can be used to reconstruct σ.

Theorem 1: By using the proposed time-stamp-enabled mechanism, permissive and biased verdicts are avoided.

Proof: We rst prove that I 1 iop A I 2 ⇒I 1 iop I 2 by using the proposed time stamp enabled mechanism.

First, the verdict I 1 iop A I 2 after using the proposed mechanism algorithm

ST implies ∃ ST (σ) ∈ T race(S 1 || A S 2 ), Out((I 1 || A I 2 ), ST (σ))⊆Out((S 1 || A S 2 ), ST (σ)). As proposition 3 said that ST can reconstruct σ. Therefore, Out((I 1 || A I 2 ), σ) ⊆ Out((S 1 || A S 2 ), σ).
Moreover, as ST (σ) reconstructs the occurrence order of both inputs and outputs.

I 1 iop A I 2 ⇒ Out(I j , σ j .σ .µ.σ k ) ⊆ Out (S j , σ j. σ , µ) where σ k ∈ (Σ Sj I ) * Therefore, I 1 iop A I 2 ⇒I 1 iopI 2 .
Then we prove that ¬(I 1 iop A I 2 )⇒ ¬(I 1 iopI 2 ). It is trivial since it is the converse of I 1 iop A I 2 ⇒I 1 iopI 2 . Therefore, passive interoperability verdicts remain non-permissive and unbiased in asynchronous environment by using the proposed time stamp enabled mechanism.

Let's review the example of Fig. 4 and Fig. 5 to see how permissiveness and bias issues can be suppressed by using the proposed time stamp enabled mechanism.

Example 2 : The suppression of permissiveness is illustrated in Fig. 8. Each event is associated with a time stamp. Time stamps are carried on-the-y with the outputs sent by each IUT. The process of time stamp decoding performed by ST is the following:

c) After analyzing(1!ACK, 3), OQ 1 =1!cnr, 1?ack -cnr, 1!ACK.; M Q 1 =1?ack -F in. (d) After analyzing(1!F in, 4),OQ 1 =1!cnr, 1?ack -cnr, 1!ACK, 1!F in.;M Q 1 =1?ack -F in.
(e) After analyzing (2!ack -F in, 4),OQ 2 =2?cnr, 2!ack -cnr, 2?ACK, 2!ack -F in.; M Q 2 =2?F in.

Therefore, by comparing with the specication of S 1 and S 2 , TS detects that IU T 3 has chosen a dierent behavior from the S 2 by sending 2!ack -F in before receiving 2?F in. ¬(I 1 iop A I 3 ). Permissiveness is avoided.

N. Chen

Similarly, bias problem can be avoided by using the method. Which are correct w.r.t the interaction of their specications. Therefore I 1 iop A I 2 , bias is avoided.

To sum up, to solve the observation problems cause by asynchronous test environment in passive interoperability testing methods, the idea is to implement a counting mechanism ST on the synchronous parallel composition of each IUT. Then, from an event trace, a kind of test driver implementing ST can reconstruct the sequence of events which occurred on both IUTs. These sequences will be checked against the specications to decide whether they satisfy the interoperability relation.

Conclusion and Future Work

In this report, a stamped interoperability testing method has been proposed to solve the observation problems in asynchronous One-to-One passive interoperability testing. By using this method, both permissiveness and bias observation issues can be avoided. The test system can reconstruct a correct trace without out-of-sequence event produced by the IUTs.

To obtain a correctly ordered trace is essential because no matter which method is used to carry out interoperability, a correct observation of the interaction of the IUTs is always necessitated. It will help the test system give a correct verdict. Normally, the trace will be analyzed so as to decide whether the IUTs are interoperable or not.

The solution proposed for One-to-One passive interoperability testing can be extended to other more complex situation such as multi-components context where more than two IUTs interact. The main diculty for multi-components context will be managing the causal relationship between inputs and outputs since several inputs can arrive simultaneously to one IUT. Future work will focus on researching the asynchronous multi-components context and solving observation issues in this context.

Figure 1 :

 1 Figure 1: Passive interoperability testing architecture

Figure 2 :

 2 Figure 2: Specications S 1 and S 2

Figure 3 :

 3 Figure 3: Implementation I 1 , I 2 and I 3

4 2 ,

 2 Out(I 1 || A I 3 , 1!Ack)⊆Out(S 1 || A S 2 , 1!Ack)= 2!F in, thus the I 1 and I 3 are determined interoperable.

Figure 5 :

 5 Figure 5: Biased verdict

Figure 6 :

 6 Figure 6: Time stamp enabled asynchronism management mechanism

Fig. 7

 7 Fig.7 illustrates in detail the logical time mechanism proposed in this report: The counting mechanism ST implements a counter CT i on the corresponding IU T i (i={1,2}). The start and the end of trace recording are managed by TS at instant t and t+δ respectively.

Figure 7 :

 7 Figure 7: Implementation of time stamp mechanism

Denition 3 :

 3 M Q i ( The Mirror Event Queue of IU T i ). M Q i isconstructed recursively by checking each output in log one by one. Formally, ∀{i, j} ={1, 2} ,i = j; ∀σ ∈ log, α ∈ Σ IU Ti O , β ∈ Σ IU Tj O

Figure 8 :

 8 Figure 8: The Suppression of Permissiveness

  (a) M Q 1 = 1?ack -cnr, 1?ack -F in. (b) M Q 2 = 2?cnr, 2?ACK, 2?F in.

2 .

 2 The construction of OQ by analyzing each event in log.

  (a) After analyzing(1!cnr, 1),OQ 1 =1!cnr.; M Q 1 = 1?ack -cnr, 1?ack -F in.(b) After analyzing(2!ack -cnr, 2),OQ 2 =2?cnr, 2!ack -cnr.; M Q 2 =2?ACK, 2?F in.

(

Figure 9 :

 9 Figure 9: The Suppression of Bias Problem

2 .

 2 OQ 2 =2?cnr, 2!ack -cnr, 2?ACK, 2?F in, 2!ack -F in.

http://www.wireshark.org/ Collection des Publications Internes de l'Irisa c IRISA

Collection des Publications Internes de l'Irisa c IRISA

P 1?cnr = def P O 1 observes output cnr sent by IU T 1 . The rest may be deduced by analogy. Collection des Publications Internes de l'Irisa c IRISA

Denition 4: OQ i : The Ordering Queue of IU T i . OQ i stores the events reordered by ST on IU T i .

The construction of OQ is in fact the trace ordering procedure which involves in checking each tuple (α, CT i ) taken in order from the log. It is composed of the following steps:

1. For each tuple (α, CT i ) where α ∈ Σ IU Ti O , ST carries out the calculation of X =CT i -1 -length(OQ i ), where length(OQ i ) is equal to the number of elements in OQ i .

is the number of unknown events that happened before α.

Proof: CT i presents the sequence number of the output α on IU T i . Thus CT i -1 states for the number of the events that happened before α. As OQ i stores the events already ordered on IU T i , the number of unknown events before α is therefore CT i -1 -length(OQ i ).

Proposition 2 Unknown events on IU T i before an output α are input events.

Proof: As the test environment is modeled as reliable FIFO queues, the observation of the outputs produced by the same IUT repect the FIFO order as well. Therefore, the unknown events before α on IU T i can only be inputs.

2. According to the value X obtained by step 1, dierent actions can be taken:

• If X = 0, α is added to the tail of OQ i . i.e., there is no unknown event before α on IU T i , α can be directly put into its ordering queue.

• If X > 0, i.e., there are unknown event(s) before α. According to Proposition 2, these unknown events can only be inputs. Therefore, ST looks into the Mirror Event Queue of IU T i M Q i , as M Q i stores the mirror events of observed outputs sent by IU T j , which will be received by IU T i in a FIFO order. M Q i can be decoupled to two parts:

Then, OQ i is updated: M Q i is taken out from M Q i and added to the tail of OQ i , so as α.

The algorithm ST is written below formally:

Algorithm 1: Algorithm ST Input: log Output: OQ i , OQ j /*reordered events on both IUTs*/ Initialization:

End

Complexity of the algorithm The algorithm is composed of two f or loops since log is examined twice for the construction of M Q and OQ respectively. For the rst f or loop, the complexity is O(n) where n is the size of log. The same, the second f or loop has the complexity of O(n) as well. Therefore, the whole algorithm has the complexity of O(n).