1470 IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS, VOL. 14, NO. 3, SEPTEMBER 2013
A Diagnostic Approach for Advanced Tracking ofCommercial Vehicles With Time
Window ConstraintsAmine Boufaied
Abstract—In this paper, we introduce a fleet supervision systemused to monitor on-road evolutions of commercial transport vehi-cles. This monitoring is accomplished by the automatic dispatch,during crossing of a tracking location, of information issued fromthe localization system on the vehicle. This information can besent to a server through a direct Transmission Control Protocol/Internet Protocol connection in a general packet radio servicenetwork (GPRS) or through a satellite network. The informationis provided by the system to some allowed users via an Internetwebsite. The fleet supervision system also enables analyzing mes-sages sent by vehicles to identify differences between real dataand planned data. We are more particularly interested in thediagnostics of delays, which can take place during deliveries. Infact, while crossing already fixed tracking locations, these delaysare detected as early as possible, and their consequences arepredicted so that corrective or preventive actions are undertakenas soon as possible.
Index Terms—Delay propagation, diagnostics, fleet supervision,time window constraint, vehicle tracking.
I. INTRODUCTION
B ECAUSE OF globalization, market liberalization, dereg-ulation in the transportation sector, and the growing
commitment of the just-in-time philosophy, the competitionbetween road carriers and the need of punctuality, reliability,flexibility, and quality of transport services has considerablyincreased and will increase even more in the future [10]. Thequick development of mobile communications and informa-tion technologies allows the use of telematics to face thesechallenges and to increase the effectiveness of the commercialvehicles that are being used. Vehicles can be then equipped withembedded units, which can communicate with monitoring andtracking systems [1]. In [19], a real-time system for monitoringthe security of commercial vehicles is presented. Based on acombination of vehicle telemetry data obtained from GPS andonboard sensors, it continuously monitors the route choice andcar-following behavior of a driver.
In fact, the monitoring and tracking systems [9] of vehiclefleets are currently active; this means that the monitoring ve-
Manuscript received October 1, 2012; revised January 15, 2013 andApril 23, 2013; accepted May 2, 2013. Date of publication May 22, 2013; dateof current version August 28, 2013. The Associate Editor for this paper wasR. I. Hammoud.
The author is with the Higher Institute of Computer Science and InformationTechnologies, University of Sousse, 4011 Sousse, Tunisia (e-mail: [email protected]).
Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TITS.2013.2262635
hicles have to send, over regular periods, useful informationto the supervision system and no longer wait for missionaccomplishment to provide this information. This informa-tion is sent via cellular or satellite networks and saved intospatiotemporal database systems. This is realized using GPS,which allows receiving the information about vehicle positions,and using Global System for Mobile Communications/generalpacket radio service network (GSM/GPRS) to transmit theuseful information [11]. In [20], a case study was used to showthat the iPhone 4 has higher accuracy than a vehicle-trackingdevice, but it can only report its location. However, if pairedwith another third-party onboard diagnostic device, it can sendthe same information similar to a vehicle-tracking device.
This information can be used in various applications, forinstance, optimization of travel plans, visualization of a traf-fic jam, GPS-assisted navigation, road design, and informa-tion and communications technology-assisted traffic congestionsystems [4].
In this paper, we propose a new application concerning theearly diagnostics of delays for commercial vehicle deliveriesand to predict their effects. In fact, by using the informationabout the location of the vehicle, it is possible to monitor theprogress of the deliveries of goods by vehicles starting fromtheir departure from the warehouse up to their arrival to thefinal client, or even between maritime terminals, intermodalinstallations, warehouses, etc. This delivery duration is widelyrepresented in the literature as a time window [12]–[17].
In this paper, we focus on the operating level, consisting ofthe progress of transport and delivery processes. In fact, only afew works have been interested in monitoring the disturbancesaffecting the preliminary defined plan and, more precisely, thedelivery delays. Our contribution is precisely situated at thislevel and offers a diagnostic approach, i.e., the first step of amonitoring and recovery process, that is able to detect delays asearly as possible and to predict delay propagation consequenceson the succeeding deliveries.
In this paper, the useful information, which is needed by thesupervision system, is the duration spent by the vehicle sinceits departure from the warehouse, which is measurable whencrossing specified locations on the route to be covered. Forexample, In [2], using conventional spot traffic data from loopdetectors and processing them to generate vehicle passage timefor individual vehicles is considered.
The aforementioned duration is represented by a timingrelationship between two events. The useful information will
BOUFAIED: DIAGNOSTIC APPROACH FOR ADVANCED TRACKING OF COMMERCIAL VEHICLES 1471
Fig. 1. Fleet management system.
allow the supervision system to detect a delay as early aspossible, with a certain possibility, affecting the deliveries to beperformed by the vehicle. The delay detection is based on thesupervision of the time windows corresponding to the timingrelationships separating deliveries to different clients.
This paper is organized as follows. Section II briefly de-scribes the proposed fleet management architecture and intro-duces the diagnostic principle. Section III shows the differentmechanisms used to determine the time window constraints.Section IV introduces the remaining duration notion and itsrole in the detection function. Section V treats the problemof the remaining duration consideration in the time constraintverification. The possibility notion associated to the satisfac-tion of a time constraint is detailed here. In Section VI, thepropagation of the measured duration is studied to predict delayconsequences on future deliveries. Section VII proposes a setof solutions considered to be a decision-making support in thecase of diagnostic achievement. Section VIII presents an appli-cation example of the given approach. Finally, a conclusion andperspectives are given in Section IX.
II. FLEET MANAGEMENT ARCHITECTURE
Nowadays, every transport company must have a system tomanage and to communicate with its fleet. This system allowsthe company to provide information to its clients about thereal-time progress of the vehicle transporting their goods, toinform them in the case of disturbances or delays, and to makenecessary decisions as early as possible.
Architecture of such a fleet management system is givenin Fig. 1.
The most known use of fleet management is the real-time geolocalization of vehicles [3]. This functionality gen-erally uses the GPS system and a telecommunications mean(GSM/GPRS/3G, satellite communication, and ultrahighfrequency/very high frequency) [11].
In Fig. 1, the module (supervision, control, and consultationstations) contains a supervision/control architecture that canbe centralized at the head office or decentralized on severalsupervision sites. The consultation of the progress state of thetransport vehicle can be successfully carried out by the clientthrough an Internet connection.
The diagnostic function, which the management system willhave to ensure, has the role to detect delivery delays by observ-ing a specified set of events sent by vehicles to the supervisionsystem when crossing predetermined tracking locations. Delaysare then detected before the vehicle arrives to its destination,
allowing the conveyor to take or to receive adequate decisionsthat allows him to address this problem.
A. Definitions
An event is associated to a state evolution in the models ofthe control and monitoring system. In this paper, we considerthat an event is associated with the beginning or the end of anactivity executed by the controlled process.
The occurrence date is the measure with a global clock of thetime coordinate of an event issued from a supervised system.An event is dated by an “occurrence” function noted O and isdefined as
O : E → Q+
ei → O(ei)
where ei is an event, and E is the set of events. Q+ is the set ofpositive rational numbers.
B. Hypothesis
– A timestamp can be assigned to each event.– An event is characterized by its occurrence date and has
no duration.
C. Constraints Between Events
Constraints are expressed by timing relationships betweenevents. A constraint can, for example, express a transport timewindow between two locations.
Two types of constraints can be distinguished:– the precedence constraint, which is defined by O(ei) <
O(ej) and expresses that event ej must occur afterevent ei;
– the time window constraint, which is defined by dj, i ≤O(ej)−O(ei) ≤ fj, i, is denoted by Cji with dj, i andfj, i ∈ Q+, and expresses that event ej must occur afterevent ei within time interval [dj, i, fj, i]. These constraintswill be determined in Section III.
D. Delay
In our case study, a delay is the fact to arrive or to occurlater than expected. A delivery delay appears when a deliveryis performed later than expected. In this paper, we propose anapproach to estimate the possibility of such a delay.
III. DETERMINING TIME WINDOW CONSTRAINTS
The timing and sequencing relationships of the transportationsystem events are used to determine whether the deliveries areachieved on time or not. These constraints are fundamental indiagnostic process and have to be determined as precisely aspossible.
In [18], a method is proposed, aiming at the determination ofsuch constraints by introducing a learning method of intereventtiming using observations of a correctly operating system. The
1472 IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS, VOL. 14, NO. 3, SEPTEMBER 2013
statistics of the observed sample and characteristics of the cor-rectly operating system are used to create a confidence space ofpossible timing relationships between events from the system.The timing relationship between two specific events under thehypothesis of a (normal) correct functioning is assumed to benormally distributed with an unknown mean μ and an unknownstandard deviation σ.
Let U be the timing interval space representing the set of allpairs (m, w), where m is the center of the interval characteriz-ing a timing relationship between two events, and w is its width.Given event pair (e1, e2), timing relationship (m, w) denotesthat, for a system operating normally, if e1 occurs at timet1, then e2 necessarily occurs with positive duration includedbetween m− w/2 and m+ w/2. If mean μ and deviation σare known, timing relationship (m, w) has values m = μ andw = vσ, where v is a constant positive real value.
As parameters μ and σ of the interevent timing are notprecisely known, parameters m and w cannot be directly de-termined. Only the true mean x and the true standard deviations of a set of n samples are available [18], i.e.,
x =1n
n∑i=1
xi, s =
√∑ni=1(xi − x)2
n− 1. (1)
These values are constructed from observations of n (n posi-tive integer) duration xi separating the occurrences of events e1and e2 and representing the normal functioning of the process.The objective is to estimate the mean and the standard deviationof the timing relationship between the occurrence of e1 andthat of e2 according to the mean x and to the deviation s ofthe sample. For that purpose, a confidence level is fixed by anexpert and is specified as being (1 − α), where α is the errorfor mean μ and standard deviation σ.
For a true standard deviation s of the samples, the standarddeviation of the process σ, given a confidence level, belongs tothe interval denoted by σα(n), and the mean μ belongs to theinterval denoted by μα(n, σ) [18].
For a 95% confidence level, zασ/2 = 1.96. We have
σα(n) :s
1 + 1.96√2n
< σ <s
1 − 1.96√2n
(2)
μα(n, σ) : x− 1.96σ√n< μ < x+ 1.96
σ√n. (3)
For every σ ∈ σα(n), a range μα(n, σ) of possible means isgiven. Let Dv ⊆ U be the set of the timing relationships (m, w)for m = μ ∈ μα(n, σ) and w = vσ, where σ ∈ σα(n), and vis a positive constant real value called a truncation factor [18],which determines how far the timing relationship extends outonto the tails of the normal distribution of the timing.
The monitored interevent timing is then chosen among thosein Dv , minimizing the cost of missed detection and of falsealarms [18] (see Fig. 2). This monitored interevent timing willbe used in the following in our monitoring process.
In [7], the problem truck route planning is called a stochastictraveling salesman problem with time windows in which trans-port and delivery timing relationships are stochastic processes.
Fig. 2. False alarms and missed detection.
The transport and delivery timing relationships between twolocations also have a mean and a standard deviation.
IV. REMAINING DURATION NOTION
Suppose having a time window constraint to check betweenthe vehicle departure (occurrence of event ei) and the deliveryof its goods to a client (occurrence of event ej). The monitoredvehicle sends timestamps (occurrence of events ek) when cross-ing predefined tracking locations. These timestamps are usedto estimate the spent duration since departure. The remainingduration is therefore the bounded timing relationship separatingthe occurrence of event ek, which is called the intermediateevent, and the occurrence of the delivery event ej .
The remaining duration allows estimating the checking ofthe timing relationship between events ei and ej before theoccurrence of ej . This mechanism improves the early detectionof the violation of the time constraint [5]. In fact, instead ofchecking the constraint when ej occurs, we use information(measured duration and in advance known remaining duration)given by the occurrence of intermediate events to detect early[6] if there is a violation of the time constraint and, therefore, adelay.
V. CHECKING PRINCIPLE OF A TIME
WINDOW CONSTRAINT
Our approach consists of checking time constraints through amembership test of a measured duration to a set of value ranges.Works presented here concern only the time window constraintintroduced earlier (see Section II). The precedence constraintcan be brought back to a time window constraint [5].
We are interested in taking into account the bounded remain-ing duration, which is denoted by Δ, in the checking of the time
BOUFAIED: DIAGNOSTIC APPROACH FOR ADVANCED TRACKING OF COMMERCIAL VEHICLES 1473
window constraint. We consider checking the Cji constraintlinking O(ej) and O(ei).
Let ek be an intermediate event indicating the vehicle cross-ing of a predefined tracking location. The remaining durationΔ is therefore the remaining bounded duration to travel by thevehicle and separating O(ek) and O(ej). The minimal boundof Δ is denoted by δm and its maximal bound by δM . We arereminded that the possible values of the remaining duration arenormally distributed on interval [δm, δM ].
Then, knowing the measured duration between the occur-rence dates O(ei) and O(ek), which is denoted by Φ(Φ =O(ek)−O(ei)), our objective is to check constraint Cji by tak-ing into account the remaining duration Δ, i.e., Δ = O(ej)−O(ek).
We can write
O(ej)−O(ei)=(O(ej)−O(ek))+(O(ek)−O(ei)) = Δ+ Φ
and change it as
δm ≤ Δ ≤ δM , δm, δM ∈ Q+. (4)
We obtain
Φ+ δm ≤ O(ej)−O(ei) ≤ Φ+ δM , Φ ∈ [−∞,+∞](5)
or constraint Cji is given offline by
dj, i ≤ O(ej)−O(ei) ≤ fj, i. (6)
The checking of the time window constraint consists thenin searching duration O(ej)−O(ei), simultaneously satisfying(5) and (6).
In a general case, the satisfaction of constraint (5) does notimplicate necessarily in all cases the satisfaction of constraint(6). Indeed, the set of the values O(ej)−O(ei) represented byconstraint (5) is not necessarily included on the set of valuesO(ej)−O(ei) represented by constraint (6).
A graphical representation of both constraints in the sameplan gives Fig. 3. In plan (O(ek)−O(ei), O(ej)−O(ei)),inequalities (5) and (6) each define a band or a region. Therequested duration belongs to the intersection of these twobands, which defines a polygon denoted by PO. Three casesappear: 1) δM < dj, i; 2) δM > dj, i; and 3) δM = dj, i. CasesδM > dj, i and δm > dj, i do not represent the reality or concernerroneous bounds. Fig. 3 schematizes these three possibilities.Time duration expressed by the axis is given in minutes.
We define the polygon PO with four points A, B, C,and D with respective coordinates (dj, i − δM , dj, i), (dj, i −δm, dj, i), (fj, i − δm, fj, i), and (fj, i − δM , fj, i). We denotexi as the abscissa of point i in the plan of our study. Fig. 4 showsthe different forms of the polygon PO for cases 1 and 3 andaccording to the result of comparison between duration (fj, i −dj, i) and (δM − δm). For case 2, the reasoning is identical.
Thus, by considering PO and for a given Φ, a range of possi-ble values for duration O(ej)−O(ei) that allows the simulta-neous satisfaction of both time constraints (5) and (6) is shownin Fig. 5.
Fig. 3. Graphical representation of constraints (5) and (6). (a) δM < dj, i.(b) δM > dj, i. (c) δM = dj, i.
Fig. 4. Graphical representation of polygon PO.
The objective is then to quantify, among the set of possibleduration O(ej)−O(ei) allowing satisfaction of constraint (5),the subset of those allowing satisfaction of both constraints(6) and (5). This quantification allows defining a possibilitymeasure with which constraint Cji is satisfied. The possibilitymeasure is expressed as the quotient of the interval width ofall duration O(ej)−O(ei) satisfying constraint Cji, on the in-terval width (equal to δM − δm) of all duration O(ej)−O(ei)satisfying constraint (5).
We obtain the following.
– All the duration O(ej)−O(ei) satisfying constraint (5)also satisfies constraint (6) when all values of Φ belong
1474 IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS, VOL. 14, NO. 3, SEPTEMBER 2013
Fig. 5. Possible values for duration O(ej)−O(ei) allowing satisfaction ofconstraints (5) and (6).
to [xB , xD] (respectively, [xD, xB ]) if the polygon POis of form 1 or 2 (respectively, of form 2 or 3) or, moregenerally, when Φ ∈ [min(xB , xD), max(xB , xD)].
– When Φ ∈ [xA, min(xB , xD)] ∪ [max(xB , xD), xC ],a subset of duration O(ej)−O(ei) satisfy constraint (5)but not constraint (6).
– When Φ ∈ [−∞, xA[∪]xC ,+∞], no duration O(ej)−O(ei) satisfying constraint (5) satisfies constraint (6).
To characterize this problem, consider Φ ∈ , where is theuniverse of discourse. Let A be the fuzzy set of real values [21]allowing to satisfy the Cji constraint.
Let μ(Φ) be the membership function of Φ to A. μ is thepossibility to satisfy constraint Cji according to Φ. μ is thenthe quotient of the interval width of duration O(ej)−O(ei)satisfying constraint (6) and, for a specific Φ, of the intervalwidth (equal to δM − δm) of duration O(ej)−O(ei) satisfyingconstraint (5).
We conclude the following.
– If Φ ∈ [min(xB , xD), max(xB , xD)], then
μ(Φ) = min
(fj, i − dj, iδM − δm
, 1
). (7)
– If Φ ∈ [xA,min(xB , xD)], then
μ(Φ) =Φ− dj, i + δM
δM − δm. (8)
– If Φ ∈ [max(xB , xD), xC ], then
μ(Φ) =−Φ+ fj, i − δm
δM − δm. (9)
– If Φ /∈ [xA, xC ], then μ(Φ) = 0; constraint (6) cannot besatisfied and is then violated.
Fig. 6 shows the values of μ according to Φ.In our case study, the polygons PO of forms 1 and 2 will be
considered in this paper, i.e., we will have δM − δm, ≤ fj, i −dj, i, in the following. This case most represents the reality andallows getting certainty in constraint Cij satisfaction. In fact,the case where δM − δm > fj, i − dj, i does not permit any
Fig. 6. Membership function to the fuzzy set A. xA ≥ 0, xB ≥ 0, xC ≥ 0,and xD ≥ 0.
Fig. 7. Different zones in a membership function. xA ≥ 0, xB ≥ 0, andxC ≥ 0.
certainty in the satisfaction of constraint Cij, (fj, i − dj, i/δM −δm < 1).
Thus, we have min(xB , xD) = xB = dj, i − δm andmax(xB , xD) = xD = fj, i − δM . In addition, Φ cannot bestrictly inferior to xB because we assume that the timingrelationship between ei and ej cannot be strictly inferior todi, j and that the timing relationship between ek and ej cannotbe strictly inferior to δm.
After a variable change, we obtain the following results withxA = dj, i − δm, xB = fj, i − δM , and xC = fj, i − δm.
– If
Φ ∈ [xA, xB ]. (10)
– If Φ ∈ [xB , xC ], then
μ(Φ) =−Φ+ fj, i − δm
δM − δm. (11)
– If Φ > xC , then μ(Φ) = 0; constraint (6) is violated.
The delay is R = sup(0,Φ− xC) = sup(0,Φ− fj, i + δm).Fig. 7 shows the values of μ according to Φ, which will be
considered later in this paper. The interval [xA, xB ] is calledthe green zone, [xB , xC ] is called the orange zone, and finally,[xC ,+∞] is called the red zone.
We notice that, when Φ ∈ [xB , xC ], the possibility to satisfythe constraint is fuzzy (∈ [0, 1]). Even when this value isnot binary, this can be useful information for the decisionfunction, which, when this value exceeds some threshold (seeSection VII), can recommend the achievement of some mainte-nance on the vehicle or the future update of the chosen route.
VI. PROPAGATION OF THE MEASURED DURATION
When a time window constraint is monitored, we notice that,as soon as we have Φ ≥ fj,i − δm, this constraint is violated. Inthe case that the vehicle makes a delivery tour, we have severaltime constraints to check, forming a constraint network.
BOUFAIED: DIAGNOSTIC APPROACH FOR ADVANCED TRACKING OF COMMERCIAL VEHICLES 1475
Fig. 8. Two time window constraints to check successively.
The violation of a constraint can then cause the violation ofsuccessive constraints on the route. This can be detected bypropagating the measured duration Φ.
We are going to study the case of two time constraints (12)and (14) to check successively (see Fig. 8).
We have
dj, i1 ≤ O(ej)−O(ei) ≤ fj, i1 (12)
Remaining duration 1 : δm ≤ Δ1 ≤ δM (13)
dj, i2 ≤ O(eh)−O(ej) ≤ fj, i2. (14)
Constraint (12) is violated when Φ > fj, i1 − δm. Therefore,when the supervision system receives event ek, this inequalityis checked to detect a delay as soon as possible. In addition,when receiving event ek, constraint (14) can also be checkedby considering a new constraint as follows:
The remaining duration associated to constraint (15), which isdenoted as remaining duration 2, is given by
δm + dj, i2 ≤ Δ2 ≤ δM + fj, i2. (16)
Let μ1 be the possibility to satisfy constraint (15) accordingto Φ. We obtain the following results with xA = dj, i1 − δm,xB = fj, i1 − δM , and xC = fj, i2 + fj, i1 − δm − dj, i2.
– If Φ ∈ [xA, xB ], then
μ1(Φ) = 1. (17)
– If Φ ∈ [xB , xC ], then
μ1(Φ) =−Φ+ fj, i2 + fj, i1 − δm − dj, i2
δM − δm. (18)
– If Φ > xC , μ1(Φ) = 0; constraint (12) is violated.
The delay is
R = sup(0,Φ−xC) = sup(0,Φ−fj, i2−fj, i1+δm+dj, i2).(19)
The representation of μ1 according to Φ in the general caseis similar to that in Fig. 7.
Fig. 9. n time window constraints to check successively.
A. General Case: n Constraints
Suppose a vehicle has to accomplish n successive deliverieson a beforehand planned route. We have therefore n time win-dow constraints to check, which are denoted by C1, C2, . . . , Cn
(see Fig. 9). We note every event delivery i as ei. Event e0 isthe “departure” event. Every time window constraint is givenas follows:
Cm : dm ≤ O(em)−O(em−1) ≤ fm, m = 1, . . . , n. (20)
The violation of a constraint can cause the violation ofthe succeeding constraints toward the final destination. Therole of the detection function is to detect the violation of theconstraint(s) before the occurrence of the events constituting it(them).
Every time an intermediate event (tracking location) or anevent delivery i appears, all the yet to be checked constraintscan be tested, and violations can be detected as soon as possible.
Suppose that the vehicle is between delivery p and deliveryp+ 1, with 1 ≤ p < n. The reception by the supervision systemof intermediate event ek will cause the checking of constraintsCp+1, . . . , Cn, where, as measured duration, the timing rela-tionship separates the occurrence of event “departure” and thatof the intermediate event and is denoted by Φ. The remainingduration, in this case, depends on the constraint to be checked.It separates the occurrence of the intermediate event and that ofevent delivery i, i = p+ 1, . . . , n.
For every constraint to check, different remaining durationΔi values are given as follows:
For Cp+1 : δm ≤ Δp+1 ≤ δM , δm, δM ∈ Q+.
For Cp+2 : dp+2 + δm ≤ Δp+2 ≤ δM + fd+2.
For Cp+3 : dp+2+dp+3+δm ≤ Δp+3 ≤ δM+fd+2+fd+3.
. . .
For Cn :
n∑i=p+2
di+ δm ≤ Δn ≤ δM +
n∑i=p+2
fi.
Finally, checking each of constraints Cp+2, . . . , Cn amountsto checking constraints C ′
1476 IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS, VOL. 14, NO. 3, SEPTEMBER 2013
Fig. 10. Supervision example of a truck transporting goods.
The checking of each of these constraints was explained inSection V. Let us denote Ri as the delay relative to the checkingof a time constraint C ′
i, i = p+ 2 . . . n.
VII. DECISION ASPECTS
If the delay is due to the transport operation, it can berecovered when achieving the next delivery; therefore, it willnot affect the following deliveries. In addition, after deliveringa client or when crossing a tracking location, the driver is in-formed by the monitoring system of his delay for the followingdelivery. He can decide, in that case, to reschedule his plan andto go a quicker route (this assumes the existence of severalroutes between both clients), which can be costlier than thefirst one.
Other solutions can be anticipated as the allocation of anothervehicle transporting the same goods to avoid the delay or thecancelation of a delivery to assure the respect of the followingtiming relationships. In addition, a log file has to be used forevery vehicle and to be updated by the monitoring system byrecording in, for example, the number of delays encountered ona certain route.
In addition, thresholds of possibilities can be predefined bythe transport companies. These thresholds are situated in orangezones of the possibility functions (see Fig. 7), i.e., zones forwhich the detection of delays is fuzzy. Then, if the number ofpossibilities smaller than this threshold exceeds some before-hand fixed rate, the delay risk is considered high, and preventiveactions have to be accomplished, e.g., the maintenance of thevehicles, the modification of the delivery time, the substitutionof the delivery stores, replanning and rerouting of vehicles, etc.The choice of the threshold and of the rate is the responsibilityof an expert from the transport company.
These decision aspects represent some research orientationsand need to be explored in relation with main existing works.
VIII. APPLICATION EXAMPLE
We propose an example showing the interest of our approachand concerning the supervision (monitoring) of goods deliveryby a truck to several clients.
The truck has to accomplish a route from a “departure loca-tion,” which is the warehouse, up to client 3 and crossing twoclients 1 and 2. Between the “departure location” and client 1,a tracking location exists. The truck is, as we had men-tioned previously, followed up by a geolocalization system (seeFig. 10). Diagnostics on a delivery delay can be accomplished
only when crossing a specified set of locations (tracking loca-tions or when delivering to a client).
A. Determining Time Constraints
In Fig. 10, the determination of tolerances on timing rela-tionships, i.e., separating the different tracking locations anddifferent destinations, is realized from real data. Indeed, on theroute between “departure location” and client 1, the followingsample of n = 50 timing relationships (xi, i = 1, . . . , 50) wasobtained from vehicle-tracking devices (see Table I).
The mean x and the standard deviation s of the sample arecalculated.
We found the following:• x = 1/n
∑ni=1 xi = 105.2.
• s =√∑n
i=1(xi − x)2/n− 1 = 5.9.For a confidence level of 95%, i.e., the values of σ and μ
have a probability of 0.95 if within the range mentioned in thefollowing and a probability of 0.05 if it does not have a valuewithin the range, we get the following intervals:
• s/1 + (1.96/√
2n)=4.9<σ<7.3 = s/1 − (1.96/√
2n)• x− 1.96(σ/
√n)=103.1<μ<107.2=x+ 1.96(σ/
√n).
We choose σ = 6 and μ = 105, and we obtained the follow-ing normal distribution (see Fig. 11). This model approximatesthe real sample data and is used to get the monitored timingrelationships.
Fig. 11 shows that the timing relationship to be monitoredis [90′, 120′] and is centered in μ = 105′ with a width equal to2.5 ∗ σ. Coefficient 2.5 is called the truncation factor. The areaunder the normal curve outside the duration defined by the in-terval [90′, 120′] is 0.002 of the total area under the curve. Then,correct measured duration of the route is declared abnormal in0.2% of the cases. False alarms due to the truncation of thenormal curve are going to be neglected following this example.
We get, in the same way, the complete example in Fig. 12.
B. Constructing Possibility Functions
We assume that when the measured duration is in the mon-itoring intervals, deliveries will be a priori not delayed. In theother cases, it is possible that a delivery would be delayed. Weshould remember that these delays are only observable whilecrossing well-defined locations (tracking locations or whendelivering a client).
Suppose that a vehicle crosses a tracking location. The mea-sured duration Φ (see Fig. 12) is that separating the occurrenceof event “departure” and the occurrence of the tracking event.We obtain the following:For client 1: Constraint to check:
Using simulation, a sample of 700 values of duration Φ, withmean of 70 and a variance of 20 (to cover cases of correctlyoperating and of delay), was generated and used for the test ofour monitoring function. Fig. 13 shows its histogram.
Fig. 14 gives the representation of the possibilities variationof satisfaction of the previous three constraints according to themeasured duration Φ.
Fig. 13. Histogram of a Φ sample.
Fig. 14. Possibility functions of constraint satisfaction relative to the threeclients.
Results will be interpreted as follows:
1478 IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS, VOL. 14, NO. 3, SEPTEMBER 2013
Fig. 15. Representation of a threshold of 0.1.
C. System Test and Results
The diagnostic function is activated when crossing a trackinglocation or at the end of a delivery. This shows the interest ofour approach, which allows detecting as early as possible theviolation of time constraints by propagating the time spent bythe vehicle since its departure, which is denoted by Φ in thispaper.
For example if Φ = 110′ (because of a problem), the diag-nostic system in Fig. 14 gives the following conclusions.
• There is a delivery delay for the client 1 of 20′.• There is a delivery delay for the client 2 of 5′.• There is no delay on client 3 delivery.As these delays are detected before the arrival to clients 1 and
2, actions can be undertaken to solve this problem. These ac-tions are out of the scope of this paper. In addition, for client 1,if the number of possibilities smaller than the threshold, whichis fixed here to 0.1 (see Fig. 15), exceeds some rate, whichis fixed here to 15%, the delay risk is considered high (seeSection VII).
From the obtained sample, we get relatively to the constraintof the client 1:
Total number : 700 values of the duration Φ.
A possibility value is calculated for each value of the 700 valuesof duration Φ, we found
Number of possibilities smaller than 0.1 = 148.
The rate of possibilities inferior to 0.1 is
Rate = (148/700) ∗ 100 = 21% > 15%.
The rate is found to be too high, and the diagnostic systemconcludes that the delay risk is high and that preventive actionsmust be accomplished.
IX. CONCLUSION
In this paper, we have discussed the supervision of a fleetof commercial vehicles. The supervision system communi-cates via the Internet with a server containing the information
received from vehicles, which also makes this informationavailable to the clients who want to know the progress stateof their deliveries. This server receives information from aGSM/GPRS network or a satellite network. In our approach,this information consists in measured duration spent by vehiclesfrom their departure to tracking locations preceding the finaldelivery to the client.
This measured duration, and with predefined remaining du-ration, allows detecting the violation of time constraints definedas bounded timing relationships between event occurrences.This variable and bounded remaining duration generates im-precision on the time constraint checking due to uncertainty ontheir values. The obtained result is a satisfaction possibility of atime constraint. Therefore, when a delay is detected (possibilityequals to 1) and quantified, the propagation of this one canallow the detection and the quantification of other future delaysas early as possible before arriving at the destination.
More generally, these mechanisms are suitable for any sys-tem in which uncertainty on remaining duration and toleranceon time constraints are of the same order, whether it is acomputer network, a logistic chain, or any other physical orlogical system.
As short-term perspectives of this paper, we are going toconsider the case where absolute dates of departure or deliveryare specified, in the estimation of the satisfaction possibility. Areal experimentation must be accomplished, and its results mustbe interpreted to quantify more precisely the performances ofthe monitoring system.
In the long term, the decision-making aspects in the case ofdiagnostics and quantification of a delay have to be consideredmore in detail to better profit from the early detection of thedelays.
ACKNOWLEDGMENT
The author would like to thank his colleagues Prof.O. Korbaa and M. C. Slama for their support in revising thispaper, as well as M. Combacau, A. Subias, and L. T. Massuyes,members of the Laboratory for Analysis and Architecture ofSystems, for their recommendations to improve this paper.
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Amine Boufaied received the Master’s degree incomputer science engineering from the Faculty ofSciences of Tunis, Tunis, Tunisia, in 1998 and thePh.D. degree in industrial systems from Paul SabatierUniversity, Toulouse, France, in 2003.
He is currently a Professor with the Higher In-stitute of Computer Science and Information Tech-nologies, Sousse, Tunisia, as well as a Researcherwith the Modeling of Automated Reasoning Sys-tems Research Unit, Faculty of Sciences, Universityof Monastir, Monastir, Tunisia. His research inter-
ests include modeling, monitoring, diagnostics, and control of discrete eventsystems.
