A F u y Control Approach for Adaptive Traffic Routing A new approach to traffic routing is essentially based on heuristic rules derived from expert knowledge and human experience. This approach has been used to develop a fuzzy routing system applied to a model of the French long-distance telephone network.

Prosper Chemouil, Jelila Khalfet, and Marc Lebourges

PROSPER CHEMOUIL is the head of the network management and traffic engineering department at CNET, France Tdlicom's research center.

JELILA KHALFET is a lecturer at the University of Evry.

MARC LEBOURGES works at France Tdlicom s headquarters.

n this articlewe investigate the use of fuzzy control techniquesfor adaptive trafficrout- ing in telephone networks. As information related to network performance is imprecise by nature, a new approach based on fuzzy logiccould prove tobeefficient. Its primary

focus is to translate expert knowledge into natural language. Thus an inference method has been derived which at tempts to represent gradual inference rules using fuzzy control techniques. T h e infer- ence method is essentially based on heuristic rules derived from expert knowledge and human expe- rience. This approach has been used to develop a fuzzy routing system applied to a model of the French long-distance telephone network. Simula- tion results are shown to compare favorably with those from previously known methods.

In most telephone networks traffic is routed under fixed rules. This requires the provision of over-capacity in o rde r to handle peak periods. However, it has been shown that, in several situa- tions, such a network cannot accommodate the demand with the required grade of service. Hence, new routing methods have been developed to enable high performance under a wider range of network conditions, including failures and over- loads. Flexibility can be achieved with adaptive traffic routing which aims at tracking and utilizing idle capacity in the network in order to provide the quality of service requested by users. This flexibil- ity allows quick and automated response to rapid changes in network loading, in order to maximize utilization of available resources. Adaptive traffic routing allows telecommunication network opera- tors toexploit non-coincidence ofreal-time traffic fluc- tuations in order to improve network efficiency and robustness, reduce network costs, and implement expansive routing controls for network traffic management. Broad methods of adaptive traffic rout- ing have been developed which utilize the network stateinformationavailable [l]. Theyaremainlyderived from probabilistic modeling to account for the stochastic characteristics of traffic which result in imprecise performance information. Therefore, the idea ofcontrolling telecommunications traffic using advanced methods such as fuzzy logic has recently arisen [2].

Fuzzy set theory, on which fuzzy logic is based, was initiated by Zadeh in 1965 [3]. Fuzzy set the- ory and logic, as a means of both capturing human expertise and dealing with uncertainty, have been applied to various domains such as industrial con- trol, medical diagnosis, management, and deci- sion making. Since human judgments, including preferences, are often vague, fuzzy logic plays an important role in decision making. Several authors have provided important results on group deci- sion making or social choice theory with the help of fuzzy sets. They have proved that fuzzy sets provided a convenient framework for dealing with information that is characterized by impreci- sion and uncertainty, providing an effective way of modeling the approximate, inexact nature of the real world [4].

Fuzzy logic allows us to take into account the continuous character of imprecise information and to avoid arbitrary rigid boundaries. It also has t h e advan tage of e s t ab l i sh ing a n i n t e r f a c e between symbolic and numerical data, i.e., it has the capacity to exploit imprecise data expressed in natural language by human observers or experts, at the same time with precise numerical data pro- vided by measurement devices. In this article we investigate the appl icat ion of a fuzzy control approach to adaptive traffic routing in particular, i.e., traffic is routed according t o a number of control rules chained by a reasoning based on fuzzy logic.

The article is organized as follows: first, we present the basic fuzzy control principles, their structure along with some of their characteristics. We then show how this approach can be applied to the routing problem, by defining an appropriate type of fuzzy control ler . Finally, a case s tudy based o n t h e F rench long dis tance network is presented to validate the approach.

Fuzzy Control Systems uzzy control was introduced by Mamdani for F t h e con t ro l of complex processes , such as

industr ia l plants , especially when no precise model of the processes exists and when most of

70 01h3-6804/95/$04.00 1905 0 IEEE IEEE Communications Magazine July 1995

the (1 priori information is available only in quali- tative form [SI. It has been observed that a human ope ra to r is sometimes more efficient than an automatic coptroller in dealing with such systems. The intuitive control strategies used by trained oper- ators may be viewed as fuzzy algorithms, which provide a possible method for handling qualita- tive information in a rigorous way.

The basic idea of fuzLy control is to make use of expert knowledge and experience to build a rule base with linguistic if-then rules. Proper control act ions a r e then der ived f rom t h e rule base, which can be considered as an emulation of the human operator behavior. Different from other control methods, fuzzy control does not involve complex mathematical operations and models of systems. Hence, fuzzy control may be viewed as a form of control ratherthanasacontrol algorithm. Itsdesign theory does not cxplicitly suggest a solution for ii particular control problem, as i s often done by most control schemes, e.g. pole-placement, adaptive, or robust controls. The question of how to solve H control problem in fuzzy control is assumed to be the responsibility of the experts. Consequently. the design of a fuzzy controller depends entirely on the knowledge and experience of experts, o r t he physical sense and intui t ion of designers which is far from systematic and reliable.

Fuzzy Control Design The basic principle used in fuzzy control is the notion of a fuzzy linguistic rule. A fuzzy rule is a conditional statement, typically expressed in the form if-then. The deduction of the rule is called the inference and requires the definit ion of a membership function characterizing this inference. This function allows us to determine the degree of truth of each proposition. Various implication methods have been developed to implement the inference mechanism. Thc operating procedures of a fuzzy logic controller arc described as follows:

Fuzzification - Each fuzzy system is realized in thc form of fuzzy rules a s in the following example:

i fX isA I and Y is Bl then Z is CI if X is A2 and Y is B3 then Z is C2

Rule 1 Rule 2

where X and Yare variables of the condition part, and Z is the variable of the action part . i l , , RI. and C, are fuzzy parameters characterized by mem- bership functions.

The condition parts of control rules makc u\e of measurements which are usually real numbers. According to their respective value domain. e.g. U1 and Uz, these real-valued measurements, e.g. x’ a n d y are matched to their corresponding fuzzy variables by determining their membership values defined as (Fig. 1 ):

Fuzzy Reasoning - Suppose that X = .yo and Y = y o . The reasoning is derived as follows:

For all the control rules in the rule base, we derive the t ruth value of each rule in the premise by building the coii,junctions of the matching mem- bership values:

H Figure 1. Firzq infereirceprocedilre for two r~ilcs (Mamdani’s type).

where the A conjunction can be, for example, the “min” function (Mamdani’s implication [5] ) .

p I and p2 represent, respectively. the degree of truth of rules 1 and 2 and define, for the mca- surementsx a n d j O , the membershipvalues pc, (Z) and p(.,(Z) of the fuzzy subsets Cl(Z) and CzfZ). W represents the value domain of t he output variable Z. The fuzzy control output C(Z) is repre- sented by the aggregation of all fuzzy subsets C,(Z). Its mcmbershipvaluespc(Z) are determined by thedisjunctionofall the membershipvalucspc,(Z):

where the ’’ disjunction is t he “max” function when used with Mamdani’s implication [4, 51. Figure I illustrates the principles of fuzzy reason- ing following Mamdani’s approach where the membership functions are arbitrarily chosen as trapezoids (the membership functions are usually defined in such a way that they overlap to account for uncertainty on the boundaries):

First, the membership of each fuzzy proposi- tion is tested. For example. pA ,i: the grade of membcrship of the fuzzy proposition “X isA Second. all grades are compared for each rule. T h e g rade o f a rule is chosen as the lowest grade among all fuzzy propositions composing the condition part (“min” conjunction). Third, the membership function of C, is trun- cated at the valuc of the grade p I for Rule 1, p2 for Rule 2 to obtain the membershipvalues ~ C , ~ ( Z ) andp<.,(Z) (medium shaded trapezoidsin Fig. I ) . Finally-thc membership values, p(.(Z), are cal- culated as the maximum of p(.,(Z) and pc,(Z) (Max disjunction represented by dark shgded trapezoids in Fig. I ) .

Defuzzification Procedure - Last. an opera- tion is carried out to transform the output of the inferences, which is a fuzzy result . i n t o a real value that could be used as control input.

From the reasoning procedure, we obtained a fuzzy controller output. In fact, what we desire is a non-fuzzy output. and so we have t o perform what is called a “defuzzification” procedure of p(-(Z) in order to dctermine a quantitative value of the control output. Several methods can be applied for defuzzification. the most widely used being the center-of-gravity method which we consid- ered in our specific application [6]. An alternative method consists in taking the mean of the two highest peaks of the membership function. This latter method iscalled thc “mean of maxima” method.

I Aggregation

W Figure 2. Fuzzy logic controller architecture.

W Figure 3. Two-legged routingscheme.

T o summarize the overall above-described procedure, Fig. 2 illustrates the general architecture of the fuzzy controller.

Fuzzy Control Properties The design of a good fuzzy controller does not require complete knowledge of the controlled system. However, it does require a good expertise and experience with the process in order to build the fuzzy rules that are the basis of the controller. Moreover, the definition of the membership func- tionsiscrucial.The“distance” between the peaksof two membership functions is especially critical. A too small distance will lead to oscillations while a too big one will lead to a steady-state error.

In the case of process control, where the sys- tem is usually controlled by skilled operators who either decide directly the control output or tune by themselves the controllers of the system, the knowledge of these experts can be directly trans- lated into fuzzy linguistic rules. It is the first and the most frequently used fuzzy control method in use until now. The fuzzy controller generally behaves even better than the experts, since it ismore reliable, i t can use the knowledge of several operators, not just one, and it can decide on an output very quickly.

T h e system nevertheless d o e s not use t h e goals of the control strategy in an explicit manner. They are only expressed implicitly, since the rules derived from expert knowledge are supposed to take these goals into account. Tosolve that problem, and also to be able to make a control system using control requirements that are very easy to change, a so-called predictive fuzzy control method has been designed. It consists in predicting the future state of the system (with a model of the system)

for each possible control action that could be made. Then the adequacy of each of these possibilities is evaluated using fuzzy rules on various criteria such as precision ofcontrol. This method permitsvarious criteria to be mixed and tuned in a very precise way. But it takes a lot of computation time and requires a model of the controlled system to be developed.

Fuzzy Adaptive Routing everal adaptive routing methods have been S developed and presented in major telecom-

munications conferences. A comprehensive survey of the approaches has also appeared in [ I ] . Our research has considered a particular state-dependent routing approach which has been the subject of several studies [7-91. Routing decisions are there- fore taken, depending on the availability of the network resources for which the occupancy status can be measured and/or estimated at periodic intervals (typically from ten seconds to five minutes) from real-time measurements according to prob- abilistic models.

Recent ly , a new s t a t e -dependen t rou t ing method, Real-Time Network Routing (RTNR), has been implemented by AT&T which defines several levels of availabil i ty according t o the number of idle circuits for each origin-destination node pair [ 101. Routing of calls is performed on a per call basis depending on the availability level and on the class-of-service of the call.

Fuzzy control allows us to combine features of these different approaches: routing can be per- formed on a periodic basis using availability levels that are more suitable when the update cycle is long (more than three minutes). In contrast to RTNR, the boundaries between the different availability levels are not rigid. This is implemented by char- acterizing the membership funct ion fo r each availability level in such a way that they overlap to account for uncertainty (trapezoids as in Fig. 1). Fuzzy logic determines the best availability level according to the effective measurement depend- ing on the context.

The fuzzy adaptive routing of telephone traffic is based on a set of consistent routing rules that describes a method for ordering and selecting the paths from an origin switch to a destination switch. The paths always have only two “legs” at most, i.e., are composed of two chained circuit groups (as depicted in Fig. 3) for a stream going from node A to node B. The routing of each traffic stream is carried out separately using periodic data related to circuit groups only.

The design methodology of a fuzzy controller. as described previously, is used for the application of fuzzy adaptive routing. It determines, for each origin-destination node pair, the availability of all the paths and the quality of all the routes, and it decides the best route to be used for routing the current traffic. Since this availability cannot be determined directly from the input data, an inter- mediate criterion is introduced: the availability of individual circuit groups. This leads to a controller designed with two blocks (Fig. 4). T h e fuzzy con t ro l m e t h o d used is t h e o n e p roposed by Mamdani [SI, which is the most widely used fuzzy control. Most of the domain-specific knowledge should be provided by telecommunications experts, typically traffic engineers and network managers.

72 IEEE Communications Magazinc July 1995

In the particular application we develop later in this article, the membership functions and the rules have been proposed by the authors. This knowledge is expressed in heuristic form directly relating thevalues of the observed parameters to the action to be implemented.

In Fig. 4, the inference engine 1 determines the availability ( A d ) of individual circuit groups according to the values of their status as determined by measurements . T h e membership functions express a fuzzy status for each value of each mea- surement, which allows the manager to build the rules required for inference engine 1. As an example, we illustrate in Table 1 the rule base for inference engine 1 which provides the various availability status of each circuit group when the measurements are the number of in-service circuits (denoted by N) and the number of idle circuits (denoted by X) for each circuit-group. These measurements are typi- cally those used in former approaches where they are reflected in the general concept of residual capacity [ 7- 101.

The output variables of the first inference engine - availabilities Avl, and AV\ of upward and down- ward circuit groups - are fuzzy variables. In order not to lose information, defuzzification of variables Avl, and AV!, is not performed. These variables directly feed the second inference engine to provide the fuzzy quality of each route. Table 2 contains the rules related to inference engine 2.

Finally, the defuzzification module makes use of the fuzzy route quality as obtained from Table 2 to determine, for each traffic stream, the route quality of each path using the center-of-gravity method. The paths are then ordered in decreas- ing order of route quality and, for each individual traffic relation. the best path is selected to route the calls for the next time period.

Application to the French Long Distance Network

uzzy adaptive routing was simulated in a model F of the transit part of the French long distance telephone network. In contrast to existing dynam- ically-routed networks where only one level of exchanges is considered, this network is composed of 80 secondary transit centers (STC), which are considered as origin-destination nodes in ou r study and five main transit centers (MTC)which are used as pure transit nodes. This results from a decision to introduce adaptive routing in the French long distance network in an evolutionary way when MTCs are still in place and used for the opera- tions of Intelligent Network services. Though this structure does not allow us to capture all the ben- efits of dynamic routing, studies carried out in the context of France Telecom’s work have shown that adaptive traffic routing still improves network performance and robustness.

The network has been engineered according to a nominal point-to-point traffic matrix cxtrapo- lated at the design stage from measurements made during busy hours of the previous year and from external forecasts. The total traffic load amounts to approximately 185,000 erlangs.

To analyze the performance of fuzzy adaptive routing, comparisons have been made with two other schemes: the fixed hierarchical routing still used

W Figure 4. Fuzzy routing system organization.

Figure 5 . a ) Hierarchical network; h ) adaptive network.

W Table 1. Rule base for inference engine 1 for the first application.

W Table 2. Rule base for in.ference engine 2.

today and the classical residual-capacity (or least loaded route) algorithm which considers only the maximum idle capacity, as mentioned in [ 7 , 1 1 , 121. For these comparisons, two networks were designed to support respectively fixed and adap- tive routing (Figs. Sa and Sb). The simulation tool we have used takes into account the subscriber behavior which is modeled considering the answer probability, the call repeat probability and an expo- nentially distributed time between re-attempts.

Traffic is first routed on direct circuit groups when they exist. In the fixed routingpolicy, overflow trafficisrouted on the final circuit groupwhile in the two other policies, it is adaptively routed on one of the five transit paths. If no direct circuit group exists betwecn two STCs. traffic is first routed o n a transit path with respect to fixed o r adaptive

IEEF Communications Magazine July I995 73

routing depending of the routing policy. In the adaptive schemes, routing is periodically updated according to measurements made in the network. Trunk reservation has been applied to protect fresh traffic (not using direct circuit groups) against traffic overflowing from direct circuit groups onto the STC-towards-MTC circuit groups. However i t should be noted that. in our case, since only traf- fic relations using two-link paths are affected by the trunk reservation mechanism, overall perfor- mance is not improved as in pure non-hierarchi- cal networks where trunk reservation allows us to give preference to traffic using a direct circuit group in case of congestion. However, this mech- anism is still a way to maintain a good grade of service for fresh traffic using two-link paths i n our study.

To analyze the robustness of fuzzy adaptive rout- ing with respect to the update interval, we varied the update period from ten seconds to one minute. In fact, the shorter this period, the more reliable the information [8]. However, collecting data at a high sampling rate is quite expensive. Then we havc to choose a trade-off between cost and per- formance [13].

To analyze the robustness with respect to net- workconditions, we studied the performance of fuzzy routing (Loss rate) under different network con- ditions. First, the behavior of the network was considered under nominal conditions to verify that the network is correctly engineered. We then analyzed the effect of daily traffic variations dur-

Figure 6. U ) Nominal-conditions performance; h) hii~~~-hoirl-performnrice.

ing busy hours on network performance. Finally we considered two cases when the network expe- riences traffic overloads ( f 10 and +20 percent) which represent typical traffic loads during peak times, such as New Year’s Eve.

Under nominal conditions, fuzzy routing pro- vides good performance and, as with the other schemes, the network meets the grade of service (GOS) constraint, i.e., 1 percent loss (Fig. ha). Note that since the COS requirement is by far mct, i t is not important that the fixed routing net- work behaves better than adaptive routing network, keeping in mind that the two different networks have been designed with different engineering rules. Dur- ing an average busy hour, the adaptively routed network behaves much better than the hierarchi- cal one which does not meet the GOS constraint (Fig. hb). This is mainly due to the adaptive nature of the routing policy ; moreover, the fuzzy routing system exhibits a better performance than the classical adaptive algorithm. T h e efficiency of both dccrcascs slightly when the update period increases. The impact on the update period o n performance has been studied [8], and i t has been shown tha t , fo r low blocking, network GOS degrades along with the ratio of the update period and the mean holding time.

During traffic overloads, t he efficiency of adaptive routing is even more significant and the degradation of the performance remains small when the update period increases (Figs. 7a and 7b). This is because any idle r e s o u r c e s b e c o m e exhausted in this situation. Here again, thc net- work acco m mod a t e s be t t e r t he traffic i nc re as c with the fuzzy approach than when using the clas- sical adaptive approach. Note that in these traffic conditions, the hierarchical network exhibits very poor performance due to the bad utilization of resources, creat ing user dissatisfaction which results in call reattempts and thercfore overload amplification.

The results described so far, though showing 21

significant impact of adaptive routing on network performance. do not demonstrate much benefit of the fuzzy approach as opposed to the classical residual-capacity approach. In fact, it should be emphasized that the maximum residual capacity decision criterion that was chosen in this prelimi- nary study is not the best indicator to be used in fuzzy adaptive routing; the reason for this is that the probability that a circuit group becomes satu- rated during an update cycle is not simply a decreas- ing function of the residual capacity. This is because thc offered traffic also has an influence on this pro b a b i 1 i ty . Thus , using the residual capacity to order the routes does not ensure call blocking minimization.

In o rde r to take the above into account, we have used, in a second set of simulations, a new indicator almost as simple as residual capacity, hut which should give better information on the possible saturat ion of the circuit group. This indicator is:

-~ ~

I , = 1 T I X

where, for each circuit group, T i s t he carr ied traffic and A’ is the residual capacity.

The rationale for this indicator is that, following the classical Poisson model, the standard devia-

74 IEEE Communications M a p r i n e Ju ly 1095

~ ~~~~

tion of the traffic is the square root of the mean. Thus, I , measures the possible fluctuations in the number of calls to be carried versus the number of idle c i rcui ts . T h e h igher I ,s , t h e h igher t h e probability that the circuit group saturates.

Additional simulations were done using a new fuzzy adaptive routing system that uses only this new indicator to characterize the circuit g roup availability. If the congestion probability is actual- ly an increasing function of I , , then, assuming that the membership values used in the fuzzification process are well defined, the indicator I , is as cffi- cient :is any other indicator. In particular, the level of performance should be close to those of algo- rithms, such as DR-5 [9], based on an explicit cal- culation of the impact of routing a call on circuit group congestion.

The use of this new criterion in our fuzzy adap- tive routing has an impact only on the first infer- ence engine of the controller system in Fig. 4, the second engine being unchanged. Because we use a single variable t o de te rmine the value of the availability, Avl, of ii circuit group, there is n o need for a decision table. The decision indicator I , is fuzzified order to characterize whether thc circui t g r o u p availability is Null. V e r ~ S m r r / l . Smdl. Mediiiin. or I ~ r g e .

Simulations have been carried o u t with the same network as previously with the only differ- ence being that the COS constraints were made morc stringent due to a recent management deci- sion. The network has therefore been redesigned t o meet the new GOS rcqui rements . W e have considered only adaptive routing schemes with longer update periods (from one to five minutes). For all the routing schemes. the grade of service is bet ter than the target o n e as an effect of the adaptive feature of the routing scheme. The use of the new criterion, I,, in the fuzzy adaptive rout- ing algorithm (Case D in Fig. 8) improves very significantly the performance compared to the pre- vious residual capacity and fuzzy routing methods (Cases A and B). In order to determine whether the improvement was due only to the new indica- tor, and to indicate what influence fuzzification had in that matter, anon-fuzzy routing algorithm based on I , was also tested (Case C). In this algorithm, if I,, and I , . are the saturation indicators of circuit groups i addj , then the saturation indicator of the route using i a n d j is Max(/, , I , ), and thc routing system chooses the route d t h 'the lowest satura- tion indicator.

For nominal and busy-hour conditions, it can be seen in Fig. 8 that for classical approaches, perfor- mance is almost insensitive to lengthening update cycles while for the new fuzzy routing method. networkloss increasessmoothly alongwith the update cycle for the reasons previously mentioned. In this la t ter case, results a r e still far be t te r than with the other methods.

For the case in which the I, criterion is used without a fuzzy control (Case C), the route avail- ability is equivalent t o the one of thc worst circuit group of the path and statistical variations are not taken into account (case C). Simulation results are then similar to those found with the classical algorithm using residual capacit ies (case A) . However, the I , indicator used in the fuzzy rout- ing context (case D) improves significantly the performance a s compared to the previous fuzzy rout-

_- __________-___ ________--

ing system (case B). Several reasons may justify the differences in performance: first, the philosophy of fuzzy logic is t o consider that , o n boundaries between two states, the evaluation is not sure and fuzzy theory (or possibility theory) allows us to decide on the most possible state according t o the inference. Second. the definition of several classes is ;I means t o discriminate availability levels in a rough way and thus to determine the best route for each traffic stream. Finally, the combination of fuzzy logic and an indicator taking into account the probabilistic variations of traffic may have an effcct on the dztermination of a robust routing control. The deep analysis of such results remains however an opcn field for future research.

These results show clearly the importance of 1 ) using an adequate indicator and 2) using rules associated with consistent membership functions of variables. on optimizing the performance of the routing method.

Conclusion h e application of fuzzy control t o adaptive T traffic routing in telephone networks is inves-

tigated in this article. W e use, on one hand, the properties of fuzzy control techniques and adap- tive routing, on the other hand, to derive a rout- ing system that is robust and efficient. We analyze the impact of various availability indicators o n performance. which indicates that the choice of a suitable indicator must be made to characterize circuit group availability. When used in the fuzzy c o n t r o l f r amework . t h e ind ica tor we use, I , , appears clearly to improve the performance of the routing algorithm as compared t o existing routing systems. On the o t h e r hand, the use of this indicator in a classical way appears to be of poor utility.

This study compares the performance of meth- ods usually applied to adaptive traffic routing and the fuzzy control approach and shows that the f u u y control approach could provide an effective framework for robust control of traffic routing in communications networks. Research studies still need to be carried out to develop fuzzy adaptive routing o n different network s t ructures and to evaluate its impact on performance.

Acknowledgments The authors are grateful to thc various reviewersfor their valuable comments.

IEEE communication^ M a p z i n e July IWS 75

- Fuzzy control could provide an eflective framework for robust control of traffic routing.

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~ _ _ _ _ ~

Biographies PROSPER CtiEMouii was graduated from the Ecole Nationale Superleure d e M e c a n i q u e d e Nantes a n d received a Docteur lngen ieur degree in control engineering in 1978 He spent one year a t the Universi ty o f Science and Technology o f Manchester, Un i ted K ingdom. i n 1979 and in 1980 he jo ined t h e Center Nat ional d 'Etudes d e Te lecommunica t ions (CNET), France Telecom's research center He is a member o f the teletraffic and planning section. where he has been involved w i th the modeling and con t ro l o f communications networks He is presently the head o f the network management and traffic engineering department He IS

also active at ITU-T as an associate rapporteur fo r the Network Management question and vice-chair of the Network Management Deve lopment G r o u p (NMDG) He is a senior m e m b e r o f t h e IEEE

JELILA KHALFET was graduated f rom Pierre et Marie Curie Universi- t y (Paris 6 University) where she received a DiplBme d'Etudes Approfondies i n Robotics in 1989 She is current ly f inal iz ing a Ph D on artificial intelligence at Paris 6 University w i t h a grant f r o m CNET The appl icat ion o f her research work is concerned w i th traffic control and has been carried ou t w i th in the network management and traffic engineering department at CNET She IS

presently a lecturer at the University of Evry France

MARC LEBOURGESwaSgradUated f rom the Ecole NationaleSuperieure des Telecommunications d e Paris in 1982 and received a Ph D in computer science f rom Paris VI University in 1992 From 1987 t o 1994. he was the supervisor o f a research group in traffic model i n 9 a t CNET. lssy les-Moul ineaux France He is n o w a t France Telecom s headquarters where he iscurrentlyinvolved ineconomical studies related t o interconnection and local loop regulations

76 IEEE Communications Maguine July 1Y9.5