Le Routage Robuste Réactif Une combinaison de techniques d
Transcription
Le Routage Robuste Réactif Une combinaison de techniques d
Le Routage Robuste Réactif Une combinaison de techniques d’ingénierie de trafic proactives et réactives pour traiter le trafic dynamique de réseau Pedro Casas et Sandrine Vaton Séminaire des Doctorants de TELECOM Bretagne Brest, France, 27-28 mars 2008 TELECOM Bretagne Département Informatique Universidad de la República Facultad de Ingenierı́a Uruguay Pedro CASAS Séminaire des Doctorants de TELECOM Bretagne Outline 1 Introduction to the problem 2 A proactive approach: the Robust Routing 3 A reactive approach: Anomaly Detection/Localization 4 A combined approach: the Reactive Robust Routing 5 Conclusions and Perspectives Pedro CASAS Séminaire des Doctorants de TELECOM Bretagne Outline 1 Introduction to the problem 2 A proactive approach: the Robust Routing 3 A reactive approach: Anomaly Detection/Localization 4 A combined approach: the Reactive Robust Routing 5 Conclusions and Perspectives Pedro CASAS Séminaire des Doctorants de TELECOM Bretagne Routing Optimization (RO) in current network scenario Current network scenario: network convergence is a tangible reality heterogeneous services make network traffic uncertain and highly variable new kinds of network anomalies increase this traffic uncertainty Pedro CASAS Séminaire des Doctorants de TELECOM Bretagne Routing Optimization (RO) in current network scenario Current network scenario: network convergence is a tangible reality heterogeneous services make network traffic uncertain and highly variable new kinds of network anomalies increase this traffic uncertainty Routing performance under all possible network situations: expected traffic variations: routing optimization for expected traffic unexpected traffic variations (Anomalies): minimize impact on other QoS services between anomalies’ detection and resolution Pedro CASAS Séminaire des Doctorants de TELECOM Bretagne Routing Optimization (RO) in current network scenario Current network scenario: network convergence is a tangible reality heterogeneous services make network traffic uncertain and highly variable new kinds of network anomalies increase this traffic uncertainty Routing performance under all possible network situations: expected traffic variations: routing optimization for expected traffic unexpected traffic variations (Anomalies): minimize impact on other QoS services between anomalies’ detection and resolution Major challenge: ...how to optimize routing for an unknown traffic demand? Pedro CASAS Séminaire des Doctorants de TELECOM Bretagne RO in current scenario: a challenging task Sources of Demands Variation Unexpected Events Daily Periodic Usage Patterns Equipment Failures Network Attacks External Routing Changes Flash Crowds Spontaneous Services (P2P) Pedro CASAS Séminaire des Doctorants de TELECOM Bretagne RO in current scenario: a challenging task Sources of Demands Variation Unexpected Events Daily Periodic Usage Patterns Equipment Failures Network Attacks External Routing Changes Flash Crowds Spontaneous Services (P2P) Pedro CASAS Séminaire des Doctorants de TELECOM Bretagne RO in current scenario: a challenging task Sources of Demands Variation Unexpected Events Daily Periodic Usage Patterns Equipment Failures Network Attacks External Routing Changes Flash Crowds Spontaneous Services (P2P) Pedro CASAS Séminaire des Doctorants de TELECOM Bretagne RO in current scenario: a challenging task Sources of Demands Variation Unexpected Events Daily Periodic Usage Patterns Equipment Failures Network Attacks External Routing Changes Flash Crowds Spontaneous Services (P2P) Pedro CASAS Séminaire des Doctorants de TELECOM Bretagne RO in current scenario: a challenging task Sources of Demands Variation Unexpected Events Daily Periodic Usage Patterns Equipment Failures Network Attacks External Routing Changes Flash Crowds Spontaneous Services (P2P) Pedro CASAS Séminaire des Doctorants de TELECOM Bretagne RO in current scenario: a challenging task Sources of Demands Variation Unexpected Events Daily Periodic Usage Patterns Equipment Failures Network Attacks External Routing Changes Flash Crowds Spontaneous Services (P2P) Pedro CASAS Séminaire des Doctorants de TELECOM Bretagne RO in current scenario: a challenging task Sources of Demands Variation Unexpected Events Daily Periodic Usage Patterns Equipment Failures Network Attacks External Routing Changes Flash Crowds Spontaneous Services (P2P) Pedro CASAS Séminaire des Doctorants de TELECOM Bretagne RO in current scenario: a challenging task Sources of Demands Variation Unexpected Events Daily Periodic Usage Patterns Equipment Failures Network Attacks External Routing Changes Flash Crowds Spontaneous Services (P2P) Pedro CASAS Séminaire des Doctorants de TELECOM Bretagne Anomalies RO in current scenario: a challenging task Sources of Demands Variation Unexpected Events Daily Periodic Usage Patterns Equipment Failures Network Attacks External Routing Changes Flash Crowds Spontaneous Services (P2P) Pedro CASAS Séminaire des Doctorants de TELECOM Bretagne Anomalies Additional source of uncertainty traffic demands are rarely available: direct traffic measurements (e.g. CISCO Netflow) seldom available for every ingress/egress links. direct traffic measurements causes router overloading. measurements are generally conducted at a higher level of aggregation, rendering the traffic process non-observable. Pedro CASAS Séminaire des Doctorants de TELECOM Bretagne Examples of Variations in Real Data 10000 Link 47 Link 58 Link 104 Link 126 Correlated volume changes 9000 Link Load (unknown unit) 8000 Unidentifiable variations 7000 6000 5000 4000 3000 2000 1000 0 0 1000 2000 3000 4000 5000 6000 Time (min) 7000 8000 (a) Traffic patterns in a large Tier-2 network. Pedro CASAS Séminaire des Doctorants de TELECOM Bretagne 9000 10000 How to tackle the problem? Proactive approach: Robust Routing Techniques consider traffic uncertainty within the routing optimization. Sources of Traffic Variation Expected variations and small load changes under normal operation Daily Traffic Patterns Unexpected Events Emerging Challenges Multi Hour Robust Routing Network Attacks (DoS/DDoS) Reactive Robust Routing Pedro CASAS External Routing Modifications Flash Crowd Events Equipment Failures Spontaneous Overlay Services (P2P) Anomaly Detection and Localization Séminaire des Doctorants de TELECOM Bretagne How to tackle the problem? Reactive approach: Anomaly Detection and Localization anomaly detection and localization from simple measurements. parsimonious traffic modeling to overcome the non-observability problem. Sources of Traffic Variation Expected variations and small load changes under normal operation Daily Traffic Patterns Unexpected Events Emerging Challenges Multi Hour Robust Routing Network Attacks (DoS/DDoS) Reactive Robust Routing Pedro CASAS External Routing Modifications Flash Crowd Events Equipment Failures Spontaneous Overlay Services (P2P) Anomaly Detection and Localization Séminaire des Doctorants de TELECOM Bretagne How to tackle the problem? Combined approach: Reactive Robust Routing robust routing for usual network operation. anomaly detection/localization for the unexpected events. robust routing reconfiguration to minimize network congestion. anomalies’ end detection (automation of the routing process). Sources of Traffic Variation Expected variations and small load changes under normal operation Daily Traffic Patterns Unexpected Events Emerging Challenges Multi Hour Robust Routing Network Attacks (DoS/DDoS) Reactive Robust Routing Pedro CASAS External Routing Modifications Flash Crowd Events Equipment Failures Spontaneous Overlay Services (P2P) Anomaly Detection and Localization Séminaire des Doctorants de TELECOM Bretagne Outline 1 Introduction to the problem 2 A proactive approach: the Robust Routing 3 A reactive approach: Anomaly Detection/Localization 4 A combined approach: the Reactive Robust Routing 5 Conclusions and Perspectives Pedro CASAS Séminaire des Doctorants de TELECOM Bretagne A Proactive Approach The Boy Scout motto: Pedro CASAS Séminaire des Doctorants de TELECOM Bretagne A Proactive Approach The Boy Scout motto: Be Prepared!!! Stable Robust Routing robust Traffic Engineering techniques. consider traffic uncertainty in advance (robustness). Pedro CASAS Séminaire des Doctorants de TELECOM Bretagne The Stable Robust Routing (SRR) Problem formulation Consider the following network scenario: Network topology: n nodes. L = {1, . . . , r } links with capacities in C = (c1 , c2 , . . . , cr ). N = {OD1 , .., ODm=n(n−1) } Origin-Destination traffic flows. Routing matrix R = {rl,k ;l=1..r ,k =1..m }, 0 6 rl,k 6 1. P(k ) = {set of paths p for ODk }, k = 1..m. Traffic OD flows d = {di,j;i,j=1..n}; d = {dk , k =1..m } Links traffic (aggregated ODs traffic) y = {yl, l=1..r } y(t) = R × d(t) ∀t. Pedro CASAS Séminaire des Doctorants de TELECOM Bretagne The Stable Robust Routing Multipath Routing Optimization Given d, C, R and P(k), RO seeks to optimally balance d in P(k) to minimize some performance criterion: Pedro CASAS Séminaire des Doctorants de TELECOM Bretagne The Stable Robust Routing Multipath Routing Optimization Given d, C, R and P(k), RO seeks to optimally balance d in P(k) to minimize some performance criterion: umax (C, d, R) = max l∈{1...r } Pedro CASAS X rl,k · dk y = max l cl l∈{1...r } cl k Séminaire des Doctorants de TELECOM Bretagne The Stable Robust Routing Multipath Routing Optimization Given d, C, R and P(k), RO seeks to optimally balance d in P(k) to minimize some performance criterion: umax (C, d, R) = max l∈{1...r } X rl,k · dk y = max l cl l∈{1...r } cl k xpk , 0 6 xpk 6 1, fraction of dk in p ∈ P(k ) xlk , 0 6 xlk 6 1, fraction of dk in l ∈ p Pedro CASAS Séminaire des Doctorants de TELECOM Bretagne The Stable Robust Routing Multipath Routing Optimization Given d, C, R and P(k), RO seeks to optimally balance d in P(k) to minimize some performance criterion: umax (C, d, R) = max l∈{1...r } xpk , 0 6 xpk 6 1, fraction of dk in p ∈ P(k ) X rl,k · dk y = max l cl l∈{1...r } cl k minimize umax subject to: P xpk >1 ∀k ∈N 6 xlk ∀ (l, k ) ∈ (L, N) p∈P(k ) xlk , 0 6 xlk dk in l ∈ p 6 1, fraction of xpk P p∈P(k ), l∈p xlk .dk 6 umax · cl xpk , xlk >0 umax 61 P k ∈N Pedro CASAS Séminaire des Doctorants de TELECOM Bretagne ∀l∈L ∀ (l, k ) ∈ (L, N), ∀ p ∈ P(k ) The Stable Robust Routing Traffic uncertainty set and routing optimization Traffic d is uncertain → belongs to a polyhedral uncertainty set D: D = minimize subject to: P k xp p∈P(k ) P xpk p∈P(k ), l∈p P k xl .dk d ∈ Rm , R × d 6 ymax , d > 0 umax >1 ∀k ∈N 6 xlk ∀ k ∈ N, ∀ l ∈ L 6 umax · cl ∀ l ∈ L, ∀ d ∈ D k ∈N xpk , xlk umax >0 61 ∀ l ∈ L, ∀ p ∈ P(k ), ∀ k ∈ N Solved by a column and constraints generation method [BAK-05]. [BAK-05] W. Ben-Ameur and H. Kerivin, “Routing of Uncertain Traffic Demands”, Optimization and Engineering, 2005. Pedro CASAS Séminaire des Doctorants de TELECOM Bretagne Trade off in the size of the uncertainty set D d ∈ Rm , R × d 6 y4:00−18:00 , d>0 max = d ∈ Rm , R × d 6 y18:00−4:00 , d>0 max = DA DB 0.8 Maximum Link Utilization 0.7 Historical Routing Robust Routing B Robust Routing A 0.6 0.5 0.4 0.3 0.2 0.1 0 5:00 7:00 9:00 11:00 13:00 15:00 17:00 19:00 21:00 23:00 1:00 3:00 Time (hours) Remark: a single stable routing scheme for long-time periods results in sub-optimal performance. Pedro CASAS Séminaire des Doctorants de TELECOM Bretagne The Multi-Hour Robust Routing (MHRR) D1 Dt D2 β1 00:00 12:00 time β2 24:00 time β3 Idea: divide the uncertainty set to reduce cost (adapt the set) and consider a SRR configuration for each sub-set. Pedro CASAS Séminaire des Doctorants de TELECOM Bretagne The Multi-Hour Robust Routing (MHRR) D1 Dt D2 β1 00:00 12:00 time β2 24:00 time β3 Idea: divide the uncertainty set to reduce cost (adapt the set) and consider a SRR configuration for each sub-set. Partitioning hyperplane α.d = β. Pedro CASAS Séminaire des Doctorants de TELECOM Bretagne The Multi-Hour Robust Routing (MHRR) D1 Dt D2 β1 00:00 12:00 time β2 24:00 time β3 Idea: divide the uncertainty set to reduce cost (adapt the set) and consider a SRR configuration for each sub-set. Partitioning hyperplane α.d = β. The optimal division is generally NP-complex. Pedro CASAS Séminaire des Doctorants de TELECOM Bretagne The Multi-Hour Robust Routing (MHRR) D1 Dt D2 β1 00:00 12:00 time β2 24:00 time β3 Idea: divide the uncertainty set to reduce cost (adapt the set) and consider a SRR configuration for each sub-set. Partitioning hyperplane α.d = β. The optimal division is generally NP-complex. However, when the direction (α) is known, it can be approximately solved [BA-07]: in our case, we take the time direction [CV-07]. [BA-07] W. Ben-Ameur, “Between Fully Dynamic Routing and Robust Stable Routing”, DRCN, 2007. [CV-07] P. Casas and S. Vaton, “An Adaptive Multi-Temporal Approach for Robust Routing”, EuroFGI WIPQoS&TC, 2007. Pedro CASAS Séminaire des Doctorants de TELECOM Bretagne Some examples in Abilene 0.8 Historical Routing Stable Robust Routing A Stable Robust Routing B M−H Robust Routing Historical Routing Stable Robust Routing A Stable Robust Routing B M−H Robust Routing 0.7 0.6 0.4 Maximum Link Utilization Maximum Link Utilization 0.45 0.35 0.3 0.5 0.4 0.3 0.2 0.25 0.1 0.2 21:00 23:00 1:00 3:00 5:00 7:00 9:00 Time (hours) 11:00 13:00 17:00 19:00 21:00 (a) Expected daily behaviour 0 5:00 7:00 9:00 11:00 13:00 15:00 17:00 19:00 21:00 23:00 1:00 Time (hours) (b) Anomalous unexpected event Observation: the MHRR outperforms the SRR, but depends on a rough knowledge of the daily uncertainty set (we use it to improve routing for the expected traffic behavior in a robust fashion). Pedro CASAS 3:00 Séminaire des Doctorants de TELECOM Bretagne Outline 1 Introduction to the problem 2 A proactive approach: the Robust Routing 3 A reactive approach: Anomaly Detection/Localization 4 A combined approach: the Reactive Robust Routing 5 Conclusions and Perspectives Pedro CASAS Séminaire des Doctorants de TELECOM Bretagne Anomaly Detection/Localization The Problem Objectives: detect and localize an abrupt change in traffic demand d(t) from link load measurements y(t) = R × d(t). d(t) is seldom available. Conversely, link load measurements are highly spread. Problem: d(t) is non-observable directly from y(t). ill-posed problem r << m. Pedro CASAS Séminaire des Doctorants de TELECOM Bretagne Anomaly Detection/Localization Proposed methodology [FNS-07] Stochastic parsimonious linear model for anomaly-free traffic demand d(t) The anomaly-free is considered as a nuisance parameter. Hypothesis testing to detect/localize an anomaly in the traffic residuals (after removing the modeled traffic) [FNS-07] L. Fillatre, I. Nikiforov and S. Vaton, “Détection Localisation Séquentielle d’Anomalies Volumiques dans un Réseau”, GRETSI, 2007. Pedro CASAS Séminaire des Doctorants de TELECOM Bretagne Anomaly Detection/Localization Stochastic Traffic model The order of increasing anomaly-free OD flows remains constant during long-time periods. The values of the ordered OD flows can be decomposed over a spline-basis with a small number of components. d(t) λk (t) 1200 1000 800 600 400 200 k 0 2000 140 120 1500 tim 1000 et (mi 500 n) 100 80 60 40 0 20 0 Small flows Large flows Medium-size flows Approximation of real OD flows by the spline-based model Pedro CASAS Séminaire des Doctorants de TELECOM Bretagne Anomaly Detection/Localization Stochastic Traffic model Model for the anomaly-free traffic: d(t) = Sµ(t) + ξ(t) ξ(t) is a white Gaussian noise with covariance matrix Σ(t). S = (s1 s2 . . . sq ), is a splines basis that describes the traffic spatial distribution. µ(t) = (µ1 (t) . . . µq (t))T ∈ Rq , with q << m. the coefficients µk (t) describe the anomaly-free intensity variations. Pedro CASAS Séminaire des Doctorants de TELECOM Bretagne Anomaly Detection/Localization Stochastic Traffic model Anomaly-free model for y(t): y(t) = Hµ(t) + ζ(t) H = RS ∈ Rr ×q , small no columns → easy to retrieve µ(t) from y(t). ζ(t)’s covariance is estimated from samples. the anomaly-free traffic is eliminated by projecting y(t) into the null space of H. Pedro CASAS Séminaire des Doctorants de TELECOM Bretagne Anomaly Detection/Localization Detection/localization of volume anomaly at time t0 as a multiple hypothesis testing: H0 = {the OD flows are anomaly-free} S Hj = t0 =1..∞ Htj0 , with Htj0 = {the j-th OD flow presents an anomalous traffic from an unknown change time t0 } compute (T , ν), T is the alarm time at which a ν-type change (ν ∈ {1, 2, . . . , m}) is detected and localized. Pedro CASAS Séminaire des Doctorants de TELECOM Bretagne Anomaly Detection/Localization Detection/localization is conducted on the residuals obtained from link load observations, after filtering the anomaly-free traffic. Optimal recursive algorithm with well-established optimality properties in terms of detection delay and false alarm rate [IN-00]. Optimal trade-off between the worst case of the average detection delay (E(T )), the false alarm rate and the false localization probabilities. Multiple recursive detection and decision functions. [IN-00] I. Nikiforov, “A Simple Recursive Algorithm for Diagnosis of Abrupt Changes in Random Signals”, IEEE Trans. on IT, 2000. Pedro CASAS Séminaire des Doctorants de TELECOM Bretagne Anomaly Detection/Localization 50 15 45 10 40 5 Alarm on OD flow 87 Level of alarm 0 35 −5 30 st (i) gt (i, 0) Another example in Abilene Anomaly begins 25 −10 −15 20 −20 15 −25 10 −30 5 0 −35 1020 1030 1040 1050 1060 1070 Time t (min) (a) Recursive detection functions −40 1020 1030 1040 1050 1060 1070 Time t (min) (b) Decision functions Figure: Typical realizations of decision functions in Abilene. Pedro CASAS Séminaire des Doctorants de TELECOM Bretagne Outline 1 Introduction to the problem 2 A proactive approach: the Robust Routing 3 A reactive approach: Anomaly Detection/Localization 4 A combined approach: the Reactive Robust Routing 5 Conclusions and Perspectives Pedro CASAS Séminaire des Doctorants de TELECOM Bretagne The Reactive Robust Routing Combination of the reactive and the proactive approaches [CFS-08]. MHRR to handle usual-traffic and small changes in traffic demands in a robust and efficient way. Anomaly Detection/Localization algorithm to deal with unexpected events. Exploits the localization ability to compute an adapted SRR after the detection, based on an expansion of the uncertainty set [PLS-08]. Detects the end of the anomaly (if applicable) and takes back the MHRR configuration. [CFV-08] P. Casas, L. Fillatre and S. Vaton, “Multi-Hour Robust Routing and Fast Load Change Detection for Traffic Engineering”, IEEE ICC, 2008. [PLS-08] P. Casas, L. Fillatre and S. Vaton, “Robust and Reactive Traffic Engineering for Dynamic Demands”, EuroNGI, 2008. Pedro CASAS Séminaire des Doctorants de TELECOM Bretagne Routing reconfiguration yimax + θR i,k D : Before the anomaly yhmax + θR h,k 0 D : After the anomaly yjmax + θR j,k before the anomaly: Pedro CASAS D = {R . d 6 ymax } Séminaire des Doctorants de TELECOM Bretagne Routing reconfiguration yimax + θR i,k yhmax + θR h,k D : Before the anomaly 0 D : After the anomaly yjmax + θR j,k D = {R . d 6 ymax } θ = θ.δ k anomaly in OD flow k : d∗ = d + θ, δ k = (δ1,k , .., δm,k )T , δi,k = Ii=k before the anomaly: Pedro CASAS Séminaire des Doctorants de TELECOM Bretagne Routing reconfiguration yimax + θR i,k D : Before the anomaly yhmax + θR h,k 0 D : After the anomaly yjmax + θR j,k D = {R . d 6 ymax } θ = θ.δ k anomaly in OD flow k : d∗ = d + θ, δ k = (δ1,k , .., δm,k )T , δi,k = Ii=k before the anomaly: 0 after the anomaly: D = {R . d 6 ymax + R . θ} Pedro CASAS Séminaire des Doctorants de TELECOM Bretagne Routing reconfiguration yimax + θR i,k D : Before the anomaly yhmax + θR h,k 0 D : After the anomaly yjmax + θR j,k D = {R . d 6 ymax } θ = θ.δ k anomaly in OD flow k : d∗ = d + θ, δ k = (δ1,k , .., δm,k )T , δi,k = Ii=k before the anomaly: 0 after the anomaly: D = {R . d 6 ymax + R . θ} 0 robust routing reconfiguration, using D as the uncertainty set (expansion of the uncertainty set). Pedro CASAS Séminaire des Doctorants de TELECOM Bretagne Anomalies’ end detection The detection algorithm focuses in the abnormal OD flow k after the routing reconfiguration. Two simple hypotheses: Ha : {the OD flow k is abnormal} Hb : {the OD flow k presents a usual behavior} simple Neyman-Pearson’s test (most powerful test for 2 simple hypotheses): ∆(z(t)) = log f0 (z(t)) − h > 0 −→ Hb fk (z(t)) The decision threshold h is fixed according to the prescribed false alarm probability. Pedro CASAS Séminaire des Doctorants de TELECOM Bretagne Reactive Robust Routing evaluation Multi-Hour Robust Routing, adapted to the expected traffic demand. Anomaly detection/localization in OD flow k = 63 at time t = 1135. Robust routing reconfiguration. Detection of the anomaly’s end at time t = 1353. Return to the MHRR configuration. Pedro CASAS Séminaire des Doctorants de TELECOM Bretagne Reactive Robust Routing evaluation 80 0.8 ∆(z(t)), k = 63 HR 0.7 40 Maximum Link Utilization ∆(z(t)) 60 k -th anomaly ends 20 0 SRR A SRR B MHRR 0.6 RRR 0.5 0.4 0.3 replacements −20 1200 1250 1300 1350 Time t (min) 1400 (a) Neyman-Pearson Test ∆(z(t)) Pedro CASAS 0.2 1020 1070 1120 1170 1220 1270 1320 1370 Time t (min) (b) Performance evaluation Séminaire des Doctorants de TELECOM Bretagne 1420 Reactive Robust Routing evaluation 0.8 HR Maximum Link Utilization 0.7 SRR A SRR B MHRR 0.6 RRR 0.5 0.4 0.3 0.2 1020 1070 1120 1170 1220 1270 1320 1370 1420 Time t (min) between 20% and 50% of utilization improvement w.r.t. the stable robust routing approach Pedro CASAS Séminaire des Doctorants de TELECOM Bretagne Outline 1 Introduction to the problem 2 A proactive approach: the Robust Routing 3 A reactive approach: Anomaly Detection/Localization 4 A combined approach: the Reactive Robust Routing 5 Conclusions and Perspectives Pedro CASAS Séminaire des Doctorants de TELECOM Bretagne Conclusions of this work Robust TE techniques can not deal by themselves with traffic uncertainty, but they should be used in current traffic scenario. We have shown that reactive and proactive techniques can work together to improve the treatment of large volume anomalies. Decision theory offers powerful and promising techniques for the automation of diagnosis in the field of network anomaly detection (still in the very early stage). Pedro CASAS Séminaire des Doctorants de TELECOM Bretagne Future directions exploit the linear parsimonious traffic model for further studies (d(t) becomes observable, many problems can be solved). use this traffic model for the traffic matrix estimation problem, tracking of traffic demands from simple link measurements, etc. consider other performance criterion for the optimization problem. Pedro CASAS Séminaire des Doctorants de TELECOM Bretagne Thank You for Your Attention!! Remarks & Questions? Pedro CASAS Séminaire des Doctorants de TELECOM Bretagne