R. Albert, H. Jeong, and A. Baraba´sibaraba´si, Error and attack tolerance of complex networks, Nature, vol.1696, issue.6794, pp.378-382, 2000.
DOI : 10.1038/35019019

E. Altman, Stochastic recursive equations with applications to queues with dependent vacations, Annals of Operations Research, vol.112, issue.1/4, pp.43-61, 2002.
DOI : 10.1023/A:1020972803727

E. Altman, On stochastic recursive equations and infinite server queues, Proceedings IEEE 24th Annual Joint Conference of the IEEE Computer and Communications Societies., 2005.
DOI : 10.1109/INFCOM.2005.1498355
URL : https://hal.archives-ouvertes.fr/inria-00070782

E. Altman, C. Barakat, and K. Avratchenkov, A stochastic model of TCP/IP with stationary ergodic random losses, ACM-Sigcomm, 2000.
URL : https://hal.archives-ouvertes.fr/inria-00072834

E. Altman, T. Jimenez, and D. Kofman, DPS queues with stationary ergodic service times and the performance of TCP in overload, IEEE INFOCOM 2004, 2004.
DOI : 10.1109/INFCOM.2004.1356984

E. Altman, P. Konstantopoulos, and Z. Liu, Stability, monotonicity and invariant quantities in general polling systems, Queueing Systems, vol.40, issue.1-2, pp.35-57, 1992.
DOI : 10.1007/BF01159286

N. Bansal and Z. Liu, Capacity, delay and mobility in wireless ad-hoc networks, IEEE INFOCOM 2003. Twenty-second Annual Joint Conference of the IEEE Computer and Communications Societies (IEEE Cat. No.03CH37428), 2003.
DOI : 10.1109/INFCOM.2003.1208990

A. Baraba´sibaraba´si and R. Albert, Emergence of scaling in random networks, Science, vol.286, pp.509-512, 1999.

A. Baraba´sibaraba´si, R. Albert, H. Jeong, and G. Bianconi, Power-law distribution of the world wide web, Science, p.287, 2000.

C. Bettstetter, Mobility modeling in wireless networks, ACM SIGMOBILE Mobile Computing and Communications Review, vol.5, issue.3, pp.55-67, 2001.
DOI : 10.1145/584051.584056

C. Bettstetter, H. Hartenstein, and X. Pérez-costa, Stochastic properties of the random waypoint mobility model, Kluwer Wireless Networks: Special Issue on Modelling and Analysis of Wireless Networks, pp.555-567, 2004.

C. Bettstetter, G. Resta, and P. Santi, The node distribution of the random waypoint mobility model for wireless ad hoc networks, IEEE Transactions on Mobile Computing, vol.2, issue.3, 2003.
DOI : 10.1109/TMC.2003.1233531

C. Bettstetter and C. Wagner, The spatial node distribution of the random waypoint mobility model, Proceedings First German Workshop Mobile Ad-Hoc Networks (WMAN), pp.41-58, 2002.

S. Bhulai, Markov Decision Processes: the Control of High-dimensional Systems, 2002.

S. Bhulai and G. Koole, On the structure of value functions for threshold policies in queueing models, Journal of Applied Probability, vol.40, issue.03, pp.613-622, 2003.
DOI : 10.1007/BF01158935

T. Bonald, M. Jonckheere, and A. Proutì-ere, Insensitive load balancing, ACM SIGMETRICS Performance Evaluation Review, vol.32, issue.1, pp.367-377, 2004.
DOI : 10.1145/1012888.1005729
URL : https://hal.archives-ouvertes.fr/hal-01284237

T. Bonald, A. Proutì-ere, G. Régnié, and J. W. Roberts, Insensitivity results in statistical bandwidth sharing, ITC, number 17, 2001.
DOI : 10.1016/S1388-3437(01)80116-5

B. Brewin, Delta has success in rfid baggage tag test, Computerworld, 2003.

L. William, . Briggs, . Van-emden, and . Henson, The DFT. An Owner's Manual for the Discrete Fourier Transform, SIAM. Society for Industrial & Applied Mathematics, 1995.

J. Broch, D. A. Maltz, D. B. Johnson, Y. Hu, and J. Jetcheva, A performance comparison of multi-hop wireless ad hoc network routing protocols, Proceedings of the 4th annual ACM/IEEE international conference on Mobile computing and networking , MobiCom '98, pp.85-97, 1998.
DOI : 10.1145/288235.288256

F. Clévenot, P. Nain, and K. Ross, Stochastic fluid models for cache clusters, Performance Evaluation, vol.59, issue.1, pp.1-18, 2005.
DOI : 10.1016/j.peva.2004.05.006

L. Comtet, Advanced Combinatorics: The Art of Finite and Infinite Expansions, D. Reidel, 1974.
DOI : 10.1007/978-94-010-2196-8

R. B. Cooper, S. Niu, M. Mandyam, and . Srinivasan, A Decomposition Theorem for Polling Models: The Switchover Times are Effectively Additive, Operations Research, vol.44, issue.4, pp.629-633, 1996.
DOI : 10.1287/opre.44.4.629

R. Durrett, Probability: Theory and Examples, 1991.
DOI : 10.1017/CBO9780511779398

M. Eisenberg, Queues with Periodic Service and Changeover Time, Operations Research, vol.20, issue.2, pp.440-451, 1972.
DOI : 10.1287/opre.20.2.440

B. J. Feder, Delta to invest in radio tags for luggage at airports. The New York Times, 2004.

B. J. Feder and . Psst, This is your sensor. Your grapes are thirsty. The New York Times, 2004.

W. Feller, An Introduction to Probability Theory and its Applications, 1950.

R. Frenkiel, B. R. Badrinath, J. Borras, and R. Yates, The Infostations challenge: balancing cost and ubiquity in delivering wireless data, IEEE Personal Communications, vol.7, issue.2, pp.66-71, 2000.
DOI : 10.1109/98.839333

S. W. Fuhrmann and R. B. Cooper, /1 Queue with Generalized Vacations, Operations Research, vol.33, issue.5, pp.1117-1129, 1985.
DOI : 10.1287/opre.33.5.1117

J. Gamal, B. Mammen, D. Prabhakar, and . Shah, Throughputdelay trade-off in wireless networks, Proc. of IEEE Infocom Conf., Hong Kong, 2004.

C. W. Gardiner, Handbook of Stochastic Processes, 1985.

Z. Ge, D. Figueiredo, S. Jaiswal, J. F. Kurose, and D. Towsley, Modeling peer-peer file sharing systems, IEEE INFOCOM 2003. Twenty-second Annual Joint Conference of the IEEE Computer and Communications Societies (IEEE Cat. No.03CH37428), pp.1312-1321, 2003.
DOI : 10.1109/INFCOM.2003.1209239
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.12.3320

I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series, and Products, 1983.

H. Green, Sensor revolution: Bugging the world; soon, sensor networks will track everything from weather to inventory, Business Week, 2003.

R. Groenevelt and E. Altman, Analysis of alternating-priority queueing models with (cross) correlated switchover times, 2004.

R. Groenevelt and E. Altman, Analysis of alternating-priority queueing models with (cross) correlated switchover times, Proc. of IEEE Infocom 2005, 2005.

R. Groenevelt, E. Altman, and P. Nain, Relaying in mobile ad hoc networks, Proc. of Workshop on Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks UK, 2004.
URL : https://hal.archives-ouvertes.fr/inria-00070689

R. Groenevelt, G. Koole, and P. Nain, On the bias vector of a two-class preemptive priority queue, Mathematical Methods of Operations Research (ZOR), vol.55, issue.1, pp.107-120, 2002.
DOI : 10.1007/s001860200175

R. Groenevelt, P. Nain, and G. Koole, The message delay in mobile ad hoc networks, Performance Evaluation, vol.62, issue.1-4, 2004.
DOI : 10.1016/j.peva.2005.07.018

R. Groenevelt, P. Nain, and G. Koole, The message delay in mobile ad hoc networks, To appear as an extended abstract in the proceedings of ACM Sigmetrics, 2005.
DOI : 10.1016/j.peva.2005.07.018

M. Grossglauser and D. Tse, Mobility increases the capacity of ad hoc wireless networks, This paper has also been published in the Proceedings of IEEE INFOCOM 2001 where it received the best paper award, pp.477-486, 2002.
DOI : 10.1109/TNET.2002.801403

R. A. Guérin, Channel occupancy time distribution in a cellular radio system, IEEE Transactions on Vehicular Technology, vol.36, issue.3, pp.89-99, 1987.
DOI : 10.1109/T-VT.1987.24106

P. Gupta and P. R. Kumar, The capacity of wireless networks, IEEE Transactions on Information Theory, vol.46, issue.2, pp.388-404, 2000.
DOI : 10.1109/18.825799

Y. Han, R. J. La, A. M. Makowski, and S. Lee, Distribution of path durations in mobile ad-hoc networks ? palm's theorem at work. Submitted to Special Issue of, Computer Networks Journal on Network Modeling and Simulation, 2004.

J. M. Harrison, A Priority Queue with Discounted Linear Costs, Operations Research, vol.23, issue.2, pp.260-269, 1975.
DOI : 10.1287/opre.23.2.260

G. Hooghiemstra and G. Koole, On the convergence of the power series algorithm, Performance Evaluation, vol.42, issue.1, pp.21-39, 2000.
DOI : 10.1016/S0166-5316(99)00081-4

E. Hyytiä, P. Lassila, L. Nieminen, and J. Virtamo, Spatial node distribution of the random waypoint mobility model with applications, IEEE Transactions on Mobile Computing, vol.5, issue.6, 2004.
DOI : 10.1109/TMC.2006.86

E. Hyytiä and J. Virtamo, Random waypoint model in n-dimensional space, 2005.

K. Itô, On stochastic differential equations. Memoirs, pp.1-51, 1951.

A. Jean-marie and P. Robert, On the transient behaviour of the processor sharing queue, QUESTA, vol.17, issue.12, pp.129-136, 1994.

B. David, . Johnson, A. David, and . Maltz, Dynamic source routing in ad hoc wireless networks, Mobile Computing, 1996.

D. B. Johnson and D. A. Maltz, Dynamic Source Routing in Ad Hoc Wireless Networks, Mobile Computing, vol.353, pp.151-181, 1996.
DOI : 10.1007/978-0-585-29603-6_5

L. Kleinrock, Queueing Systems, Volume I: Theory, volume I, 1976.

G. Koole, CONVEXITY IN TANDEM QUEUES, Probability in the Engineering and Informational Sciences, pp.13-31, 2004.
DOI : 10.1017/S0269964804181023

G. Koole and P. Nain, On the value function of a priority queue with an application to a controlled polling model, Queueing Systems, vol.34, issue.1/4, pp.199-214, 2000.
DOI : 10.1023/A:1019109103725

G. Koole and P. Nain, An Explicit Solution for the Value Function of a Priority Queue, Queueing Systems, vol.47, issue.3, pp.251-282, 2004.
DOI : 10.1023/B:QUES.0000035315.17476.0b

Q. Li and D. Rus, Sending messages to mobile users in disconnected ad-hoc wireless networks, Proceedings of the 6th annual international conference on Mobile computing and networking , MobiCom '00, 2000.
DOI : 10.1145/345910.345918

D. Nain, N. Petigara, and H. Bakakrishnan, Integrated Routing and Storage for Messaging Applications in Mobile Ad Hoc Networks, the Proc. of Workshop on Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks (WiOpt'03), pp.595-604, 2004.
DOI : 10.1023/B:MONE.0000042498.60917.e8
URL : https://hal.archives-ouvertes.fr/inria-00466607

P. Nain, D. Towsley, B. Liu, and Z. Liu, Properties of random direction models, Proceedings IEEE 24th Annual Joint Conference of the IEEE Computer and Communications Societies., 2005.
DOI : 10.1109/INFCOM.2005.1498468
URL : https://hal.archives-ouvertes.fr/inria-00070716

W. Navidi and T. Camp, Stationary distributions for the random waypoint mobility model, IEEE Transactions on Mobile Computing, vol.3, issue.1, pp.99-108, 2004.
DOI : 10.1109/TMC.2004.1261820

T. Ozawa, An analysis for multi-queueing systems with cyclic-service discipline -models with exhaustive and gated services, IEICE), 1987.

M. L. Puterman, Markov Decision Processes, 1994.
DOI : 10.1002/9780470316887

S. Redner, A Guide to First-Passage Processes, 2001.

P. Nain, R. Groenevelt, and G. Koole, Message delay in mobile ad hoc networks, Proceedings of Performance, Juan-les-Pins, 2005.

R. Sedgewick and P. Flajolet, An Introduction to the Analysis of Algorithms, 1996.

G. Sharma and R. R. Mazumdar, Delay and capacity trade-offs for wireless ad hoc networks with random mobility, 2004.

G. Sharma and R. R. Mazumdar, Scaling laws for capacity and delay in wireless ad hoc networks with random mobility, 2004 IEEE International Conference on Communications (IEEE Cat. No.04CH37577), 2004.
DOI : 10.1109/ICC.2004.1313277

T. Small and Z. Haas, The shared wireless infostation model -a new ad hoc networking paradigm (or where there is a whale, there is a way), Proc. of ACM International Symposium on Mobile Ad Hoc Networking and Computing (Mobihoc), 2003.

R. P. Stanley, Enumerative Combinatorics, volume II Page 221-247 are available at http://wwwmath, 2001.

J. S. Sykes, Simplified Analysis of an Alternating-Priority Queuing Model with Setup Times, Operations Research, vol.18, issue.6, pp.1182-1192, 1970.
DOI : 10.1287/opre.18.6.1182

V. Syrotiuk and C. J. Colbourn, Routing in mobile aerial networks, Proc. of Workshop on Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks (WiOpt'03), 2003.
URL : https://hal.archives-ouvertes.fr/inria-00466673

H. Takagi, Analysis of polling systems, Performance Evaluation, vol.5, issue.3, 1986.
DOI : 10.1016/0166-5316(85)90016-1

H. Takagi, Queueing analysis of polling models: An update. Stochastic Analysis of Computer and Communication Systems, pp.267-318, 1990.

H. Takagi, Queueing Analysis, Vacations and Priority Systems, Part 1 The Netherlands, 1991.

T. J. Ott and K. R. Krishnan, Separable routing: A scheme for state-dependent routing of circuit switched telephone traffic, Annals of Operations Research, vol.35, issue.1, pp.43-68, 1992.
DOI : 10.1007/BF02023090

N. G. Van-kampen, Stochastic Processes in Physics and Chemistry. North-Holland, 1997.

J. Duncan, S. Watts, and . Strogatz, Collective dynamics of small-world networks, Nature, vol.393, pp.440-442, 1998.

G. H. Weiss, Aspects and Applications of the Random Walk, Random Materials and Processes. Elsevier Science B.V, 1994.

J. Yoon, M. Liu, and B. Noble, Random waypoint considered harmful, IEEE INFOCOM 2003. Twenty-second Annual Joint Conference of the IEEE Computer and Communications Societies (IEEE Cat. No.03CH37428), pp.1312-1321, 2003.
DOI : 10.1109/INFCOM.2003.1208967

R. M. Young, Euler's constant, Math.Gazette, vol.472, pp.187-190, 1975.

R. D. Wing-ho-yuen, S. Yates, and . Mau, Exploiting data diversity and multiuser diversity in noncooperative mobile infostation networks, Proc. of IEEE Infocom Conf, 2003.

W. Zhao and M. Ammar, Message ferrying: Proactive routing in highly-partioned wireless ad hoc networks, Proc. of the 9th IEEE Workshop on Future Trends in Distributed Computed Systems (FTDCS'03), 2003.

G. Zussman, U. Yechiali, and A. Segall, Exact Probabilistic Analysis of the Limited Scheduling Algorithm for Symmetrical Bluetooth Piconets, Personal Wireless Communications (PWC), 2003.
DOI : 10.1007/978-3-540-39867-7_29

. Dans-lapremì-ere-partie-de-cette-thèse, nousétudionsnousétudions la mobilité dans les réseaux ad hoc mobiles Plus précisément, nousétudionsnousétudions le temps de transfert d'un message, défini commé etant le temps requis pour transmettre un message d'un noeudànoeud`noeudà un autre noeud, en utilisantéventuellementutilisantéventuellement d'autres noeuds comme relais . Dans un premier temps, pour plusieurs modèles de mobilité, nous trouvons le temps requis afin que deux noeuds puissent communiquer. Dans undeuxì eme temps