Abstract
The performance evaluation of wireless networks is severely complicated by the specific features of radio communication, such as highly variable channel conditions, interference issues, and possible hand-offs among base stations. The latter elements have no natural counterparts in wireline scenarios, and create a need for novel performance models that account for the impact of these characteristics on the service rates of users.
Motivated by the above issues, we review several models for characterizing the capacity and evaluating the flow-level performance of wireless networks carrying elastic data transfers. We first examine the flow-level performance and stability of a wide family of so-called α-fair channel-aware scheduling strategies. We establish that these disciplines provide maximum stability, and describe how the special case of the Proportional Fair policy gives rise to a Processor-Sharing model with a state-dependent service rate. Next we turn attention to a network of several base stations with inter-cell interference. We derive both necessary and sufficient stability conditions and construct lower and upper bounds for the flow-level performance measures. Lastly we investigate the impact of user mobility that occurs on a slow timescale and causes possible hand-offs of active sessions. We show that the mobility tends to increase the capacity region, both in the case of globally optimal scheduling and local α-fair scheduling. It is additionally demonstrated that the capacity and user throughput improve with lower values of the fairness index α.
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References
Agrawal, R., Subramanian, V.: Optimality of certain channel-aware scheduling policies. In: Proc. 40th Annual Allerton Conf. Commun., Control, Comp., pp. 1532–1541 (2002)
Andrews, D.M.: Instability of the Proportional Fair scheduling algorithm for HDR. IEEE Trans. Wirel. Commun. 3, 1422–1426 (2004)
Andrews, D.M., Kumaran, K., Ramanan, K., Stolyar, A.L., Vijayakumar, R., Whiting, P.A.: Scheduling in a queueing system with asynchronously varying service rates. Probab. Eng. Inf. Sci. 18, 191–217 (2004)
Andrews, D.M., Qian, L., Stolyar, A.L.: Optimal utility-based throughput allocation subject to throughput constraints. In: Proc. Infocom 2005 (2005)
Bender, P., Black, P., Grob, M., Padovani, R., Sindhushayana, N., Viterbi, A.: CDMA/HDR: a bandwidth-efficient high-speed wireless data service for nomadic users. IEEE Commun. Mag. 38(7), 70–77 (2000)
Bonald, T.: A score-based opportunistic scheduler for fading radio channels. In: Proc. European Wireless Conf. 2004 (2004)
Bonald, T., Borst, S.C., Hegde, N., Proutière, A.: Wireless data performance in multi-cell scenarios. In: Proc. ACM Sigmetrics/Performance 2004, pp. 378–388 (2004)
Bonald, T., Borst, S.C., Proutière, A.: How mobility impacts the flow-level performance of wireless data systems. In: Proc. IEEE Infocom 2004 (2004)
Bonald, T., Borst, S.C., Proutière, A.: Inter-cell scheduling in wireless data networks. In: Proc. European Wireless Conf. 2005 (2005)
Bonald, T., Borst, S.C., Proutière, A.: Inter-cell coordination in wireless data networks. In:. Eur. Trans. Telecommun. 17, 303–312 (2006)
Bonald, T., Massoulié, L.: Impact of fairness on Internet performance. In: Proc. ACM Sigmetrics/Performance 2001, pp. 82–91 (2001)
Bonald, T., Massoulié, L., Proutière, A., Virtamo, J.: A queueing analysis of max-min fairness, proportional fairness and balanced fairness. Queueing Syst. 53, 65–84 (2003)
Bonald, T., Proutière, A.: Wireless downlink data channels: User performance and cell dimensioning. In: Proc. ACM Mobicom 2003, pp. 339–352 (2003)
Bonald, T., Proutière, A.: On performance bounds for the integration of elastic and adaptive streaming flows. In: Proc. ACM Sigmetrics/Performance 2004, pp. 235–245 (2004)
Bonald, T., Proutière, A.: Flow-level stability of utility-based allocations for non-convex rate regions. In: Proc. CISS 2006 (2006)
Bonald, T., Proutière, A., Régnié, G., Roberts, J.W.: Insensitivity results in statistical bandwidth sharing. In: de Souza, J.M., da Fonseca, N.L.S., de Souza e Silva, E.A. (eds.) Teletraffic Engineering in the Internet Era, Proc. ITC-17. Salvador da Bahia, pp. 125–136. North-Holland, Amsterdam (2001)
Borst, S.C.: User-level performance of channel-aware scheduling algorithms in wireless data networks. In: Proc. Infocom 2003 (2003)
Borst, S.C.: User-level performance of channel-aware scheduling algorithms in wireless data networks. IEEE/ACM Trans. Netw. 13, 636–647 (2005)
Borst, S.C.: Flow-level performance and user mobility in wireless data networks. Philos. Trans. R. Soc. A 366(1872), 2047–2058 (2008)
Borst, S.C., Hegde, N.: Integration of streaming and elastic traffic in wireless networks. In: Proc. Infocom 2007 (2007)
Borst, S.C., Hegde, N., Proutière, A.: Capacity of wireless networks with intra- and inter-cell mobility. In: Proc. Infocom 2006 (2006)
Borst, S.C., Hegde, N., Proutière, A.: Mobility-driven scheduling in wireless networks. In: Proc. Infocom 2009
Borst, S.C., Jonckheere, M.: Flow-level stability of channel-aware scheduling-algorithms. In: Proc. WiOpt ’06 (2006)
Borst, S.C., Jonckheere, M., Leskelä, L.: Stability of parallel queueing systems with coupled service rates. Discrete Event Dyn. Syst. 18, 447–472 (2008)
Borst, S.C., Whiting, P.A.: Dynamic rate control algorithms for HDR throughput optimization. In: Proc. Infocom 2001, pp. 976–985 (2001)
Borst, S.C., Whiting, P.A.: Dynamic channel-sensitive scheduling algorithms for wireless data throughput optimization. IEEE Trans. Veh. Techn. 52, 569–586 (2003)
Chaponniere, E.F., Black, P.J., Holtzman, J.M., Tse, D.N.C.: Transmitter directed code division multiple access system using path diversity to equitably maximize throughput. US Patent 6,449,490 (2002)
Cohen, J.W., Boxma, O.J.: Boundary Value Problems in Queueing System Analysis. North-Holland, Amsterdam (1983)
Cohen, J.W.: On a functional relation in three complex variables; three coupled processors. Technical Report 359, Mathematical Institute, University of Utrecht (1984)
Cohen, J.W.: The multiple phase service network with generalized processor sharing. Acta Inform. 12, 245–284 (1979)
Dai, J.G.: On positive Harris recurrence of multiclass queueing networks: A unified approach via fluid limit models. Ann. Appl. Probab. 5, 49–77 (1995)
Delcoigne, F., Proutière, A., Régnié, G.: Modelling integration of streaming and data traffic. Perform. Eval. 55, 185–209 (2004)
Fayolle, G., Iasnogorodski, R.: Two coupled processors: the reduction to a Riemann–Hilbert problem. Z. Wahr. Verw. Geb. 47, 325–351 (1979)
Georgiadis, L., Neely, M.J., Tassiulas, L.: Resource allocation and cross-layer control in wireless networks. Found. Trends Netw. 1, 1–144 (2006)
Grossglauser, M., Tse, D.N.C.: Mobility increases the capacity of ad hoc wireless networks. IEEE/ACM Trans. Netw. 10, 477–486 (2002)
Hansen, J., Reynolds, C., Zachary, S.: Stability of processor sharing networks with simultaneous resource requirements. J. Appl. Probab. 44, 636–651 (2007)
Jalali, A., Padovani, R., Pankaj, R.: Data throughput of CDMA-HDR a high efficiency–high data rate personal communication wireless system. In: Proc. IEEE VTC 2000 Spring Conf., pp. 1854–1858 (2000)
Jonckheere, M., Borst, S.C.: Stability of multi-class queueing systems with state-dependent service rates. In: Proc. ValueTools 2006, Pisa, Italy, October 11–13 (2006)
Jonckheere, M.: Stability of two interfering processors with load balancing. In: Proc. ValueTools 2008. Athens, Greece, October 20–24 (2008)
Kelly, F.P.: Reversibility and Stochastic Networks. Wiley, New York (1979)
Kelly, F.P., Maulloo, A., Tan, D.: Rate control for communication networks: Shadow prices, proportional fairness and stability. J. Oper. Res. Soc. 49, 237–252 (1998)
Key, P.B., Massoulié, L., Bain, A., Kelly, F.P.: Fair Internet traffic integration: network flow models and analysis. Ann. Telecommun. 59, 1338–1352 (2004)
Knopp, R., Humblet, P.A.: Information theory and power control in single-cell multi-user communications. In: Proc. ICC ’95 (1995)
Kushner, H.J., Whiting, P.A.: Convergence of Proportional-Fair sharing algorithms under general conditions. IEEE Trans. Wirel. Commun. 3, 1250–1259 (2004)
Lin, X., Shroff, N.B.: The impact of imperfect scheduling on cross-layer congestion control in wireless networks. IEEE/ACM Trans. Netw. 14, 302–315 (2006)
Lin, X., Shroff, N.B., Srikant, R.: On the connection-level stability of congestion-controlled communication networks. IEEE Trans. Inf. Theory 54, 2317–2338 (2008)
Litjens, R., Roijers, F., van den Berg, J.L., Boucherie, R.J., Fleuren, M.J.: Performance analysis of wireless LAN’s: an integrated packet/flow level approach. In: Charzinski, J., Lehnert, R., Tran Gia, P. (eds.) Providing QoS in Heterogeneous Environments, Proc. ITC-18, Berlin, pp. 931–940. North-Holland, Amsterdam (2003)
Liu, X., Chong, E.K.P., Shroff, N.B.: A framework for opportunistic scheduling in wireless networks. Comput. Netw. 41, 451–474 (2003)
Liu, J., Proutière, A., Yi, Y., Chiang, M., Poor, H.V.: Flow-level stability of data networks with non-convex and time-varying rate regions. In: Proc. ACM Sigmetrics 2007, pp. 239–250 (2007)
Massoulié, L.: Structural properties of proportional fairness: stability and insensitivity. Ann. Appl. Probab. 17, 809–839 (2007)
Meyn, S.P., Tweedie, R.L.: Markov Chains and Stochastic Stability. Springer, Berlin (1993)
Mo, J., Walrand, J.C.: Fair end-to-end window-based congestion control. IEEE/ACM Trans. Netw. 8, 556–567 (2000)
Müller, A., Stoyan, D.: Comparison Methods for Stochastic Models and Risks. Wiley, New York (2002)
Neely, M.J., Modiano, E., Li, C.-P.: Fairness and optimal stochastic control for heterogeneous networks. In: Proc. Infocom 2005 (2005)
Prakash, R., Veeravalli, V.V.: A time-scale separation technique for the analysis of random access systems with incremental redundancy. In: Proc. ISIT 2002 (2002)
Simatos, F., Tibi, D.: Spatial homogenization in a stochastic network with mobility. Ann. Appl. Probab. (to appear). http://arxiv.org/abs/0807.1205
Stolyar, A.L.: On the asymptotic optimality of the gradient scheduling algorithm for multi-user throughput allocation. Oper. Res. 53, 12–25 (2005)
Szpankowski, W.: Stability conditions for multidimensional queueing systems with computer applications. Oper. Res. 36, 944–957 (1988)
Szpankowski, W.: Stability conditions for some distributed systems: buffered random access systems. Adv. Appl. Probab. 26, 498–515 (1994)
Tassiulas, L., Ephremides, A.: Stability properties of constrained queueing systems and scheduling policies for maximum throughput in multihop radio networks. IEEE Trans. Automat. Contr. 37, 1936–1948 (1992)
Tassiulas, L., Ephremides, A.: Dynamic server allocation to parallel queues with randomly varying connectivity. IEEE Trans. Inf. Theory 30, 466–478 (1993)
Tchen, A.H.: Inequalities for distributions with given marginals. Ann. Appl. Probab. 8, 812–827 (1980)
Telatar, I.E., Gallager, R.G.: Combining queueing theory with information theory for multi-access. IEEE J. Sel. Areas Commun. 13, 963–969 (1995)
Viswanath, P., Tse, D.N.C., Laroia, R.: Opportunistic beam-forming using dumb antennas. IEEE Trans. Inf. Theory 48, 1277–1294 (2002)
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Bonald, T., Borst, S., Hegde, N. et al. Flow-level performance and capacity of wireless networks with user mobility. Queueing Syst 63, 131 (2009). https://doi.org/10.1007/s11134-009-9144-7
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DOI: https://doi.org/10.1007/s11134-009-9144-7
- Channel-aware scheduling
- Flow-level performance
- Processor sharing
- Proportional fair allocation
- Stability
- Transfer delay
- User mobility
- Wireless networks