Flow-level Stability of Utility-Based Allocations for Non-Convex Rate Regions

We investigate the stability of utility-maximizing allocations in networks with arbitrary rate regions. We consider a dynamic setting where users randomly generate data flows according to some exogenous traffic processes. Network stability is then defined as the ergodicity of the process describing the number of active flows. When the rate region is convex, the stability region is known to coincide with the rate region, independently of the considered utility function. We show that for non-convex rate regions, the choice of the utility function is crucial to ensure maximum stability. The results are illustrated on the simple case of a wireless network consisting of two interacting base stations.

[1]  Mor Armony,et al.  Queueing networks with interacting service resources , 1999 .

[2]  Dimitri P. Bertsekas,et al.  Data Networks , 1986 .

[3]  Frank Kelly,et al.  Rate control for communication networks: shadow prices, proportional fairness and stability , 1998, J. Oper. Res. Soc..

[4]  Laurent Massoulié,et al.  A queueing analysis of max-min fairness, proportional fairness and balanced fairness , 2006, Queueing Syst. Theory Appl..

[5]  Gustavo de Veciana,et al.  Stability and performance analysis of networks supporting elastic services , 2001, TNET.

[6]  L. Massouli'e.  Structural properties of proportional fairness: Stability and insensitivity , 2007, 0707.4542.

[7]  Sean P. Meyn.  Transience of Multiclass Queueing Networks Via Fluid Limit Models , 1995 .

[8]  Steven H. Low,et al.  Optimization flow control—I: basic algorithm and convergence , 1999, TNET.

[9]  Xiaojun Lin,et al.  The Impact of Imperfect Scheduling on Cross-Layer Rate Control in Multihop Wireless Networks , 2022 .

[10]  Ao Tang,et al.  Is fair allocation always inefficient , 2004, IEEE INFOCOM 2004.

[11]  Frank Kelly,et al.  Charging and rate control for elastic traffic , 1997, Eur. Trans. Telecommun..

[12]  J. Dai.  On Positive Harris Recurrence of Multiclass Queueing Networks: A Unified Approach Via Fluid Limit Models , 1995 .

[13]  Nicholas Bambos,et al.  Queueing Dynamics and Maximal Throughput Scheduling in Switched Processing Systems , 2003, Queueing Syst. Theory Appl..

[14]  Ness B. Shroff,et al.  The impact of imperfect scheduling on cross-layer rate control in wireless networks , 2005, Proceedings IEEE 24th Annual Joint Conference of the IEEE Computer and Communications Societies..

[15]  Heng-Qing Ye,et al.  Stability of data networks under an optimization-based bandwidth allocation , 2003, IEEE Trans. Autom. Control..

[16]  Laurent Massoulié,et al.  Bandwidth sharing: objectives and algorithms , 2002, TNET.

[17]  Sem C. Borst,et al.  Wireless data performance in multi-cell scenarios , 2004, SIGMETRICS '04/Performance '04.

[18]  Laurent Massoulié,et al.  Impact of fairness on Internet performance , 2001, SIGMETRICS '01.

[19]  Jean C. Walrand,et al.  Fair end-to-end window-based congestion control , 2000, TNET.