Heavy-Traffic Optimality of a Stochastic Network Under Utility-Maximizing Resource Allocation

Published Online:https://doi.org/10.1287/opre.1070.0455

References

  • Bertsekas D., Gallager R.Data Networks (1992) (Prentice-Hall, Englewood Cliffs, NJ) Google Scholar
  • Billingsley P.Convergence of Probability Measures (1999) 2nd ed.(John Wiley & Sons, New York) CrossrefGoogle Scholar
  • Bonald T., Massoulie L. Impact of fairness on Internet performance. Proc. ACM Sigmetrics (2001) (Cambridge, MA)82–91CrossrefGoogle Scholar
  • Bramson M. State space collapse with application to heavy traffic limits for multiclass queueing networks. Queueing Systems, Theory Appl. (1998) 30:89–148CrossrefGoogle Scholar
  • Chen H., Yao D. D.Fundamentals of Queueing Networks: Performance, Asymptotics, and Optimization (2001) (Springer-Verlag, New York) CrossrefGoogle Scholar
  • Chen H., Ye H. Q. Existence condition for the diffusion approximations of priority multiclass queueing networks. Queueing Systems, Theory Appl. (2001) 38:435–470CrossrefGoogle Scholar
  • Chen H., Zhang H. Diffusion approximations for Kumar-Seidman network under a priority service discipline. Oper. Res. Lett. (1998) 23:171–181CrossrefGoogle Scholar
  • Chen H., Zhang H. A sufficient condition and a necessary condition for the diffusion approximations of multiclass queueing networks under priority service disciplines. Queueing Systems, Theory Appl. (2000) 34:237–268CrossrefGoogle Scholar
  • Dai J. G. On positive Harris recurrence of multiclass queueing networks: A unified approach via fluid limit models. Ann. Appl. Probab. (1995) 5:49–77CrossrefGoogle Scholar
  • de Veciana G., Lee T. J., Konstantopoulos T. Stability and performance analysis of networks supporting elastic services. IEEE/ACM Trans. Networking (2001) 9:2–14CrossrefGoogle Scholar
  • Fayolle G., de La Fortell A., Lasgouttes J.-M., Massoulié L., Roberts J. Best-effort networks: Modeling and performance analysis via large networks asymptotics. Proc. IEEE INFOCOM (2001) Anchorage, AK:709–716CrossrefGoogle Scholar
  • Harrison J. M. Brownian models of open processing networks: Canonical representation of workload. Ann. Appl. Probab. (2000) 10:75–103CrossrefGoogle Scholar
  • Harrison J. M. A broader view of Brownian networks. Ann. Appl. Probab. (2003) 13(3):1119–1150CrossrefGoogle Scholar
  • Harrison J. M., López M. J. Heavy traffic resource pooling in parallel-server systems. Queueing Systems Theory Appl. (1999) 33:339–368CrossrefGoogle Scholar
  • Harrison J. M., Van Mieghem J. A. Dynamic control of Brownian networks: State space collapse and equivalent workload formulations. Ann. Appl. Probab. (1997) 7:747–771CrossrefGoogle Scholar
  • Kelly F. P. Blocking probabilities in large circuit-switched networks. Adv. Appl. Probab. (1986) 18:473–505CrossrefGoogle Scholar
  • Kelly F. P. Routing in circuit-switched networks: Optimization, shadow prices and decentralization. Adv. Appl. Probab. (1988) 20:112–144CrossrefGoogle Scholar
  • Kelly F. P. Charging and rate control for elastic traffic. Eur. Trans. Telecomm. (1997) 29:1009–1016Google Scholar
  • Kelly F. P., Engquist B., Schmid W. Mathematical modeling of the Internet. Mathematics Unlimited—2001 and Beyond (2001) (Springer-Verlag, Berlin, Germany) 685–702CrossrefGoogle Scholar
  • Kelly F. P., Laws C. N. Dynamic routing in open queueing networks: Brownian models, cut constraints and resource pooling. Queueing Systems, Theory Appl. (1993) 13:47–86CrossrefGoogle Scholar
  • Kelly F. P., Williams R. J. Fluid model for a network operating under a fair bandwidth-sharing policy. Ann. Appl. Probab. (2004) 14:1055–1083CrossrefGoogle Scholar
  • Kelly F. P., Maulloo A., Tan D. Rate control in communication networks: Shadow prices, proportional fairness and stability. J. Oper. Res. Soc. (1998) 49:237–252CrossrefGoogle Scholar
  • Laws C. N. Resource pooling in queueing networks with dynamic routing. Adv. Appl. Probab. (1992) 24:699–726CrossrefGoogle Scholar
  • Low S. A duality model of TCP and queue management algorithms. IEEE/ACM Trans. Networking (2003) 11(4):525–536CrossrefGoogle Scholar
  • Mandelbaum A., Stolyar A. L. Scheduling flexible servers with convex delay costs: Heavy-traffic optimality of the generalized cμ-rule. Oper. Res. (2004) 52(6):836–855LinkGoogle Scholar
  • Massoulie L., Roberts J. W. Bandwidth sharing: Objectives and algorithms. Proc. IEEE INFOCOM (1999) (New York)1395–1403CrossrefGoogle Scholar
  • Massoulie L., Roberts J. W. Bandwidth sharing and admission control for elastic traffic. Telecomm. Systems (2000) 15:185–201CrossrefGoogle Scholar
  • Mo J., Walrand J. C. Fair end-to-end window-based congestion control. IEEE/ACM Trans. Networking (2000) 8:556–567CrossrefGoogle Scholar
  • Ross K. W.Multiservice Loss Models for Broadband Telecommunication Networks (1995) (Springer-Verlag, New York) CrossrefGoogle Scholar
  • Rudin W.Real and Complex Analysis (1987) 3rd ed.(McGraw-Hill, New York) Google Scholar
  • Stolyar A. L. Max-weight scheduling in a generalized switch: State space collapse and workload minimization in heavy traffic. Ann. Appl. Probab. (2004) 14:1–53CrossrefGoogle Scholar
  • Stolyar A. L. On the asymptotic optimality of the gradient scheduling algorithm for multi-user throughput allocation. Oper. Res. (2005) 53:12–25LinkGoogle Scholar
  • Wen J. T., Arcak M. A unifying passivity framework for network flow control. IEEE Trans. Automatic Control (2004) 49(2):162–174CrossrefGoogle Scholar
  • Whitt W. Blocking when service is required from several facilities simultaneously. AT&T Tech. J. (1985) 64:1807–1856CrossrefGoogle Scholar
  • Williams R. J., McDonald D. R., Turner S. R. E. On dynamic scheduling of a parallel server system with complete resource pooling. Analysis of Communication Networks: Call Centres, Traffic and Performance (2000) 28(Fields Institute Communications, American Mathematical Society, Providence, RI) 49–71CrossrefGoogle Scholar
  • Ye H. Q. Stability of data networks under an optimization-based bandwidth allocation. IEEE Trans. Automatic Control (2003) 48(7):1238–1242CrossrefGoogle Scholar
  • Ye H. Q., Ou J., Yuan X. M. Stability of data networks: Stationary and bursty models. Oper. Res. (2005) 53(1):107–125LinkGoogle Scholar
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