Journal of Applied Probability

Utility optimization in congested queueing networks

N. S. Walton

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

We consider a multiclass single-server queueing network as a model of a packet switching network. The rates packets are sent into this network are controlled by queues which act as congestion windows. By considering a sequence of congestion controls, we analyse a sequence of stationary queueing networks. In this asymptotic regime, the service capacity of the network remains constant and the sequence of congestion controllers act to exploit the network's capacity by increasing the number of packets within the network. We show that the stationary throughput of routes on this sequence of networks converges to an allocation that maximises aggregate utility subject to the network's capacity constraints. To perform this analysis, we require that our utility functions satisfy an exponential concavity condition. This family of utilities includes weighted α-fair utilities for α > 1.

Article information

Source
J. Appl. Probab., Volume 48, Number 1 (2011), 68-89.

Dates
First available in Project Euclid: 15 March 2011

Permanent link to this document
https://projecteuclid.org/euclid.jap/1300198137

Digital Object Identifier
doi:10.1239/jap/1300198137

Mathematical Reviews number (MathSciNet)
MR2809888

Zentralblatt MATH identifier
1223.60079

Subjects
Primary: 90B15: Network models, stochastic 60K25: Queueing theory [See also 68M20, 90B22]
Secondary: 90B22: Queues and service [See also 60K25, 68M20] 90B18: Communication networks [See also 68M10, 94A05]

Keywords
Utility optimization queueing network quasi-reversible large deviation congestion window congestion control

Citation

Walton, N. S. Utility optimization in congested queueing networks. J. Appl. Probab. 48 (2011), no. 1, 68--89. doi:10.1239/jap/1300198137. https://projecteuclid.org/euclid.jap/1300198137


Export citation

References

  • Asmussen, S. (2003). Applied Probability and Queues (Appl. Math. 51), 2nd edn. Springer, New York.
  • Bonald, T. and Massoulié, L. (2001). Impact of fairness on internet performance. In ACM SIGMETRICS Performance Evaluation Review (Proc. SIGMETRICS 2001), Association for Computing Machinery, New York, pp. 82–91.
  • Bonald, T. and Proutière, A. (2004). On performance bounds for balanced fairness. Performance Evaluation 55, 25–50.
  • Dembo, A. and Zeitouni, O. (1998). Large Deviations Techniques and Applications (Appl. Math. 38), 2nd edn. Springer, New York.
  • Eryilmaz, A. and Srikant, R. (2007). Fair resource allocation in wireless networks using queue-length-based scheduling and congestion control. IEEE/ACM Trans. Networking 15, 1333–1344.
  • Ganesh, A., O'Connell, N. and Wischik, D. (2004). Big Queues (Lecture Notes Math. 1838). Springer, Berlin.
  • Johari, R. and Tan, D. K. H. (2001). End-to-end congestion control for the internet: delays and stability. IEEE/ACM Trans. Networking 9, 818–832.
  • Kelly, F. P. (1979). Reversibility and Stochastic Networks. John Wiley, Chicester.
  • Kelly, F. P. (1982). Networks of quasireversible nodes. In Applied Probability–-Computer Science: the Interface, Vol. 1, Birkhäuser, Boston, MA, pp. 3–29.
  • Kelly, F. P. (1989). On a class of approximations for closed queueing networks. Queueing Systems 4, 69–76.
  • Kelly, F. P. (1997). Charging and rate control for elastic traffic. Europ. Trans. Telecommun. 8, 33–37.
  • Kelly, F. P. (2003). Fairness and stability of end-to-end congestion control. Europ. J. Control 9, 159–176.
  • Kelly, F. P., Massoulié, L. and Walton, N. S. (2009). Resource pooling in congested networks: proportional fairness and product form. Queueing Systems 63, 165–194.
  • Kelly, F., Maulloo, A. and Tan, D. (1998). Rate control in communication networks: shadow prices, proportional fairness and stability. J. Operat. Res. Soc. 49, 237–252.
  • Kunniyur, S. S. and Srikant, R. (2003). Stable, scalable, fair congestion control and AQM schemes that achieve high utilization in the internet. IEEE Trans. Automatic Control 48, 2024–2029.
  • Massoulié, L. and Roberts, J. W. (1998). Bandwidth sharing and admission control for elastic traffic. Telecommun. Systems 15, 185–201.
  • Massoulié, L. and Roberts, J. (1999). Bandwidth sharing: objectives and algorithms. IEEE/ACM Trans. Networking 10, 320–328.
  • Mo, J. and Walrand, J. (2000). Fair end-to-end window-based congestion control. IEEE/ACM Trans. Networking 8, 556–567.
  • Pittel, B. (1979). Closed exponential networks of queues with saturation: the Jackson-type stationary distribution and its asymptotic analysis. Math. Operat. Res. 4, 357–378.
  • Schweitzer, P. J. (1979). Approximate analysis of multiclass closed networks of queues. In Proc. Intern. Conf. Stochastic Control and Optimization, pp. 25–29.
  • Srikant, R. (2004). The Mathematics of Internet Congestion Control. Birkhäuser, Boston, MA.
  • Stolyar, A. L. (2005). Maximizing queueing network utility subject to stability: greedy primal-dual algorithm. Queueing Systems 50, 401–457.
  • Vojnovic, M., Le Boudec, J.-Y. and Boutremans, C. (2000). Global fairness of additive-increase and multiplicative-decrease with heterogeneous round-trip times. In Proc. INFOCOM 2000 (March 2000), pp. 1303–1312.
  • Walton, N. S. (2009). Proportional fairness and its relationship with multi-class queueing networks. Ann. Appl. Prob. 19, 2301–2333.