## Journal of Applied Probability

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

### Utility optimization in congested queueing networks

#### 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