## Stochastic Systems

- Stoch. Syst.
- Volume 6, Number 2 (2016), 251-300.

### Asymptotic behavior of a critical fluid model for a processor sharing queue via relative entropy

Amber L. Puha and Ruth J. Williams

#### Abstract

In this paper, we develop a new approach to studying the asymptotic behavior of fluid model solutions for critically loaded processor sharing queues. For this, we introduce a notion of relative entropy associated with measure-valued fluid model solutions. In contrast to the approach used in [12], which does not readily generalize to networks of processor sharing queues, we expect the approach developed in this paper to be more robust. Indeed, we anticipate that similar notions involving relative entropy may be helpful for understanding the asymptotic behavior of critical fluid model solutions for stochastic networks operating under various resource sharing protocols naturally described by measure-valued processes.

#### Article information

**Source**

Stoch. Syst., Volume 6, Number 2 (2016), 251-300.

**Dates**

Received: July 2015

First available in Project Euclid: 22 March 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.ssy/1490148013

**Digital Object Identifier**

doi:10.1214/15-SSY198

**Mathematical Reviews number (MathSciNet)**

MR3633537

**Zentralblatt MATH identifier**

1359.60113

**Subjects**

Primary: 60K25: Queueing theory [See also 68M20, 90B22] 60F17: Functional limit theorems; invariance principles

Secondary: 60G57: Random measures 68M20: Performance evaluation; queueing; scheduling [See also 60K25, 90Bxx] 90B22: Queues and service [See also 60K25, 68M20]

**Keywords**

Queueing processor sharing critical fluid model fluid model asymptotics relative entropy

**Rights**

Creative Commons Attribution 4.0 International License.

#### Citation

Puha, Amber L.; Williams, Ruth J. Asymptotic behavior of a critical fluid model for a processor sharing queue via relative entropy. Stoch. Syst. 6 (2016), no. 2, 251--300. doi:10.1214/15-SSY198. https://projecteuclid.org/euclid.ssy/1490148013