Electronic Communications in Probability

On the risk-sensitive cost for a Markovian multiclass queue with priority

Rami Atar, Anindya Goswami, and Adam Shwartz

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Abstract

A multi-class M/M/1 system, with service rate $\mu_in$ for class-$i$ customers, is considered with the risk-sensitive cost criterion $n^{-1}\log E\exp\sum_ic_iX^n_i(T)$, where $c_i>0$, $T>0$ are constants, and $X^n_i(t)$ denotes the class-$i$ queue-length at time $t$, assuming the system starts empty. An asymptotic upper bound (as $n\to\infty$) on the performance under a fixed priority policy is attained, implying that the policy is asymptotically optimal when $c_i$ are sufficiently large. The analysis is based on the study of an underlying differential game.

Article information

Source
Electron. Commun. Probab., Volume 19 (2014), paper no. 11, 13 pp.

Dates
Accepted: 27 February 2014
First available in Project Euclid: 7 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465316713

Digital Object Identifier
doi:10.1214/ECP.v19-2905

Mathematical Reviews number (MathSciNet)
MR3174829

Zentralblatt MATH identifier
1315.60096

Subjects
Primary: 60F10: Large deviations
Secondary: 60K25: Queueing theory [See also 68M20, 90B22] 49N70: Differential games 93E20: Optimal stochastic control

Keywords
Multi-class M/M/1 risk-sensitive control large deviations differential games

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

Atar, Rami; Goswami, Anindya; Shwartz, Adam. On the risk-sensitive cost for a Markovian multiclass queue with priority. Electron. Commun. Probab. 19 (2014), paper no. 11, 13 pp. doi:10.1214/ECP.v19-2905. https://projecteuclid.org/euclid.ecp/1465316713


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References

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