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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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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

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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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