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

**Rami Atar**

*(Technion - Israel Institute of Technology)*

**Anindya Goswami**

*(IISER Pune)*

**Adam Shwartz**

*(Technion - Israel Institute of Technology)*

#### 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.

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Pages: 1-13

Publication Date: February 27, 2014

DOI: 10.1214/ECP.v19-2905

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