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

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.