On the non-Markovian multiclass queue under risk-sensitive cost

Abstract

This paper studies a control problem for the multiclass G/G/1 queue for a risk-sensitive cost of the form $n^{-1}\log E\exp \sum _ic_iX^n_i(T)$, where $c_i>0$ and $T>0$ are constants, $X^n_i$ denotes the class-i queue length process, and the numbers of arrivals and service completions per unit time are of order n. The main result is the asymptotic optimality, as $n\rightarrow \infty$, of a priority policy, provided that $c_i$ are sufficiently large. Such a result has been known only in the Markovian (M/M/1) case. The index which determines the priority is explicitly computed in the case of Gamma-distributed interarrival and service times.