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

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 Sigma(i) c(i) X-n(i) (T), where c(i) > 0 and T > 0 are constants, X-i(n) 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 -> infinity, 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.