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 logE exp ∑ i ciX n i (T ), where ci > 0 and T > 0 are constants, X n i denotes the class-i queue length process, and the number of arrivals and service completions per unit time are of order n. The main result is the asymptotic optimality, as n → ∞, of a priority policy, provided that ci 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 inter-arrival and service times. AMS subject classifications: 60F10, 60K25, 49N70, 93E20