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

A multi-class M/M/1 system, with service rate μ_in for class-i customers, is considered with the risk-sensitive cost criterion n^-1log E exp∑_ic_iXⁿ_i(T), where c_i>0, T>0 are constants, and Xⁿ_i(t) denotes the class-i queue-length at time t, assuming the system starts empty. An asymptotic upper bound (as n→∞) 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.