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Published in:
18-10-2016
On the non-Markovian multiclass queue under risk-sensitive cost
Published in: Queueing Systems | Issue 3-4/2016
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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.