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.
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Research supported in part by the ISF (grant 1315/12)
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Atar, R., Mendelson, G. On the non-Markovian multiclass queue under risk-sensitive cost. Queueing Syst 84, 265–278 (2016). https://doi.org/10.1007/s11134-016-9503-0
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DOI: https://doi.org/10.1007/s11134-016-9503-0