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On the risk-sensitive cost for a Markovian multiclass queue with priority. (English) Zbl 1315.60096
Summary: A multi-class \(\mathrm{M}/\mathrm{M}/1\) system, with service rate \(\mu_i n\) for class-\(i\) customers, is considered with the risk-sensitive cost criterion \(n^{-1}\log E\exp\sum_i c_iX^n_i(T)\), where \(c_i>0, T>0\) are constants, and \(X^n_i(t)\) denotes the class-\(i\) queue-length at time \(t\), assuming the system starts empty. An asymptotic upper bound (as \(n\to\infty\)) on the performance under a fixed priority policy is attained, implying that the policy is asymptotically optimal when the \(c_i\) are sufficiently large. The analysis is based on the study of an underlying differential game.

60K25 Queueing theory (aspects of probability theory)
60F10 Large deviations
49N70 Differential games and control
93E20 Optimal stochastic control
90B22 Queues and service in operations research
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