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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.

MSC:
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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