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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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