On the risk-sensitive cost for a Markovian multiclass queue with priority
On the risk-sensitive cost for a Markovian multiclass queue with priority
复制标题
具有优先级的马尔可夫多类队列的风险敏感成本
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
A. Shwartz
中科院分区：
文献类型：
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作者：
R. Atar;Anindya Goswami;A. Shwartz
考虑一个多类别的M/M/1系统，对类别- $i$的客户的服务率为$\mu_in$，使用风险敏感成本准则$n^{-1}\log E\exp\sum_ic_iX^n_i(T)$，其中$c_i>0$、$T>0$是常量，$X^n_i(t)$表示类别- $i$在时间$t$时的队列长度，假设系统开始时为空。得到了固定优先级策略下性能的渐近上界（如$n\to\infty$），这意味着当$c_i$足够大时，策略是渐近最优的。这一分析是基于对一个潜在微分博弈的研究。
A multi-class M/M/1 system, with service rate $\mu_in$ for class-$i$ customers, is considered with the risk-sensitive cost criterion $n^{-1}\log E\exp\sum_ic_iX^n_i(T)$, 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 $c_i$ are sufficiently large. The analysis is based on the study of an underlying differential game.