A Duality Approach to Queues with Service Restrictions and Storage Systems with State-Dependent Rates
A Duality Approach to Queues with Service Restrictions and Storage Systems with State-Dependent Rates
复制标题
具有服务限制的队列和具有状态相关速率的存储系统的二元方法
DOI：
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发表时间：
2013
影响因子：
1
通讯作者：
S. Zacks
中科院分区：
文献类型：
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作者：
D. Perry;W. Stadje;S. Zacks
基于路径对偶结构，通过将工作负载（内容）过程转换为某些“双”M/G/1 类型过程，得出了关于 G/M/1 类型截断队列和存储系统的几个新结果。我们考虑排队系统，其中（a）任何会增加总工作量超出容量的服务要求都会被截断，以便将相关的停留时间保持在某一常数以下，或者（b）如果新到达者必须排队等待超过一个时间单位，则他们不会进入系统。对于这些系统，我们得出工作负载和系统中存在的客户数量的稳态分布，以及繁忙和空闲时段长度的分布。此外，我们使用对偶方法来研究具有一般状态相关流出率的有限容量存储系统。在这里，我们的对偶性导致了具有状态相关跳转大小的马尔可夫有限存储系统，其内容级别过程可以使用级别交叉技术进行分析。我们还推导了具有状态相关流出规则的 G/M/1 有限存储系统的非马尔可夫连续时间内容水平过程的稳态密度与相应的峰值点（局部最大值）嵌入序列之间的联系。
Based on pathwise duality constructions, several new results on truncated queues and storage systems of the G/M/1 type are derived by transforming the workload (content) processes into certain ‘dual’ M/G/1-type processes. We consider queueing systems in which (a) any service requirement that would increase the total workload beyond the capacity is truncated so as to keep the associated sojourn time below a certain constant, or (b) new arrivals do not enter the system if they have to wait more than one time unit in line. For these systems, we derive the steady-state distributions of the workload and the numbers of customers present in the systems as well as the distributions of the lengths of busy and idle periods. Moreover, we use the duality approach to study finite capacity storage systems with general state-dependent outflow rates. Here our duality leads to a Markovian finite storage system with state-dependent jump sizes whose content level process can be analyzed using level crossing techniques. We also derive a connection between the steady-state densities of the non-Markovian continuous-time content level process of the G/M/1 finite storage system with state-dependent outflow rule and the corresponding embedded sequence of peak points (local maxima).