本文考虑了具有破坏性和非破坏性服务中断的离散重试排队系统.两类中断都发生在顾客接受服务的过程中, 假设服务台在工作时发生破坏性中断,则正在接受服务的顾客中断服务,进入到重试空间中去,重新尝试以接受服务; 若服务台在工作时发生非破坏性中断, 则正在接受服务的顾客将等待中断结束后再继续完成剩余的服务量.求出了系统存在稳态的充分必要条件. 利用补充变量法,求出了系统稳态时系统和重试区域中队长分布的概率母函数, 以及其他一些重要的排队指标, 并且给出了对应的连续时间下具有两类服务中断的M/G/1排队的队长分布的概率母函数. 最后, 通过数值算例研究了各种参数对平均队长的影响.
Abstract
We consider a discrete queueing system with disruptive and non-disruptive server interruptions. Both disruptive and non-disruptive interruptions may start when there is a customer in service. If a disruptive interruption occur, the customer is obliged to join the orbit; Otherwise, if a non-disruptive interruption occur, the customer waits and contin-ues its service after a non-disruptive interruption. We analyze the equilibrium distribution of the system and obtain the generating functions of the limiting distribution. Moreover, we prover that M/G/1 retrial queue with two types of server interruptions. Finally, some numerical examples are presented.
关键词
离散重试排队 /
服务中断 /
不可靠服务台
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Key words
discrete-time retrial queue /
server interruptions /
unreliable server
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参考文献
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脚注
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基金
国家自然科学基金(NO.90820302)和安徽省高校省级自然科学研究重点项目(KJ2010A253).
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