Synchronous working vacation policy for finite-buffer multiserver queueing system
Synchronous working vacation policy for finite-buffer multiserver queueing system
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DOI：
10.1016/j.amc.2011.04.008
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发表时间：
2011-08
期刊：
影响因子：
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通讯作者：
Madhu Jain;Shweta Upadhyaya
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文献类型：
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作者：
Madhu Jain;Shweta Upadhyaya
本文对不可靠马尔可夫多服务器有限缓冲队列进行了建模和分析，并考虑了不可靠马尔可夫多服务器有限缓冲队列的激励和同步休假策略。根据该策略，服务器将继续为客户服务，直到空闲服务器的数量达到阈值水平；Thendidle服务器完全休假。在这些休假服务器中，dWservers可能会选择工作假期，即它们在假期期间以不同的费率为次要客户提供服务。另一方面，其余的d - dW= dvserver继续休假。在d台服务器休假期间，系统中必须存在其他c台服务器，即使它们处于空闲状态。休假结束返回时，如果队列大小没有超过，则这些服务器一起休假；否则就开始为顾客服务吧。在正常繁忙时段和工作休假时段，由于某个主控单元出现故障，服务器可能同时发生故障。然后由修理工最多在两个阶段对这个主要单元进行修理。我们得到了固定的性能指标，如期望队列长度、平均拒绝率和违约率、吞吐量等。分别采用矩阵解析法和基于四阶龙格-库塔方法的数值方法研究了到达的顾客和服务器的稳态和瞬态行为。通过对暂态模型进行敏感性分析，验证了分析结果的有效性，并检验了不同参数对各性能指标的影响。
This paper presents modeling and analysis of unreliable Markovian multiserver finite-buffer queue with discouragement and synchronous working vacation policy. According to this policy,cservers keep serving the customers until the number of idle servers reaches the threshold leveld; thendidle servers take vacation altogether. Out of these d vacationing servers,dWservers may opt for working vacation i.e. they serve the secondary customers with different rates during the vacation period. On the other hand, the remainingd−dW=dVservers continue to be on vacation. During the vacation of d servers, the othere=c−dservers must be present in the system even if they are idle. On returning from vacation, if the queue size does not exceede, then these d servers take another vacation together; otherwise start serving the customers. The servers may undergo breakdown simultaneously both in regular busy period and working vacation period due to the failure of a main control unit. This main unit is then repaired by the repairman in at most two phases. We obtain the stationary performance measures such as expected queue length, average balking and reneging rate, throughput, etc. The steady state and transient behaviours of the arriving customers and the servers are examined by using matrix analytical method and numerical approach based on Runge–Kutta method of fourth order, respectively. The sensitivity analysis is facilitated for the transient model to demonstrate the validity of the analytical results and to examine the effect of different parameters on various performance indices.