Assembly-like queues with finite capacity: Bounds, asymptotics and approximations
Assembly-like queues with finite capacity: Bounds, asymptotics and approximations
复制标题
具有有限容量的类似组装的队列：界限、渐近和近似
DOI：
10.1007/bf01149328
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发表时间：
1986
期刊：
影响因子：
1.2
通讯作者：
B. Sengupta
中科院分区：
文献类型：
--
作者：
E. H. Lipper;B. Sengupta
在本文中，我们研究了装配式制造操作的装配模型。本研究的动机是在AT & T工厂的电路包测试程序的检查。然而，该模型可以代表许多制造装配操作。我们假设顾客从m类到达根据独立的泊松过程具有相同的到达率到一个单服务器的服务时间是指数分布的排队站。服务规程要求同时向一组客户提供服务，该组客户由每个类别中的一个成员组成。如果没有足够的客户组成一个组，服务器将处于空闲状态。属于同一类的客户有一个单独的等候区，等候区的大小对所有类都是一样的。顾客到达时发现他们的班级的等候区已经满了，他们迷路了。感兴趣的性能指标包括阻塞概率，吞吐量，平均队列长度和平均逗留时间。由于该离散系统的状态空间可能很大，因此即使是合理的参数值也不容易获得精确的答案。因此，我们着重于两种办法。首先，我们找到平均逗留时间的上界和下界。从这些界限，我们得到的渐近解的到达率（等候室，服务率）接近零（无穷大）。其次，对于这些参数的中等值，我们建议一个近似的解决方案。我们比较我们的近似模拟结果和报告良好的对应关系。
In this paper we study a queueing model of assembly-like manufacturing operations. This study was motivated by an examination of a circuit pack testing procedure in an AT & T factory. However, the model may be representative of many manufacturing assembly operations. We assume that customers fromn classes arrive according to independent Poisson processes with the same arrival rate into a single-server queueing station where the service times are exponentially distributed. The service discipline requires that service be rendered simultaneously to a group of customers consisting of exactly one member from each class. The server is idle if there are not enough customers to form a group. There is a separate waiting area for customers belonging to the same class and the size of the waiting area is the same for all classes. Customers who arrive to find the waiting area for their class full, are lost. Performance measures of interest include blocking probability, throughput, mean queue length and mean sojourn time. Since the state space for this queueing system could be large, exact answers for even reasonable values of the parameters may not be easy to obtain. We have therefore focused on two approaches. First, we find upper and lower bounds for the mean sojourn time. From these bounds we obtain the asymptotic solutions as the arrival rate (waiting room, service rate) approaches zero (infinity). Second, for moderate values of these parameters we suggest an approximate solution method. We compare the results of our approximation against simulation results and report good correspondence.