Approximations for Product Departures from a Single-Server Station with Batch Processing in Multi-Product Queues
研究单服务器站点处理多类产品、固定批量大小为r的排队系统，给出平均任务数的估计和产品离开流的两种互补刻画，包括离开间隔的变异系数平方和批量大小概率分布的计算方法，适用于开放排队网络分解分析。
In this paper we consider a single-server station processing jobs belonging to multiple product classes. The processing at the station is in batches of fixed size, r. Job arrivals in different product classes are independent of the arrivals in other classes. The arrivals within each product class and the service times are assumed to have general, independent and identical distributions. Based on approximate analyses, we present an estimate for the mean number of jobs and provide two complementary characterizations of the product departure streams. We present methods to compute the squared coefficient of variation of the departure intervals and the probability distribution of the lot sizes of product departures. The computational results reported in this paper demonstrate that the accuracy of the approximations is acceptable in most applications. Based on these results, we identify conditions under which the estimates can be expected to perform well. The methods developed in this paper complement the decomposition approach for open queueing networks proposed by Shanthikumar and Buzacott (Shanthikumar, J. G., J. A. Buzacott. 1981. Open queueing network models of job shops. Internat. J. Production Res. 19(3) 255–266.) and Whitt (Whitt, W. 1983. The queueing network analyzer. Bell System Tech. J. 62(9) 2779–2815.) and permit analysis of networks with some types of batch processing.