摘要
The two-stage tandem queueing system M(z)/M/c→/PH(r)/1/K is studied in this paper. Customers arrive at stage-Ⅰ system in batches according to a Poisson process, and the size of the batch, x , is a r. v. within a range of a finite number of positive integers. The stage- Ⅱ ststem has finite capacity, where customers are served in batches with a PH-distribution and the size of the batch is a positive integer r. Only after served in stage- Ⅰ system, and then served in stage- Ⅱ system, can the customers depart from the whole system. Several definitions such as the stage- Ⅰ service blocked time, the first-class and the second-class batch waiting times, and the batch sojourn time are introduced, and their distributions are obtained respectively.
The two-stage tandem queueing system M(z)/M/c→/PH(r)/1/K is studied in this paper. Customers arrive at stage-Ⅰ system in batches according to a Poisson process, and the size of the batch, x , is a r. v. within a range of a finite number of positive integers. The stage- Ⅱ ststem has finite capacity, where customers are served in batches with a PH-distribution and the size of the batch is a positive integer r. Only after served in stage- Ⅰ system, and then served in stage- Ⅱ system, can the customers depart from the whole system. Several definitions such as the stage- Ⅰ service blocked time, the first-class and the second-class batch waiting times, and the batch sojourn time are introduced, and their distributions are obtained respectively.
出处
《高校应用数学学报（A辑）》
CSCD
北大核心
1992年第3期422-432,共11页
Applied Mathematics A Journal of Chinese Universities(Ser.A)
基金
This paper is supported by the National Natural Science Foundation of China
关键词
排队系统
排队论
Two-stage Tandem Queueing System, Stage- I Service Blocked Time, The First-class Batch Waiting Time, The Second-class Batch Waiting Time, Batch Sojourn Time.
