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 ran...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.展开更多
基金This paper is supported by the National Natural Science Foundation of China
文摘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.
