e consider a two-station tandem queue with no intermediate buffer. Jobs at the first station may be blocked when the following station is occupied by another job. The objective is to control the arrival and departure ...e consider a two-station tandem queue with no intermediate buffer. Jobs at the first station may be blocked when the following station is occupied by another job. The objective is to control the arrival and departure processes, subject to some capacity limits, so that an expected discounted profit function is maximized. We prove that the optimal control policy is of a threshold type, and the characterization of the threshold is provided.展开更多
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
文摘e consider a two-station tandem queue with no intermediate buffer. Jobs at the first station may be blocked when the following station is occupied by another job. The objective is to control the arrival and departure processes, subject to some capacity limits, so that an expected discounted profit function is maximized. We prove that the optimal control policy is of a threshold type, and the characterization of the threshold is provided.
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.
