Analysis of the queue-length distribution for the discrete-time batch-service Geo/G(a,Y)/1/K queue

作者：Yi Xeung W; Kim Nam K; Yoon Bong K^*; Chae Kyung C

来源：European Journal of Operational Research, 2007, 181(2): 787-792.

DOI：10.1016/j.ejor.2006.08.016

• queueing
• discrete time
• batch service
• variable service capacity
• finite waiting capacity
• queue length

In this paper, we consider a discrete-time finite-capacity queue with Bernoulli arrivals and batch services. In this queue, the single server has a variable service capacity and serves the customers only when the number of customers in system is at least a certain threshold value. For this queue, we first obtain the queue-length distribution just after a service completion, using the embedded Markov chain technique. Then we establish a relationship between the queue-length distribution just after a service completion and that at a random epoch, using elementary 'rate-in = rate-out' arguments. Based on this relationship, we obtain the queue-length distribution at a random (as well as at an arrival) epoch, from which important performance measures of practical interest, such as the mean queue length, the mean waiting time, and the loss probability, are also obtained. Sample numerical examples are presented at the end.

• 出版日期2007-9-1
• 单位中国人民解放军国防大学