The GI/M/1 queue with exponential vacations |
| |
Authors: | Naishou Tian Daqing Zhang Chengxuan Cao |
| |
Institution: | (1) Department of Mathematics, Jiamusi Teachers' College, Heilongjiang Province, People's Republic of China |
| |
Abstract: | In this paper, we give a detailed analysis of the GI/M/1 queue with exhaustive service and multiple exponential vacation. We express the transition matrix of the imbedded Markov chain as a block-Jacobi form and give a matrix-geometric solution. The probability distribution of the queue length at arrival epochs is derived and is shown to decompose into the distribution of the sum of two independent random variables. In addition, we discuss the limiting behavior of the continuous time queue length processes and obtain the probability distributions for the waiting time and the busy period. |
| |
Keywords: | GI/M/1 queue vacation queue length matrix geometric solution semi Markov process stable distribution decomposition |
本文献已被 SpringerLink 等数据库收录! |