In this paper, the transient solutions for M/G/1 queues with single server vacation and multiple server vacations are firstly studied, and the recursion expressions of their Laplace transform are given. Further the di...In this paper, the transient solutions for M/G/1 queues with single server vacation and multiple server vacations are firstly studied, and the recursion expressions of their Laplace transform are given. Further the distribution and stochastic decomposition result of the queue length at a random point in equilibrium are directly obtained from the transient solution. As will be seen this paper provides a intuitive and elegant method for studying transient solutions for M/G/1 queues with single server.展开更多
This paper studies the bulk-arrival M-x/G/1 queue with single server vacation. By introducing the server busy period and using the Laplace transform, the recursion expression of the Laplace transform of the transient ...This paper studies the bulk-arrival M-x/G/1 queue with single server vacation. By introducing the server busy period and using the Laplace transform, the recursion expression of the Laplace transform of the transient queue-length distribution is derived. Furthermore, the distribution and stochastic decomposition result of the queue length at a random point in equilibrium are obtained. Especially some results for the single-arrival M/G/1 queue with single server vacation and bulk-arrival M-x/G/1 queue but with no server vacation can be derived directly by the results obtained in this paper.展开更多
In this paper we study the transient and equilibrium distributions of the queue length for the M/G/1 queueing system with delay single server vacation.By the server busy period and the Laplace transformation we direct...In this paper we study the transient and equilibrium distributions of the queue length for the M/G/1 queueing system with delay single server vacation.By the server busy period and the Laplace transformation we directly obtain the recursion formula of the L transformation of the transient queue length distribution at any time t , as well as the recursion formula of the equilibrium distribution for calculating conveniently.Furthermore we obtain the stochastic decompositions of the queue length and waiting time in equilibrium.展开更多
文摘In this paper, the transient solutions for M/G/1 queues with single server vacation and multiple server vacations are firstly studied, and the recursion expressions of their Laplace transform are given. Further the distribution and stochastic decomposition result of the queue length at a random point in equilibrium are directly obtained from the transient solution. As will be seen this paper provides a intuitive and elegant method for studying transient solutions for M/G/1 queues with single server.
基金the National Outstanding Youth Science Foundation !(79725002) the Youth Science Foundation of UEST.
文摘This paper studies the bulk-arrival M-x/G/1 queue with single server vacation. By introducing the server busy period and using the Laplace transform, the recursion expression of the Laplace transform of the transient queue-length distribution is derived. Furthermore, the distribution and stochastic decomposition result of the queue length at a random point in equilibrium are obtained. Especially some results for the single-arrival M/G/1 queue with single server vacation and bulk-arrival M-x/G/1 queue but with no server vacation can be derived directly by the results obtained in this paper.
基金This work was supported by the National Outstanding Youth Science Foundation ( 7972 50 0 2 ) andthe Nature Education Minister
文摘In this paper we study the transient and equilibrium distributions of the queue length for the M/G/1 queueing system with delay single server vacation.By the server busy period and the Laplace transformation we directly obtain the recursion formula of the L transformation of the transient queue length distribution at any time t , as well as the recursion formula of the equilibrium distribution for calculating conveniently.Furthermore we obtain the stochastic decompositions of the queue length and waiting time in equilibrium.
