On the steady-state queue size distribution of the discrete-timeGeo/G/1 queue with repeated customers |
| |
Authors: | Tao Yang Hui Li |
| |
Institution: | (1) Department of Industrial Engineering, Technical University of Nova Scotia, B3J 2X4 Halifax, Nova Scotia, Canada;(2) Department of Mathematics, Mount Saint Vincent University, Halifax, Nova Scotia, Canada |
| |
Abstract: | In this paper, we study the steady-state queue size distribution of the discrete-timeGeo/G/1 retrial queue. We derive analytic formulas for the probability generating function of the number of customers in the system in steady-state. It is shown that the stochastic decomposition law holds for theGeo/G/1 retrial queue. Recursive formulas for the steady-state probabilities are developed. Computations based on these recursive formulas are numerically stable because the recursions involve only nonnegative terms. Since the regularGeo/G/1 queue is a special case of theGeo/G/1 retrial queue, the recursive formulas can also be used to compute the steady-state queue size distribution of the regularGeo/G/1 queue. Furthermore, it is shown that a continuous-timeM/G/1 retrial queue can be approximated by a discrete-timeGeo/G/1 retrial queue by dividing the time into small intervals of equal length and the approximation approaches the exact when the length of the interval tends to zero. This relationship allows us to apply the recursive formulas derived in this paper to compute the approximate steady-state queue size distribution of the continuous-timeM/G/1 retrial queue and the regularM/G/1 queue.Partially supported by the Natural Sciences and Engineering Research Council of Canada through grant OGP0046415.Partially supported by the Natural Sciences and Engineering Research Council of Canada through grant OGP0105828. |
| |
Keywords: | Discrete-time queues generating functions recursive computation retrial queues stochastic decomposition |
本文献已被 SpringerLink 等数据库收录! |
|