On finite capacity queues with time dependent arrival rates |
| |
Authors: | Xiaoqian Tan Charles Knessl Yongzhi Yang |
| |
Affiliation: | 1. Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, 851 South Morgan Street, Chicago, IL 60607-7045, United States;2. Department of Mathematics, University of St. Thomas, 2115 Summit Ave., St. Paul, MN 55105-1079, United States |
| |
Abstract: | We consider the finite capacity M/M/1−K queue with a time dependent arrival rate λ(t). Assuming that the capacity K is large and that the arrival rate varies slowly with time (as t/K), we construct asymptotic approximations to the probability of finding n customers in the system at time t, as well as the mean number. We consider various time ranges, where the system is nearly empty, nearly full, or is filled to a fraction of its capacity. Extensive numerical studies are used to back up the asymptotic analysis. |
| |
Keywords: | Time-dependent queues Asymptotics Finite capacity |
本文献已被 ScienceDirect 等数据库收录! |
|