Lattice path counting andM/M/c queueing systems |
| |
| Authors: | Kiyoshi Muto Haruo Miyazaki Yoichi Seki Yoshihiro Kimura Yukio Shibata |
| |
| Institution: | (1) Department of Computer Science, Gunma University, 1- 5- 1 Tenjin-cho, Kiryu, 376 Gunma, Japan;(2) SHARP Co., Hayakawa-cho, Yaita, 329-21 Tochigi, Japan |
| |
| Abstract: | We apply the lattice path counting method to the analysis of the transientM/M/c queueing system. A closed-form solution is obtained for the probability of exactlyi arrivals andj departures within a time interval of lengtht in anM/M/c queueing system that is empty at the initial time. The derivation of the probability is based on the counting of paths from the origin to(i,j) on thexy-plane, that have exactly rd x-steps whose depth from the liney=x isd (d=0,1,...,c–1). The closed-form solution has an expression useful for numerical calculation. |
| |
| Keywords: | M/M/c queue transient solution lattice path counting depth of path |
| 本文献已被 SpringerLink 等数据库收录！ |
|
