Journal of Applied Mathematics and Stochastic Analysis 
Volume 9 (1996), Issue 2, Pages 143-157
doi:10.1155/S1048953396000159

M/G/1/K system with push-out scheme under vacation policy

Shoji Kasahara,1 Hideaki Takagi,2 Yutaka Takahashi,3 and Toshiharu Hasegawa3

 1Kyoto University, Educational Center for Information Processing, Kyoto 606-01, Japan
2University of Tsukuba, Institute of Socio-Economic Planning, 1-1-1 Tennoudai, Tsukuba-shi, Ibaraki 305, Japan
3Kyoto University, Department of Applied Mathematics and Physics, Faculty of Engineering, Kyoto 606-01, Japan
Received 1 July 1995; Revised 1 November 1995

Abstract

We consider an M/G/1/K system with push-out scheme and multiple vacations. This model is particularly important in situations where it is essential to provide short waiting times to messages which are selected for service. We analyze the behavior of two types of messages: one that succeeds in transmission and the other that fails. We derive the Laplace-Stieltjes transform of the waiting time distribution for the message which is eventually served. Finally, we show some numerical results including the comparisons between the push-out and the ordinary blocking models.