Busy period analysis for M/G/1 and G/M/1 type queues with restricted accessibility

被引：35

作者：

Perry, D

Stadje, W ^{[1
]}

Zacks, S

机构：

[1] Univ Haifa, Dept Stat, IL-31905 Haifa, Israel

[2] Univ Osnabruck, Fachbereich Math Informat, D-49069 Osnabruck, Germany

[3] SUNY Binghamton, Dept Math Sci, Binghamton, NY 13902 USA

来源：

OPERATIONS RESEARCH LETTERS | 2000年 / 27卷 / 04期

关键词：

M/G/1; G/M/1; restricted accessibility; busy period; stopping time; compound Poisson process; linear boundary; virtual waiting time; elapsed waiting time;

D O I：

10.1016/S0167-6377(00)00043-2

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

We consider two models of M/G/1 and G/M/1 type queueing systems with restricted accessibility. Let(V(t))(t greater than or equal to0) be the virtual waiting time process, let S-n be the time required for a full service of the nth customer and let tau (n) be his arrival time. Tn both models there is a capacity bound nu* is an element of (0, infinity). In Model I the amount of service given to the nth customer is equal to min[S-n,nu* - V(tau (n)-)], i.e. the full currently free workload is assigned to the new customer. In Model II the customer is rejected iff the currently used workload V(tau (n)-) exceeds nu*, but the service times of admitted customers are not censored. We obtain closed-form expressions for the Laplace transforms of the lengths of the busy periods. (C) 2000 Elsevier Science B.V. All rights reserved.

引用

页码：163 / 174

页数：12

共 20 条

[11] WAITING TIME DISTRIBUTION IN A GENERALIZED QUEUING SYSTEM WITH UNIFORMLY BOUNDED SOJOURN TIMES [J].