Stability conditions for a multiserver queueing system with a regenerative input flow and simultaneous service of a customer by a random number of servers

被引：5

作者：

Afanaseva, L. G. ^{[1
]}

Grishunina, S. A. ^{[1
,2
]}

机构：

[1] Lomonosov Moscow State Univ, Fac Math & Mech, Dept Probabil, Moscow, Russia

[2] Natl Res Univ Higher Sch Econ, Moscow Inst Elect & Math, Moscow, Russia

来源：

QUEUEING SYSTEMS | 2020年 / 94卷 / 3-4期

基金：

俄罗斯基础研究基金会;

关键词：

Stability condition; Queueing system; Regenerative input flow; Synchronization; REQUIRE; TIME; NETWORKS; QUEUES;

D O I：

10.1007/s11134-020-09648-w

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

We investigate the stability condition of a multiserver queueing system. Each customer needs simultaneously a random number of servers to complete the service. The times taken by each server are independent. The input flow is assumed to be a regenerative one. The service time has an exponential, phase-type or hyper-exponential distribution. The stability criteria for the models are established. It turns out that the stability conditions do not depend on the structure of the input flow, but only on the rate of the process. However, the distribution of the service times is a very important factor. We give examples which show that the stability condition cannot be expressed only in terms of the mean of the service time.

引用

页码：213 / 241

页数：29

共 26 条

[1] Stability conditions for a multiserver queueing system with a regenerative input flow and simultaneous service of a customer by a random number of servers
L. G. Afanaseva
S. A. Grishunina
[J]. Queueing Systems, 2020, 94 : 213 - 241
[2] MULTISERVER QUEUEING SYSTEM WITH CONSTANT SERVICE TIME AND SIMULTANEOUS SERVICE OF A CUSTOMER BY RANDOM NUMBER OF SERVERS
Grishunina, S. A.
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[J]. THEORY OF PROBABILITY AND ITS APPLICATIONS, 2019, 63 (04) : 507 - 531
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[10] Stability Analysis of a Multi-server Model with Simultaneous Service and a Regenerative Input Flow
Larisa Afanaseva
Elena Bashtova
Svetlana Grishunina
[J]. Methodology and Computing in Applied Probability, 2020, 22 : 1439 - 1455

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