A STEADY-STATE BEHAVIOUR OF AN M M 1 QUEUE WITH OPTIONAL DIFFERENTIATED WORKING VACATIONS, SERVER BREAKDOWN, AND CUSTOMER BALKING

被引：0

作者：

Muthukumar, S. ^{[1
,2
]}

Bagyam, J. Ebenesar Anna ^{[2
]}

机构：

[1] Ramco Inst Technol, Dept Math, Rajapalayam 626117, Tamil Nadu, India

[2] Karpagam Acad Higher Educ, Dept Math, Coimbatore 641021, Tamil Nadu, India

来源：

ADVANCES AND APPLICATIONS IN STATISTICS | 2025年 / 92卷 / 04期

关键词：

single server queue; optional working vacations; breakdown; balking; stability analysis and optimization; SYSTEM;

D O I：

10.17654/0972361725025

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

This paper analyses the steady-state behaviour of an M M 1 queueing system incorporating optional differentiated working vacations, server breakdowns, and customer balking. Following a busy period, the server might transition into an optional I or II working vacation, leading to a reduction in the service rate. Customers may balk when the server is on vacation or experiencing a breakdown. The model's stable solution is derived using probability-generating functions, enabling the evaluation of key performance metrics. A cost optimization framework is employed to minimize the cost by balancing system parameters. Numerical examples demonstrate the impact of varying arrival and service rates on customer queue length and waiting times.

引用

页码：603 / 631

页数：29

共 32 条

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