Equilibrium balking behavior in the Geo/Geo/1 queueing system with multiple vacations

被引:30
作者
Ma, Yan [1 ,2 ]
Liu, Wei-qi [2 ]
Li, Ji-hong
机构
[1] Cent S Univ, Sch Math & Stat, Changsha 410075, Hunan, Peoples R China
[2] Shanxi Univ, Coll Math Sci, Taiyuan 030006, Peoples R China
关键词
Economics of queues; Multiple vacations; Equilibrium balking strategies; Stationary distribution; Social benefit; Matrix-geometric solution method; SINGLE; STRATEGIES; SERVER; TOLLS;
D O I
10.1016/j.apm.2012.08.017
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
This paper studies the equilibrium behavior of customers in the Geo/Geo/1 queueing system under multiple vacation policy. The server leaves for repeated vacations as soon as the system becomes empty. Customers decide for themselves whether to join or to balk, which is more sensible than the classical viewpoint in queueing theory. Equilibrium customer behavior is considered under four cases: fully observable, almost observable, almost unobservable and fully unobservable, which cover all the levels of information. Based on the reward-cost structure, we obtain the equilibrium balking strategies in all cases. Furthermore, the stationary system behavior is analyzed and a variety of performance measures are developed under the corresponding strategies. Finally, we present several numerical experiments that demonstrate the effect of the information level as well as several parameters on the equilibrium behavior and social benefit. The research results not only offer the customers optimal strategies but also provide the managers with a good reference to discuss the pricing problem in the queueing system. (C) 2012 Elsevier Inc. All rights reserved.
引用
收藏
页码:3861 / 3878
页数:18
相关论文
共 35 条
[31]   PERFORMANCE ANALYSIS OF A DISCRETE-TIME Geo/G/1 RETRIAL QUEUE WITH NON-PREEMPTIVE PRIORITY, WORKING VACATIONS AND VACATION INTERRUPTION [J].
Lan, Shaojun ;
Tang, Yinghui .
JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION, 2019, 15 (03) :1421-1446
[32]   The Mt/M/1 queueing system with impatient customers and multiple vacation [J].
Yousefi, Ali ;
Pourtaheri, Reza .
OPSEARCH, 2024, 61 (04) :2002-2022
[33]   Analysis of Customer Behavior under Uncertainty on Distribution of Service Time Parameter in M/M/1 Queueing System [J].
Zheng, Wenxiang .
2015 12TH INTERNATIONAL CONFERENCE ON SERVICE SYSTEMS AND SERVICE MANAGEMENT (ICSSSM), 2015,
[34]   The Two-Phases-Service M/M/1/N Queuing System with the Server Breakdown and Multiple Vacations [J].
Hui, Zeng ;
Wei, Guan .
INFORMATION COMPUTING AND APPLICATIONS, 2011, 7030 :200-207
[35]   Analysis of a Multiple M/M/1/DV Queueing System with a Dual-Threshold Policy, Vacation Interruption and a Waiting Server [J].
Ramupillai, Sudhesh ;
Shapique, Mohammed ;
Selvamuthu, Dharmaraja .
BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, 2022, 48 (06) :3561-3591