Analysis of a Pre-Emptive Two-Priority Queuing System with Impatient Customers and Heterogeneous Servers

被引:4
|
作者
Yin, Mingang [1 ]
Yan, Ming [1 ]
Guo, Yu [2 ]
Liu, Minghe [3 ]
机构
[1] Shenyang Univ Technol, Sch Mech Engn, Shenyang 110870, Peoples R China
[2] Northeastern Univ, Sch Mech Engn & Automat, Shenyang 110819, Peoples R China
[3] Shenyang Jianzhu Univ, Sch Mech Engn, Shenyang 110168, Peoples R China
基金
美国国家科学基金会;
关键词
interstate transition frequency; Markov processes; queueing analysis; systems modeling; QUEUES; BALKING; APPROXIMATION; PERFORMANCE;
D O I
10.3390/math11183878
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
This paper presents a queuing system model that incorporates multiple priorities, multiple abandonments, and heterogeneous servers. Waiting for service easily leads to impatient behaviors. The impact of two kinds of impatient behaviors, balking and reneging, on queueing system performance is examined. The problem is formulated as continuous-time Markov chains. It also introduces a special state called the non-sojourn state to record the number of customers who abandon the system. The state transition rate matrix is transformed into a block tridiagonal matrix by appropriately setting the state numbers. A novel indicator called interstate transition frequency is proposed, which aids in distinguishing state transitions during the system evaluation process. Based on the interstate transition frequency, a set of indicators is derived to offer additional analytical perspectives for the queuing system. Finally, the proposed model is applied to an automobile repair shop to validate its effectiveness in practical scenarios.
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页数:16
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