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

Mingang Yin, Ming Yan (), Yu Guo and Minghe Liu
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Mingang Yin: School of Mechanical Engineering, Shenyang University of Technology, Shenyang 110870, China
Ming Yan: School of Mechanical Engineering, Shenyang University of Technology, Shenyang 110870, China
Yu Guo: School of Mechanical Engineering & Automation, Northeastern University, Shenyang 110819, China
Minghe Liu: School of Mechanical Engineering, Shenyang Jianzhu University, Shenyang 110168, China

Mathematics, 2023, vol. 11, issue 18, 1-16

Abstract: 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.

Keywords: interstate transition frequency; Markov processes; queueing analysis; systems modeling (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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