An approximation method for 2-chain flexible queues with preemptive priority

Wang, Yaolei; Fan, Yiming; Zhu, Taozeng; Cao, Ping; Xie, Jingui

doi:10.1080/00207543.2018.1556410

Cited by 2 publications

(1 citation statement)

References 36 publications

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“…Kleinrock [2] proposed a time-dependent priority queue and derived the expressions for the average waiting times for different priorities. Priorities can be classified into two categories [3]: pre-emptive priority [4][5][6], in which a higher-priority customer entering the system will cause any ongoing work to be interrupted, and the maintainer will immediately serve the higher-priority customer, and non-pre-emptive priority [7], in which a customer with priority entering the system will be placed at the front of the queue automatically.…”

Section: Introductionmentioning

confidence: 99%

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

Yin,

Yan,

Guo

et al. 2023

Mathematics

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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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