Modeling and simulation of first-come, first-served queueing system with impatient multiclass customers

Vinay Kumar () and Neelesh Shankar Upadhye ()
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Vinay Kumar: Indian Institute of Technology Madras
Neelesh Shankar Upadhye: Indian Institute of Technology Madras

Operational Research, 2025, vol. 25, issue 1, No 12, 37 pages

Abstract: Abstract This article examines a first-come, first-served queueing system serving impatient customers from c distinct classes. Each customer class is characterized by independent patience and service time distributions. The study focuses on two specific queueing systems: $$M/G/1+M$$ M / G / 1 + M and $$M/M/m+M$$ M / M / m + M . Steady-state analyses for $$M/G/1 + M$$ M / G / 1 + M and $$M/M/m + M$$ M / M / m + M are derived, and a case where all customer classes share the same mean service time is explored. Performance measures in the steady state are derived for both systems. Numerical analysis for the $$M/M/m + M$$ M / M / m + M system is conducted using the proposed characterizations. The actual and simulated $$M/M/m + M$$ M / M / m + M systems are then compared using steady-state metrics, including the proportion of served customers in each class, the mean waiting times for customers in each class, and the system throughput derived analytically. The numerical results highlight the effectiveness of this queueing model in addressing a range of real-world applications.

Keywords: Multi-class multi-server queue; Virtual waiting time; Impatient customer; Steady-state analysis; 90B22; 68M20; 60K25 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s12351-024-00877-y

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