Optimal control of a two-phase heterogeneous service retrial queueing system with collisions and delayed vacations

This paper proposes a novel two-phase heterogeneous service retrial queueing system with collisions and delayed vacations. We consider services for two types of customers: ordinary customers (service completed in two phases) and priority customers (service completed in one phase). Collisions only oc...

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Bibliographic Details
Published in:Journal of applied mathematics & computing Vol. 70; no. 4; pp. 2879 - 2906
Main Authors: Xu, Wei, Li, Linhong, Fan, Wentao, Liu, Liwei
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2024
Subjects:
Computational Mathematics and Numerical Analysis
Mathematical and Computational Engineering
Mathematics
Mathematics and Statistics
Mathematics of Computing
Original Research
Theory of Computation
Canonical particle swarm optimization algorithm
Two-phase service
Delayed vacation
Multi-objective evolution algorithm based on decomposition
60K25
Collision
ISSN:1598-5865, 1865-2085
Online Access:Get full text
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Summary:This paper proposes a novel two-phase heterogeneous service retrial queueing system with collisions and delayed vacations. We consider services for two types of customers: ordinary customers (service completed in two phases) and priority customers (service completed in one phase). Collisions only occur in the first phase of service; if the collision does not happen, the server will proceed to the second phase of service. When the server turns to an idle state, it reserves a random period before taking formal vacations. We investigate two models for this system with and without orbit constraints and numerically analyze the sensitivity of the system performance metrics to validate the results and methodology. The expected total cost function is formulated. To prevent falling into the local optimal solution too fast, we utilize the canonical particle swarm optimization algorithm. Furthermore, we evaluate a bi-objective optimization problem to seek the balance of the expected total cost and the quality of service. Then, we apply the multi-objective evolutionary algorithm based on decomposition (MOEA/D) to obtain the Pareto front. Several numerical examples are presented for illustrative purposes.
ISSN:1598-5865
1865-2085
DOI:10.1007/s12190-024-02074-8