Reliability and transient analysis of discrete-time multi-class priority queue with energy saving vacation policy

Department of Mathematics, Birla Institute of Technology and Science Pilani, Pilani 333031, India

^* Corresponding author: rakhee@pilani.bits-pilani.ac.in

Received: 24 June 2024
Accepted: 8 May 2025

Abstract

The wireless communication systems can be modeled using discrete-time multi-class priority queues. Also, it is desired to reduce energy consumption in these systems, which can be achieved by implementing a vacation policy with priority queues. This study investigates a Geo/Geo/1 multi-class priority G-queue system featuring a vacation policy and server breakdowns. In this model, customers arrive at discrete time intervals and are classified into three priority classes. Virus attacks (considered hostile customers) may disrupt the server’s functionality during the service, leading to interruptions. If the server has completed serving all classes of customers and no customers are waiting in the queues, it will go on vacation. The entire system is represented as a three-dimensional Markov chain, and its transient behavior is analyzed using the recursive method. By utilizing transient probability distribution, we compute various performance metrics for the system, taking both reliability and queueing analyses into account. In conclusion, we develop a cost function based on successful customer transmissions, and then the quasi-Newton method and particle swarm optimization (PSO) algorithm are used to determine the optimal reward cost.