Analysis and optimisation of a heterogeneous servers with vacation scheme, system disaster and repair

This paper investigates a heterogeneous server system that incorporates vacation schemes, system disasters, server failures, and repairs. Servers are categorized into two types based on their service capabilities. Vacation durations vary for each server, and jobs are assigned to servers using a fastest-first policy. Time-dependent solutions are derived explicitly using generating functions and Laplace transforms, alongside steady-state solutions. The study delves into essential performance measures and conducts a comprehensive cost-revenue analysis for the proposed model. To optimize system performance, the particle swarm optimization algorithm is employed to minimize the total expected cost function. Numerical results are presented to illustrate the impact of system and cost parameters, providing insights into the dynamic behavior and economic implications of the system.