Performance Evaluation of a GI/M (a, b)/1 Queueing Model for a Diagnostic Laboratory with Multiple Working Vacations and Equipment Breakdown

Abstract

This paper analysis a Non-Markovian queueing model applied to a diagnostic laboratory system, where patient samples arrive according to a general distribution single server pattern with batch service where server undergoes multiple working vacations with server breakdown. The laboratory begins processing only when at least “a” number of samples are available and can handle up to a maximum of “b” samples per batch. The testing equipment described as a server may enter multiple working vacation periods. Patient samples arriving follows General distribution and the service follows Exponential distribution. The breakdown that may happens during working vacation periods or during regular busy periods are considered in this model. The system is formulated through a discrete-time Markov chain at pre-arrival epochs. The steady state equation, steady state solution for the described model are derived to determine key performance measures known as mean queue length. Finally, this paper computes the numerical analysis of mean queue length with the types of breakdown to study how breakdown parameters influence laboratory congestion and service reliability. The results offer practical insights for diagnostic centres to optimize maintenance scheduling, batch processing, and equipment validity.