Analysis of second optional service system with a cold standby server that is reliant on the system size

Abstract

In this article, we examine a second optional service queueing system using two types of servers, viz. the main operating server and a reliable standby server. All arriving customers receive the first essential service (FES), and only a few may thereafter request a second optional service (SOS) with some probability. During FES and SOS services, the primary operational server may break down. The server is promptly sent for repair if a break down arises and the standby server will be replaced only if the system size is q (≥ 1); otherwise, customers would queue up while the main server is being repaired and resumes the service. We also derive the necessary and sufficient condition for the system to be stable. The model’s steady state solution is discovered using the matrix geometric approach. Further, multiple system performance measures are obtained and a cost optimization problem is taken into consideration. Graphs are used to display the numerical outcomes.