M/M/1/K Loss and Delay Interdependent Queueing Model with Vacation and Controllable Arrival Rates

Abstract

Objectives: In this study, we assume that the vacation is taken while there are no consumers in the queue. There are several servicemen who will take the synchronous multiple vacations in the system. Methods: Assumed some loss and delay in consumers (Elective and emergency) and solve the steady-state probability equations using recursive approach and acquired some obvious iterative expressions. Findings: Carried out some numerical analysis using MATLAB and investigated the movement of , , and through graph. Further, , , and increase when increases; decrease when M increases. Additionally, when L increases remains constant and increase. Novelty: Expanded the preceding models in this study by including vacations and performing the numerical analysis. Using vacation with controllable arrival rates in an optimal way in order to benefit both the server and the customer will minimise waiting time and provide the most feasible, affordable service to the consumer. Keywords: Markovian Queueing System, Vacation, Loss and Delay, Finite Capacity, Interdependent Arrival and Service Rates, Varying Arrival Rates, Bivariate Poisson Process