Abstract
This paper investigates a single server batch service queueing system with second optional service and reneging. The transient state probabilities of the queueing model are computed by using fourth order Runge Kutta method. Cost analysis is performed to determine the optimal values of the service rates of First Essential Service (FES) and Second Optional Service (SOS) simultaneously at the minimum total expected cost per unit time. Some important performance measures and numerical illustrations are provided in order to show the managerial intuitions of the model.
)