An M/G/1 queue with two types of general heterogeneous service and optional repeated service subject to server’s breakdown and delayed repair

ABSTRACT

In this paper, we study the steady state behaviour of an M/G/1 queue with two types of general heterogeneous service and optional repeated service subject to server’s breakdowns occurring randomly at any instant while serving the customers and delayed repair. We assume that customers arrive to the system according to a Poisson process with rate ‘λ’ and the server provides two types of general heterogeneous service. At the beginning of a service, a customer has the option to choose any one type of service. After completion of either type of service, the customer has the further option to repeat the same type of service. For this model, we first derive the joint distribution of state of the server and queue size by considering both elapsed and remaining time, which is one of the objectives of this paper. Secondly, we derive the probability generating function of the stationary queue size distribution at departure epoch. Next, we derive Laplace–Stieltjes transform of busy period distribution and waiting time distribution. Finally, we obtain some important performance measure and reliability indices of this model.

KEYWORDS:

• M/G/1 queue
• two types of service
• optional repeated service
• server’s breakdown
• delay time
• remaining time
• reliability analysis