A Batch Arrival Unreliable Queue with Two Types of General Heterogeneous Service and Delayed Repair under Repeated Service Policy

Abstract

This paper deals with a single server / / 1 M G X queue under two types of general heterogeneous service with optional repeated service subject to server’s breakdowns and delayed repair. We assume that customers arrive at the system according to a compound Poisson process with rate λ. The server provides two types of general heterogeneous service and a customer has the option to choose any type of service. After the completion of either type of service, the customer has the further option to repeat the same type of service. While the server is working with any types of service or repeated service, it may breakdown at any instant and the service channel will fail for a short interval of time. Furthermore, the concept of delay time is also introduced. We carry out an extensive analysis of this model. Finally, we obtain some important performance measure and reliability indices of this model.

Keywords

• Two types of service
• optional repeated service
• elapsed times
• remaining time
• delay time