Balking and Re-service in a Vacation Queue with Batch Arrival and Two Types of Heterogeneous Service

MONITA BARUAH, Kailash C. Madan, Tillal Eldabi


In this paper we have considered a single server queue with customers or units arriving in groups or batches in a system providing two types of general heterogeneous service. The server provides type 1 or type 2 services on a first come first served basis. At the beginning of a service, a customer has the option to choose either type 1 or type 2 service. Also we added the concept of balking and re-service in this study. Balking is a kind of customer behavior. If a batch on arrival for service is reluctant or refuses to join the system for some reasons is said to balk.  Once a service is completed the customer may leave the system or he has the option to demand re-service for the same service taken. Further as soon as service of any type gets completed, the server may take vacation or continue staying at the system even if the system is empty. For this model we have derived the steady state queue size distribution at random epoch and some particular cases have been developed and compared with known results.

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Journal of Mathematics Research   ISSN 1916-9795 (Print)   ISSN 1916-9809 (Online)

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