Abstract
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.
Highlights
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
Research studies on queues with batch arrival and vacations have been increased tremendously and still many researchers have been developing on the theory of different aspects of queuing
We can find vast literature on the extensive amount of studies been done on different queuing models with server vacations, arrival pattern and customers behavior
Summary
Research studies on queues with batch arrival and vacations have been increased tremendously and still many researchers have been developing on the theory of different aspects of queuing. We can find vast literature on the extensive amount of studies been done on different queuing models with server vacations, arrival pattern and customers behavior. Queues with vacations and behavior of impatient customers have been studied by many for mainly single server but balking in case of two parallel servers for a general distribution has still not been worked on. We find many real life applications of queues with balking and re-service in sectors as telecommunication, computer networking, call centers, inventory and production, maintenance and quality control in industrial organisations etc. The mathematical model has been defined under the following assumptions
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