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Article Content:-
Abstract
A single server queue with two type of services and with single vacation has been considered. The type 1 service is a phase type service with two service phases. Both the service time distributions are generally distributed. The type 2 service has only one phase of service. In addition the server also provides an optional service. These service time distributions are also general. After completion of service, the server takes vacation if there are no customers in the queue and vacation time distribution is general. The server returns to the queue, independent of the number of customers in the queue, after taking a single vacation.
For this model the probability generating function for the number of customers in the queue at different server's state are obtained using supplementary variable technique. Some performance measures and particular models are calculated. Numerical results are presented and a web server model has analyzed under the given frame work.
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References
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