Abstract
This paper analyses a queueing model consisting of two units I and II connected in series, separated by a finite buffer of size N. Unit I has only one exponential server capable of serving customers one at a time. Unit II consists of c parallel exponential servers and they serve customers in groups according to the bulk service rule. This rule admits each batch served to have not less than ‘a’ and not more than ‘b’ customers such that the arriving customers can enter service station without affecting the service time if the size of the batch being served is less than ‘d’ ( a ≤ d ≤ b ). The steady stateprobability vector of the number of customers waiting and receiving service in unit I and waiting in the buffer is obtained using the modified matrix-geometric method. Numerical results are also presented. AMS Subject Classification number: 60k25 and 65k30
Highlights
Queueing models consisting of two units in series with an intermediate waiting room of finite capacity have been studied by several authors
Unit I of this model contains one server with a general service time distribution and unit II consists of c parallel exponential servers
For the model describe above, the steady state probability vector of the number of customers waiting and receiving service in unit I, waiting in the buffer and the stability condition are obtained by using the matrixgeometric method
Summary
Queueing models consisting of two units in series with an intermediate waiting room of finite capacity have been studied by several authors. The service rule is assumed to operate as follows: the server starts service only when a minimum of ‘a’ customers is in the buffer, and the maximum capacity is ‘b’ customers. Such a rule for bulk service, first introduced by Neuts [7], may be called general bulk service rule. For the model describe above, the steady state probability vector of the number of customers waiting and receiving service in unit I, waiting in the buffer and the stability condition are obtained by using the matrixgeometric method
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