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This paper presents a mathematical queue model for passport office system .It provides a more realistic description of queue model for passport office system on priority basis .Now a days almost in every system priority is given in some cases for example medical cases, to some officials and customers\applicants having some emergency .This model consists two rows, one for high priority and other for low priority customers. It is assumed that the arrival and service process follow the Poisson distribution. It is supposed that the service will be completed when the customer\applicant pass through all the service channels. This model can also be applicable in many real life situations like hospital management, in market, in offices etc.
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