Single line queue with repeated demands |
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Authors: | K Farahmand |
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Institution: | (1) Department of Mathematical Statistics, University of Natal, South Africa;(2) Present address: Department of Mathematical Statistics, University of Cape Town, 7700 Rondebosch, South Africa |
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Abstract: | We analyze a model of a queueing system in which customers can only call in to request service: if the server is free, the
customer enters service immediately, but if the service system is occupied, the unsatisfied customer must break contact and
reinitiate his request later. Such a customer is said to be in “orbit”. In this paper we consider three models characterized
by the discipline governing the order of re-request of service from orbit. First, all customers in orbit can reapply, but
are discouraged and reduce their rate of demand as more customers join the orbit. Secondly, the FCFS discipline operates for
the unsatisfied customers in orbit. Finally, the LCFS discipline governs the customers in orbit and the server takes an exponentially
distributed vacation after each service is completed. We calculate several characteristics quantities of such systems, assuming
a general service-time distribution and different exponential distributions for the times between arrivals of first and repeat
requests. |
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Keywords: | Single-line queue repeated demands orbit size waiting time ergodic state generating function |
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