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Single line queue with repeated demands

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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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Author notes

  1. K. Farahmand

    Present address: Department of Mathematical Statistics, University of Cape Town, 7700, Rondebosch, South Africa

Authors and Affiliations

  1. Department of Mathematical Statistics, University of Natal, South Africa

    K. Farahmand

Authors
  1. K. Farahmand
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Farahmand, K. Single line queue with repeated demands. Queueing Syst 6, 223–228 (1990). https://doi.org/10.1007/BF02411475

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  • DOI: https://doi.org/10.1007/BF02411475

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