Abstract
This paper investigates a queueing system, which consists of Poisson input of customers, some of whom are lost to balking, and a single server working a shift of lengthL and providing a service whose duration can vary from customer to customer. If a service is in progress at the end of a shift, the server works overtime to complete the service. This process was motivated by the behavior of fishermen interviewed in the NY Great Lakes Creel Survey.
We derive the distributions of the number of services (X), overtime and total server idle time (T), both unconditionally (for Poisson arrivals) and conditionally on the number (n) of arrivals per shift, assuming that the arrival times are not recorded in the data. These distributions provide the basis for estimation of the parameters from asingle realization of the queueing process during [0,L]. The conditional distributions also can be used to estimate common service time,w, when (n, X) or (n, T) are observed. Confidence intervals based onT are of shorter length, for all confidence coefficients, than the corresponding intervals based onX.
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This paper is Technical Report #BU-1019-M in the Biometrics Unit Series. The authors are grateful to N.U. Prabhu for suggestions on streamlining the distributional derivations and to D.R. Cox and C.E. McCulloch for helpful comments.
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Rubin, G., Robson, D.S. A single server queue with random arrivals and balking: Confidence interval estimation. Queueing Syst 7, 283–306 (1990). https://doi.org/10.1007/BF01154547
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DOI: https://doi.org/10.1007/BF01154547