Single-Server Queues with Service Time Dependent on Waiting Time

Abstract

This paper discusses a class of queuing models in which the service time of a customer at a single-server facility is dependent on the amount of time that customer has spent queuing for service. A complete investigation is carried out in the particular case of exponential service times with the parameter having a step-function dependency on the waiting time. The stationary waiting-time distribution is investigated for the queue discipline by which customers are served in order of arrival. This class of model is particularly suited for applications wherein customer or item deterioration occurs during waiting or where the server wishes to provide a more appropriate level of service to counter the negative effects of customer impatience and loss of good will.

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