A Service System with Unfilled Requests Repeated

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Abstract
The object of this paper is to analyze a model of a queuing system in which customers cannot be in continuous contact with the server, but must call in to request service: If the server is free, then the next request to arrive is served immediately; if the server is occupied, however, the unsatisfied customer must break contact and later re-initiate his request. Thus, repeat requests for service from the pool of unsatisfied customers are superimposed on the normal stream of arrivals of first attempts. This system is characteristic of situations in which there is a single operator or source of information that must be called and busy signals are not held. This paper calculates several characteristic quantities of such systems, assuming a general service-time distribution and different exponential distributions for the times between arrivals of first requests and repeat requests.

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