On a simple discrete cyclic-waiting queueing problem
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On the basis of a real problem connected with the landing of airplanes, the paper investigates a queueing system with geometrically distributed interarrival and service times in which the service of a request may be started upon arrival (in the case of a free system) or (in the case of a busy server, a queue, or noncorresponding position of the request) at moments differing from it by multiples of the cycle time. For the service discipline the FIFO rule is assumed. Using the embedded-Markov-chain technique (considering the system at moments just before starting the service of a request), the generating function of ergodic probabilities is found and the condition of existence of an ergodic distribution is established.
KeywordsCycle Time Service Time Time Slice Service Process Geometrical Distribution
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