GI/GI/1 FIFO Queues and Random Walks
The arrival process of this queue is a renewal point process, services of the customers form an i.i.d. sequence and the service discipline is First In First Out (FIFO). It works as follows: When a customer requiring a service x ≥ 0 arrives at the queue, it joins the queue and as soon as it is at the head of the queue (i.e. all the customers arrived before him have left the queue), it is served for a duration of time x by the server.
KeywordsRandom Walk Busy Period Geometric Distribution Service Discipline Ergodic Markov Chain
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- [Nev84]J. Neveu, Files d’attente, 1983–1984, Cours de troisième cycle, Laboratoire de Probabilités de l’Université de Paris VI.Google Scholar