Abstract
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.
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References
J. Neveu, Files d’attente, 1983–1984, Cours de troisième cycle, Laboratoire de Probabilités de l’Université de Paris VI.
P. Greenwood and J. Pitman, Fluctuation identities for Lévy processes and splitting at the maximum, Advances in Applied Probability 12 (1980), 893–902.
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© 2003 Springer-Verlag Berlin Heidelberg
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Robert, P. (2003). GI/GI/1 FIFO Queues and Random Walks. In: Stochastic Networks and Queues. Applications of Mathematics, vol 52. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-13052-0_2
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DOI: https://doi.org/10.1007/978-3-662-13052-0_2
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