GI/GI/1 FIFO Queues and Random Walks

  • Philippe Robert
Part of the Applications of Mathematics book series (SMAP, volume 52)


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.


Random Walk Busy Period Geometric Distribution Service Discipline Ergodic Markov Chain 
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    J. Neveu, Files d’attente, 1983–1984, Cours de troisième cycle, Laboratoire de Probabilités de l’Université de Paris VI.Google Scholar
  2. [GP80]
    P. Greenwood and J. Pitman, Fluctuation identities for Lévy processes and splitting at the maximum, Advances in Applied Probability 12 (1980), 893–902.MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Philippe Robert
    • 1
  1. 1.Domaine de VoluceauINRIALe ChesnayFrance

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