Queueing Systems

, Volume 90, Issue 1–2, pp 89–123 | Cite as

The state-dependent M / G / 1 queue with orbit

  • Opher Baron
  • Antonis Economou
  • Athanasia Manou


We consider a state-dependent single-server queue with orbit. This is a versatile model for the study of service systems, where the server needs a non-negligible time to retrieve waiting customers every time he completes a service. This situation arises typically when the customers are not physically present at a system, but they have a remote access to it, as in a call center station, a communication node, etc. We introduce a probabilistic approach for the performance evaluation of this queueing system, that we refer to as the queueing and Markov chain decomposition approach. Moreover, we discuss the applicability of this approach for the performance evaluation of other non-Markovian service systems with state dependencies.


State-dependent queueing system Orbit Retrial queue Non-negligible retrieval time Steady-state distribution Conditional sojourn time distributions Variable arrival rate Variable service speed Queueing and Markov chain decomposition 

Mathematics Subject Classification

60K25 90B22 



We thank the associate editor, and two anonymous reviewers for their valuable comments that greatly improved the paper. We thank Professor Mor Harchol-Balter of Carnegie Mellon University for pointing us to the application of our model for the analysis of load sharing algorithms. Professor Baron’s work on this research was supported by a grant from the Natural Science and Engineering Research Council of Canada. Athanasia Manou was supported by AXA Research Fund.


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Rotman School of ManagementUniversity of TorontoTorontoCanada
  2. 2.Department of MathematicsNational and Kapodistrian University of AthensAthensGreece
  3. 3.Department of Industrial EngineeringKoç UniversityIstanbulTurkey

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