Queueing Systems

, Volume 87, Issue 1–2, pp 1–22 | Cite as

On preemptive-repeat LIFO queues

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Abstract

In this paper, we study the basic properties of last-in first-out (LIFO) preemptive-repeat single-server queues in which the server needs to start service from scratch whenever a preempted customer reaches the server. In particular, we study the question of when such queues are stable (in the sense that the equilibrium time-in-system is finite-valued with probability one) and show how moments of the equilibrium customer sojourn time can be computed when the system is stable. A complete analysis of stability is provided in the setting of Poisson arrivals and in that of the Markovian arrival process. The stability region depends upon the detailed structure of the interarrival and service time distributions and cannot be expressed purely in terms of expected values. This is connected to the fact that such preemptive-repeat queues are not work conserving.

Keywords

Branching process Iterative scheme Markovian arrival process Random walk Sojourn time Stability Stochastic fixpoint equation 

Mathematics Subject Classification

60K25 
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Notes

Acknowledgements

We are grateful to Onno Boxma, Mor Harchol-Balter and V. Ramaswami for valuable remarks and references. Special thanks go to Jonathan Goodman for providing the differential equation argument in Remark 6 that provided the initial scientific impetus for this project. Patrick Laub supplied helpful answers to our programming queries.

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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Dpartment of MathematicsNy MunkegadeAarhusDenmark
  2. 2.Huang Engineering Center 359AStanford UniversityStanfordUSA

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