Queueing Systems

, Volume 70, Issue 2, pp 145–164 | Cite as

Invariance of fluid limits for the shortest remaining processing time and shortest job first policies

  • H. Christian Gromoll
  • Martin Keutel


We consider a single-server queue with renewal arrivals and i.i.d. service times, in which the server employs either the preemptive Shortest Remaining Processing Time (SRPT) policy, or its non-preemptive variant, Shortest Job First (SJF). We show that for given stochastic primitives (initial condition, arrival and service processes), the model has the same fluid limit under either policy. In particular, we conclude that the well-known queue length optimality of preemptive SRPT is also achieved, asymptotically on fluid scale, by the simpler-to-implement SJF policy. We also conclude that on fluid scale, SJF and SRPT achieve the same performance with respect to state-dependent response times.


Queueing Queue length Shortest remaining processing time Shortest job first Shortest job next Fluid limit 

Mathematics Subject Classification (2000)

60K25 60F17 60G57 68M20 90B22 


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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of VirginiaCharlottesvilleUSA

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