Queueing Systems

, Volume 85, Issue 3–4, pp 361–381 | Cite as

A general workload conservation law with applications to queueing systems



In the spirit of Little’s law \(L=\lambda W\) and its extension \(H=\lambda G\) we use sample-path analysis to give a general conservation law. For queueing models the law relates the asymptotic average workload in the system to the conditional asymptotic average sojourn time and service times distribution function. This law generalizes previously obtained conservation laws for both single- and multi-server systems, and anticipating and non-anticipating scheduling disciplines. Applications to single- and multi-class queueing and other systems that illustrate the versatility of this law are given. In particular, we show that, for anticipative and non-anticipative scheduling rules, the unconditional delay in a queue is related to the covariance of service times and queueing delays.


Conservation law Workload invariance Multi-server queues Sample-path analysis Scheduling 

Mathematics Subject Classification

Primary 60K25 Secondary 68M20 90B36 



The author wishes to thank the reviewers for their helpful comments.


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© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of Southern MainePortlandUSA

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