Queueing Systems

, Volume 55, Issue 2, pp 131–138 | Cite as

Estimation for queues from queue length data

  • J. V. Ross
  • T. Taimre
  • P. K. Pollett


We consider the estimation of arrival and service rates for queues based on queue length data collected at successive, not necessarily equally spaced, time points. In particular, we consider the M/M/c queue, for c large, but application of the method to the repairman problem is almost identical, and the general approach presented should extend to other queue types. The estimation procedure makes use of an Ornstein-Uhlenbeck diffusion approximation to the Markov process description of the queue. We demonstrate the approach through simulation studies and discuss situations in which the approximation works best.


Diffusion approximation M/M/c queues Maximum likelihood Queue length Rate estimation Traffic intensity 


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© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Mathematics InstituteUniversity of WarwickCoventryUK
  2. 2.Department of MathematicsUniversity of QueenslandQueenslandAustralia

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