Estimation for queues from queue length data

Authors:
J. V. Ross;T. Taimre;P. K. Pollett
Affiliations:
Mathematics Institute, University of Warwick, Coventry, UK CV4 7AL;Department of Mathematics, University of Queensland, Queensland, Australia QLD 4072;Department of Mathematics, University of Queensland, Queensland, Australia QLD 4072
Venue:
Queueing Systems: Theory and Applications
Year:
2007

Citing 7
Cited 2

Statistical analysis of queueing systems

Queueing Systems: Theory and Applications
Large sample inference from single server queues

Queueing Systems: Theory and Applications
On normal approximation for maximum likelihood estimation from single server queues

Queueing Systems: Theory and Applications
A Diffusion Approximation for a Markovian Queue with Reneging

Queueing Systems: Theory and Applications
Properties of the Reflected Ornstein–Uhlenbeck Process

Queueing Systems: Theory and Applications
The Cross Entropy Method: A Unified Approach To Combinatorial Optimization, Monte-carlo Simulation (Information Science and Statistics)

The Cross Entropy Method: A Unified Approach To Combinatorial Optimization, Monte-carlo Simulation (Information Science and Statistics)
A Diffusion Approximation for a GI/GI/1 Queue with Balking or Reneging

Queueing Systems: Theory and Applications

Analysis of an unobservable queue using arrival and departure times

Computers and Industrial Engineering
Identification and approximations for systems with multi-stage workflows

Proceedings of the Winter Simulation Conference

Quantified Score

Hi-index	0.00

Visualization

Abstract

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.