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Exploiting Markov chains to infer queue length from transactional data

Part of: Special processes Stochastic processes

Published online by Cambridge University Press:  14 July 2016

D. J. Daley  and
L. D. Servi
D. J. Daley*
Affiliation:
The Australian National University
L. D. Servi*
Affiliation:
GTE Laboratories Inc.
*
∗Postal address: Statistics Research Section, School of Mathematical Sciences, Australian National University, Canberra, GPO Box 4, ACT 2601, Australia.
∗∗Postal address: GTE Laboratories Incorporated, 40 Sylvan Road, Waltham, MA 02254, USA.
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Abstract

The use of taboo probabilities in Markov chains simplifies the task of calculating the queue-length distribution from data recording customer departure times and service commencement times such as might be available from automatic bank-teller machine transaction records or the output of telecommunication network nodes. For the case of Poisson arrivals, this permits the construction of a new simple exact O(n3) algorithm for busy periods with n customers and an O(n2 log n) algorithm which is empirically verified to be within any prespecified accuracy of the exact algorithm. The algorithm is extended to the case of Erlang-k interarrival times, and can also cope with finite buffers and the real-time estimates problem when the arrival rate is known.

Keywords

M/GI/1 QUEUEEK/GI/1 QUEUETABOO PROBABILITIESPOISSON PROCESSCROSS-COUPLING

MSC classification

Primary: 60K25: Queueing theory
Secondary: 60G55: Point processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 29 , Issue 3 , September 1992 , pp. 713 - 732
Copyright
Copyright © Applied Probability Trust 1992 

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References

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