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Change point estimation of service rate in an M/M/1/m queue

Author

Listed:
  • Sarat Kumar Acharya
  • César Emilio Villarreal-Rodríguez

Abstract

The paper is concerned with the maximum likelihood estimation of the change point of arrival rate for an M/M/1/m queueing system. It is assumed that the change takes place after a fixed unknown number of completed services. We also calculate the maximum likelihood estimators of the traffic intensities after and before the change point and we prove that these estimators are weakly consistent. This work is applicable in planning economic models, social events and service to customers, where the service rate changes due to fatigue of the server or there is a shift change policy after a fixed amount of services done.

Suggested Citation

  • Sarat Kumar Acharya & César Emilio Villarreal-Rodríguez, 2013. "Change point estimation of service rate in an M/M/1/m queue," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 5(1), pages 110-120.
    • Handle: RePEc:ids:ijmore:v:5:y:2013:i:1:p:110-120
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    Citations

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    Cited by:

    1. Singh, Saroja Kumar & Cruz, Gabriel M.B. & Cruz, Frederico R.B., 2024. "Change point estimation of service rate in M/M/1/m queues: A Bayesian approach," Applied Mathematics and Computation, Elsevier, vol. 465(C).
    2. Singh, Saroja Kumar & Acharya, Sarat Kumar & Cruz, F.R.B. & Cançado, André L.F., 2023. "Change point estimation in an M/M/2 queue with heterogeneous servers," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 212(C), pages 182-194.
    3. Saroja Kumar Singh, 2022. "Change point problem for Markovian arrival queueing models: Bayes factor approach," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 13(6), pages 2847-2854, December.
    4. Saroja Kumar Singh & Sarat Kumar Acharya, 2022. "A Bayesian inference to estimate change point for traffic intensity in M/M/1 queueing model," OPSEARCH, Springer;Operational Research Society of India, vol. 59(1), pages 166-206, March.

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