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ML Estimation of Intensity Function in Non-homogeneous Poisson Processes

Author

Listed:
  • Anjale Ramesh

    (University of Calicut)

  • Manoharan M.

    (University of Calicut)

Abstract

Real-world service systems, such as call centres, hospitals, and transportation networks, often experience time-varying arrivals due to fluctuating demand patterns throughout the day. Accurately modelling these systems requires incorporating realistic characteristics. A commonly used approach for modelling time-varying arrival processes is the non-homogeneous Poisson process (NHPP), which allows the arrival rate to vary over time. Unlike the traditional Poisson process with a constant intensity, NHPP captures fluctuations in arrival patterns by incorporating a time-dependent intensity function. Estimating this intensity function is crucial for accurately modelling the time-varying arrivals. In this study, we explore the maximum likelihood estimation (MLE) method to estimate the intensity function of an NHPP. We model call arrivals using a simulated dataset from a customer care call centre and compare the actual and estimated intensity functions. The results demonstrate that the estimated intensity function provides a good fit to the data. Additionally, we model real-time bus arrival events using NHPP and estimate their intensity function. Python is the chosen programming language for this study.

Suggested Citation

  • Anjale Ramesh & Manoharan M., 2025. "ML Estimation of Intensity Function in Non-homogeneous Poisson Processes," SN Operations Research Forum, Springer, vol. 6(2), pages 1-10, June.
    • Handle: RePEc:spr:snopef:v:6:y:2025:i:2:d:10.1007_s43069-025-00447-8
    DOI: 10.1007/s43069-025-00447-8
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    References listed on IDEAS

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    1. Anjale Ramesh & M. Manoharan, 2025. "Transient behaviour of time-varying tandem queueing networks," OPSEARCH, Springer;Operational Research Society of India, vol. 62(1), pages 104-118, March.
    2. Slimacek, Vaclav & Lindqvist, Bo Henry, 2016. "Nonhomogeneous Poisson process with nonparametric frailty," Reliability Engineering and System Safety, Elsevier, vol. 149(C), pages 14-23.
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