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Solving semi-open queuing networks with time-varying arrivals: An application in container terminal landside operations

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  • Dhingra, Vibhuti
  • Kumawat, Govind Lal
  • Roy, Debjit
  • Koster, René de

Abstract

Semi-open queuing networks (SOQNs) are widely applied to measure the performance of manufacturing, logistics, communications, restaurant, and health care systems. Many of these systems observe variability in the customer arrival rate. Therefore, solution methods, which are developed for SOQNs with time-homogeneous arrival rate, are insufficient to evaluate the performance of systems which observe time-varying arrivals. This paper presents an efficient solution approach for SOQNs with time-varying arrivals. We use a Markov-modulated Poisson Process to characterize variability in the arrival rate and develop a matrix-geometric method (MGM)-based approach to solve the network. The solution method is validated through extensive numerical experiments. Further, we develop a stochastic model of the landside operations at an automated container terminal with time-varying truck arrivals and evaluate using the MGM-based approach. Results show that commonly used time-homogeneous approximation of time-varying truck arrivals is inaccurate (error is more than 15% in expected waiting time and expected number of trucks waiting outside the terminal) for performance evaluation of the landside operations. The application results are insightful in resource planning, demand leveling, and regulating the number of trucks permitted inside the terminal.

Suggested Citation

  • Dhingra, Vibhuti & Kumawat, Govind Lal & Roy, Debjit & Koster, René de, 2018. "Solving semi-open queuing networks with time-varying arrivals: An application in container terminal landside operations," European Journal of Operational Research, Elsevier, vol. 267(3), pages 855-876.
    • Handle: RePEc:eee:ejores:v:267:y:2018:i:3:p:855-876
    DOI: 10.1016/j.ejor.2017.12.020
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    3. Amir Gharehgozli & Debjit Roy & Suruchika Saini & Jan-Kees Ommeren, 2023. "Loading and unloading trains at the landside of container terminals," Maritime Economics & Logistics, Palgrave Macmillan;International Association of Maritime Economists (IAME), vol. 25(3), pages 549-575, September.
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    6. Chesoong Kim & Sergei Dudin & Olga Dudina, 2019. "Queueing Network with Moving Servers as a Model of Car Sharing Systems," Mathematics, MDPI, vol. 7(9), pages 1-17, September.
    7. Valeriy A. Naumov & Yuliya V. Gaidamaka & Konstantin E. Samouylov, 2019. "On Truncation of the Matrix-Geometric Stationary Distributions," Mathematics, MDPI, vol. 7(9), pages 1-10, September.
    8. Lamballais, T. & Merschformann, M. & Roy, D. & de Koster, M.B.M. & Azadeh, K. & Suhl, L., 2022. "Dynamic policies for resource reallocation in a robotic mobile fulfillment system with time-varying demand," European Journal of Operational Research, Elsevier, vol. 300(3), pages 937-952.
    9. Roy, Debjit & van Ommeren, Jan-Kees & de Koster, René & Gharehgozli, Amir, 2022. "Modeling landside container terminal queues: Exact analysis and approximations," Transportation Research Part B: Methodological, Elsevier, vol. 162(C), pages 73-102.
    10. Lange, Ann-Kathrin & Nellen, Nicole & Jahn, Carlos, 2022. "Truck appointment systems: How can they be improved and what are their limits?," Chapters from the Proceedings of the Hamburg International Conference of Logistics (HICL), in: Kersten, Wolfgang & Jahn, Carlos & Blecker, Thorsten & Ringle, Christian M. (ed.), Changing Tides: The New Role of Resilience and Sustainability in Logistics and Supply Chain Management – Innovative Approaches for the Shift to a New , volume 33, pages 615-655, Hamburg University of Technology (TUHH), Institute of Business Logistics and General Management.
    11. Amir Gharehgozli & Nima Zaerpour & Rene Koster, 2020. "Container terminal layout design: transition and future," Maritime Economics & Logistics, Palgrave Macmillan;International Association of Maritime Economists (IAME), vol. 22(4), pages 610-639, December.
    12. Carmen, Raïsa & Van Nieuwenhuyse, Inneke & Van Houdt, Benny, 2018. "Inpatient boarding in emergency departments: Impact on patient delays and system capacity," European Journal of Operational Research, Elsevier, vol. 271(3), pages 953-967.
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