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Semi-open queuing networks: a review of stochastic models, solution methods and new research areas

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  • Debjit Roy

Abstract

Capturing the waiting times (at an external queue) for a customer to access a movable resource is an important step towards measuring customer service and system performance in manufacturing, logistics, communication and health care systems. Such waiting time measures are typically used for sizing resource and buffer capacities, and thereby minimising customer waiting time probabilities. In this regard, semi-open queuing networks (SOQNs), which decouple the arriving customers/transactions from the network resources using a synchronisation station (also known as a semaphore queue), can potentially capture the customer/transaction waiting times/costs more precisely and provide a rich network modelling construct. Hence, modelling manufacturing or service systems using SOQNs is an important step towards measuring customer flow times (sojourn times) wherein the customer waiting times at an external queue are a critical component. In this paper, we present several stochastic models for manufacturing and service systems using SOQNs and also discuss the potential applications of SOQNs. We then review the solution methods for SOQNs and also compare the numerical accuracies for three promising methods. Finally, we include the potential research areas in SOQNs.

Suggested Citation

  • Debjit Roy, 2016. "Semi-open queuing networks: a review of stochastic models, solution methods and new research areas," International Journal of Production Research, Taylor & Francis Journals, vol. 54(6), pages 1735-1752, March.
    • Handle: RePEc:taf:tprsxx:v:54:y:2016:i:6:p:1735-1752
    DOI: 10.1080/00207543.2015.1056316
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    Cited by:

    1. Tappia, Elena & Roy, Debjit & Melacini, Marco & De Koster, René, 2019. "Integrated storage-order picking systems: Technology, performance models, and design insights," European Journal of Operational Research, Elsevier, vol. 274(3), pages 947-965.
    2. Azadeh, K. & de Koster, M.B.M. & Roy, D., 2017. "Robotized Warehouse Systems: Developments and Research Opportunities," ERIM Report Series Research in Management ERS-2017-009-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    3. 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.
    4. Chen, Wanying & Gong, Yeming & Chen, Qi & Wang, Hongwei, 2024. "Does battery management matter? Performance evaluation and operating policies in a self-climbing robotic warehouse," European Journal of Operational Research, Elsevier, vol. 312(1), pages 164-181.
    5. Marvin Carl May & Alexander Albers & Marc David Fischer & Florian Mayerhofer & Louis Schäfer & Gisela Lanza, 2021. "Queue Length Forecasting in Complex Manufacturing Job Shops," Forecasting, MDPI, vol. 3(2), pages 1-17, May.
    6. 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.
    7. 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.
    8. Emilio Moretti & Elena Tappia & Martina Mauri & Marco Melacini, 2022. "A performance model for mobile robot-based part feeding systems to supermarkets," Flexible Services and Manufacturing Journal, Springer, vol. 34(3), pages 580-613, September.
    9. 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.
    10. Sonja Otten & Ruslan Krenzler & Lin Xie & Hans Daduna & Karsten Kruse, 2022. "Analysis of semi-open queueing networks using lost customers approximation with an application to robotic mobile fulfilment systems," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 44(2), pages 603-648, June.
    11. Kumawat, Govind Lal & Roy, Debjit & De Koster, René & Adan, Ivo, 2021. "Stochastic modeling of parallel process flows in intra-logistics systems: Applications in container terminals and compact storage systems," European Journal of Operational Research, Elsevier, vol. 290(1), pages 159-176.
    12. 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.
    13. Kaveh Azadeh & René De Koster & Debjit Roy, 2019. "Robotized and Automated Warehouse Systems: Review and Recent Developments," Transportation Science, INFORMS, vol. 53(4), pages 917-945, July.
    14. Chesoong Kim & Sergey Dudin & Alexander Dudin & Konstantin Samouylov, 2019. "Analysis of a Semi-Open Queuing Network with a State Dependent Marked Markovian Arrival Process, Customers Retrials and Impatience," Mathematics, MDPI, vol. 7(8), pages 1-19, August.

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