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A discrete-time queueing network approach to performance evaluation of autonomous vehicle storage and retrieval systems

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  • Martin Epp
  • Simon Wiedemann
  • Kai Furmans

Abstract

In this paper, we present a method for performance evaluation of autonomous vehicle storage and retrieval systems (AVS/RSs) with tier-captive single-aisle vehicles. A discrete-time open queueing network approach is applied. The data obtained from the evaluation of the lift and vehicle movements can be used directly as input for the general discrete service time distributions of the queueing network. Furthermore, the approach allows for the computation of the retrieval transaction time distribution as well as of the distribution of the number of transactions waiting to be stored. Consequently, not only expected values and variances but also quantiles of the performance measures can be obtained. Comparison to discrete-event simulation quantifies approximation errors resulting from the decomposition approach in the discrete-time domain. Moreover, the errors obtained by the discrete-time approach are compared to the errors obtained using a continuous-time open queueing network approach. Finally, it will be outlined how the model can be used for designing AVS/RSs according to given system requirements, such as storage capacity, throughput, height and length of the system as well as the 95% quantile of the retrieval transaction time.

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  • Martin Epp & Simon Wiedemann & Kai Furmans, 2017. "A discrete-time queueing network approach to performance evaluation of autonomous vehicle storage and retrieval systems," International Journal of Production Research, Taylor & Francis Journals, vol. 55(4), pages 960-978, February.
    • Handle: RePEc:taf:tprsxx:v:55:y:2017:i:4:p:960-978
    DOI: 10.1080/00207543.2016.1208371
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    References listed on IDEAS

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    1. Roy, Debjit & Krishnamurthy, Ananth & Heragu, Sunderesh & Malmborg, Charles, 2015. "Queuing models to analyze dwell-point and cross-aisle location in autonomous vehicle-based warehouse systems," European Journal of Operational Research, Elsevier, vol. 242(1), pages 72-87.
    2. Fukunari, Miki & Malmborg, Charles J., 2009. "A network queuing approach for evaluation of performance measures in autonomous vehicle storage and retrieval systems," European Journal of Operational Research, Elsevier, vol. 193(1), pages 152-167, February.
    3. Li Zhang & Ananth Krishnamurthy & Charles J. Malmborg & Sunderesh S. Heragu, 2009. "Variance-based approximations of transaction waiting times in autonomous vehicle storage and retrieval systems," European Journal of Industrial Engineering, Inderscience Enterprises Ltd, vol. 3(2), pages 146-169.
    4. Debjit Roy & Ananth Krishnamurthy & Sunderesh Heragu & Charles Malmborg, 2012. "Performance analysis and design trade-offs in warehouses with autonomous vehicle technology," IISE Transactions, Taylor & Francis Journals, vol. 44(12), pages 1045-1060.
    5. Winfried K. Grassmann & Joti L. Jain, 1989. "Numerical Solutions of the Waiting Time Distribution and Idle Time Distribution of the Arithmetic GI/G/1 Queue," Operations Research, INFORMS, vol. 37(1), pages 141-150, February.
    6. Roodbergen, Kees Jan & Vis, Iris F.A., 2009. "A survey of literature on automated storage and retrieval systems," European Journal of Operational Research, Elsevier, vol. 194(2), pages 343-362, April.
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    Cited by:

    1. 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.
    2. Wu, Guangmei & Xu, Xianhao & Gong, Yeming (Yale) & De Koster, René & Zou, Bipan, 2019. "Optimal design and planning for compact automated parking systems," European Journal of Operational Research, Elsevier, vol. 273(3), pages 948-967.
    3. 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.

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