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Metamodels for estimating waterway delays through series of queues

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  • Dai, Melody D. M.
  • Schonfeld, Paul

Abstract

A numerical method has been developed for estimating delays on congested waterways. Analytic and numerical results are presented for series of G/G/1 queues, i.e. with generally distributed arrivals and service times and single chambers at each lock. One or two-way traffic operations are modelled. A metamodelling approach which develops simple formulas to approximate the results of simulation models is presented. The structure of the metamodels is developed from queueing theory while their coefficients are statistically estimated from simulation results. The numerical method consists of three modules: (1) delays, (2) arrivals and (3) departures. The first estimates the average waiting time for each lock when the arrival and service time distributions at this lock are known. The second identifies the relations between the arrival distributions at one lock and the departure distributions from the upstream and downstream locks. The third estimates the mean and variance of inter-departure times when the inter-arrival and service time distributions are known. The method can be applied to systems with two-way traffic through common bi-directional servers as well as to one-way traffic systems. Algorithms for both cases are presented. This numerical method is shown to produce results that are close to the simulation results. The metamodels developed for estimating delays and variances of inter-departure times may be applied to waterways and other series of G/G/1 queues. These metamodels for G/G/1 queues may provide key components of algorithms for analyzing networks of queues.

Suggested Citation

  • Dai, Melody D. M. & Schonfeld, Paul, 1998. "Metamodels for estimating waterway delays through series of queues," Transportation Research Part B: Methodological, Elsevier, vol. 32(1), pages 1-19, January.
    • Handle: RePEc:eee:transb:v:32:y:1998:i:1:p:1-19
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    1. L D Smith & D C Sweeney & J F Campbell, 2009. "Simulation of alternative approaches to relieving congestion at locks in a river transportion system," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(4), pages 519-533, April.
    2. Yuan, Yanbin & Ji, Bin & Yuan, Xiaohui & Huang, Yuehua, 2015. "Lockage scheduling of Three Gorges-Gezhouba dams by hybrid of chaotic particle swarm optimization and heuristic-adjusted strategies," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 74-89.
    3. Deng, Yao & Sheng, Dian & Liu, Baoli, 2021. "Managing ship lock congestion in an inland waterway: A bottleneck model with a service time window," Transport Policy, Elsevier, vol. 112(C), pages 142-161.
    4. Ji, Bin & Zhang, Dezhi & Yu, Samson S. & Zhang, Binqiao, 2021. "Optimally solving the generalized serial-lock scheduling problem from a graph-theory-based multi-commodity network perspective," European Journal of Operational Research, Elsevier, vol. 288(1), pages 47-62.
    5. Ji, Bin & Zhang, Dezhi & Zhang, Zheng & Yu, Samson S. & Van Woensel, Tom, 2022. "The generalized serial-lock scheduling problem on inland waterway: A novel decomposition-based solution framework and efficient heuristic approach," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 168(C).
    6. Caris, An & Limbourg, Sabine & Macharis, Cathy & van Lier, Tom & Cools, Mario, 2014. "Integration of inland waterway transport in the intermodal supply chain: a taxonomy of research challenges," Journal of Transport Geography, Elsevier, vol. 41(C), pages 126-136.
    7. Xiqun (Michael) Chen & Xiang He & Chenfeng Xiong & Zheng Zhu & Lei Zhang, 2019. "A Bayesian Stochastic Kriging Optimization Model Dealing with Heteroscedastic Simulation Noise for Freeway Traffic Management," Transportation Science, INFORMS, vol. 53(2), pages 545-565, March.

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