APPROXIMATE EXPRESSIONS FOR QUEUEING SYSTEMS WITH SCHEDULED ARRIVALS AND ESTABLISHED SERVICE ORDER

This paper examines a single server queueing model in which customers have scheduled arrival times and must be served in the order of the schedule. This model can be used to represent the ship competition for berth space (or cranes) at a seaport. The paper is organized as follows: Section 1 introduces the model and its notation. It also introduces a recursive equation for the customer departure times, and two light traffic approximations for the steady state solution: a first order approximation, involving one iteration of the recursion, and a second order approximation, involving two iterations. The main section, Section 2, includes analytical expressions for arrivals whose unpunctuality is described by a distribution with exponential tails either on one side or on both. The results are compared with: (a) simulated results (to illustrate the accuracy of the expressions for various traffic levels and levels of unpunctuality), and (b) exact results for a special case with Gumbel arrivals (to test the robustness of the expressions when the unpunctuality distribution is not as assumed). A short discussion explains how the results can be used and suggests extensions to this research. Appendix A develops the exact results for the Gumbel model.

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• Authors:
  • Sabria, F
  • Daganzo, C F
• Publication Date: 1989-8

Media Info

• Features: Appendices; References; Tables;
• Pagination: p. 159-165
• Serial:
  • Transportation Science
  • Volume: 23
  • Issue Number: 3
  • Publisher: Institute for Operations Research and the Management Sciences (INFORMS)
  • ISSN: 0041-1655
  • Serial URL: http://transci.journal.informs.org/

Subject/Index Terms

• TRT Terms: Equations; Forecasting; Intermodal terminals; Ports; Queuing; Ships; Traffic delays
• Subject Areas: Highways; Marine Transportation; Planning and Forecasting; Terminals and Facilities; Vehicles and Equipment;

Filing Info

• Accession Number: 00488564
• Record Type: Publication
• Files: TRIS
• Created Date: Oct 31 1989 12:00AM