TRAJECTORY ANALYSIS OF THE STOCHASTIC QUEUE MEDIAN IN A PLANE WITH RECTILINEAR DISTANCES

This paper analyzes the trajectory of the stochastic queue median (SQM) location problem in a planar region with a rectilinear travel metric. The location objective is to minimize expected response time to customers. A methodology is introduced for parametric analysis of planar location problems which is potentially applicable to other location problems as well. Using the methodology, strong parallels are demonstrated between the planar SQM problem and the same problem on a tree network. It is shown how the optimal SQM location must occur in a certain region of the plane. Given a mild regularity condition, trajectory results are developed for the optimal location as a function of the customer call rate, and a simple necessary and sufficient ratio condition is derived which characterizes points on the optimal trajectory. An algorithm is presented for finding that trajectory. Also analyzed is the problem in the degenerate case when the regularity condition is violated. Finally, the results are extended to the planar stochastic expected queue median problem, which incorporates stochastic travel times.

• Availability:
  • Find a library where document is available. Order URL: http://worldcat.org/oclc/1767714
• Corporate Authors:

  Operations Research Society of America

  Mount Royal and Guilford Avenue
  Baltimore, MD  United States  21202
• Authors:
  • Brandeau, M L
  • Chiu, S S
• Publication Date: 1990-8

Media Info

• Features: Appendices; Figures; References; Tables;
• Pagination: p. 230-243
• Serial:
  • Transportation Science
  • Volume: 24
  • 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: Algorithms; Emergency response time; Facilities; Location; Methodology; Minimization; Optimization; Queuing; Reaction time; Stochastic processes; Trajectory; Travel time; Vehicle trajectories
• Old TRIS Terms: Customer call rate
• Subject Areas: Data and Information Technology; Highways; Planning and Forecasting;

Filing Info

• Accession Number: 00496729
• Record Type: Publication
• Files: TRIS
• Created Date: Aug 31 1990 12:00AM