FLOW OVER TIME PROBLEM WITH INFLOW-DEPENDENT TRANSIT TIMES

Authors

  • Durga Prasad Khanal Central Department of Mathematics, Tribhuvan University, Kirtipur, Kathmandu
  • Urmila Pyakurel Central Department of Mathematics, Tribhuvan University, Kirtipur, Kathmandu
  • Tanka Nath Dhamala Central Department of Mathematics, Tribhuvan University, Kirtipur, Kathmandu

Keywords:

Inflow-dependent transit times, Bow graph, Inflow-preserving flow, Quickest flow, Earliest arrival flow

Abstract

 Network flow over time is an important area for the researcher relating to the traffic assignment problem. Transmission times of the vehicles directly depend on the number of vehicles entering the road. Flow over time with fixed transit times can be solved by using classical (static) flow algorithms in a corresponding time expanded network which is not exactly applicable for flow over time with inflow dependent transit times. In this paper we discuss the time expanded graph for inflow-dependent transit times and non-existence of earliest arrival flow on it. Flow over time with inflow-dependent transit times are turned to inflow-preserving flow by pushing the flow from slower arc to the fast flow carrying arc. We gave an example to show that time horizon of quickest flow in bow graph GB was strictly smaller than time horizon of any inflow-preserving flow over time in GB satisfying the same demand. The relaxation in the modified bow graph turns the problem into the linear programming problem.

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Published

2018-12-30

How to Cite

FLOW OVER TIME PROBLEM WITH INFLOW-DEPENDENT TRANSIT TIMES. (2018). Journal of Institute of Science and Technology, 23(1), 49-56. https://doi.org/10.3126/jist.v23i1.22161

Issue

Vol. 23 No. 1 (2018)

Section

Research Articles

License

The copyright of the articles is held by the Institute of Science and Technology, Tribhuvan University (IoST- TU). The views and interpretations in this journal are those of the author(s). They are not attributable to the IoST-TU and do not imply the expression of any opinion concerning the legal status of any country, territory, city, area of its authorities, or concerning the delimitation of its frontiers or boundaries. The corresponding author is responsible for any conflict of interest between authors and others.

The articles in the Journal of Institute of Science and Technology are licensed under a Creative Commons Attribution- Share Alike 4.0 International License (CC: BY-NC), which permits use, distribution and reproduction in any medium or format, remix, transfer, and build upon the materials for any purpose, even commercially, provided the original work is properly cited.

How to Cite

FLOW OVER TIME PROBLEM WITH INFLOW-DEPENDENT TRANSIT TIMES. (2018). Journal of Institute of Science and Technology, 23(1), 49-56. https://doi.org/10.3126/jist.v23i1.22161