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Markov Renewal Modelling of Poisson Traffic at Intersections having Separate Turn Lanes

In: Semi-Markov Models and Applications

Author

Listed:
  • Rudy Gideon

    (University of Montana)

  • Ronald Pyke

    (University of Washington)

Abstract

Consider a two-lane road which is intersected on one side by a single-lane secondary road. A single car waiting on the secondary road may merge into either the nearest or the farthest lane. It is assumed that the traffic in each lane is independent of the other lanes and that the inter-arrival times of cars at the intersection in their respective lanes is exponential. The main purpose of this paper is to study the queue size on the secondary road when the secondary road has a special right-turn lane (or left-turn lane in some countries) which allows some cars to merge into the nearest lane of the main road even when other cars waiting to enter the far lane are present. The problem is approached by first setting up a four-state Markov Renewal process to describe the traffic on the main road. Next the merging process on the secondary road is described as a Markov Renewed process with a random environment. The event that the queue is empty is studied, and conditions are stated under which this event is recurrent or transient. Finally, the quantities which occur in the conditions for recurrence of an empty queue are derived explicitly for a one-car right turn lane.

Suggested Citation

  • Rudy Gideon & Ronald Pyke, 1999. "Markov Renewal Modelling of Poisson Traffic at Intersections having Separate Turn Lanes," Springer Books, in: Jacques Janssen & Nikolaos Limnios (ed.), Semi-Markov Models and Applications, chapter 0, pages 285-310, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4613-3288-6_18
    DOI: 10.1007/978-1-4613-3288-6_18
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