Walking-Distance Introduced Queueing Theory

  • Daichi Yanagisawa
  • Akiyasu Tomoeda
  • Ayako Kimura
  • Katsuhiro Nishinari
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5191)


We introduce the effect of delay in walking from the head of the queue to the service windows in the queueing theory, and obtain the suitable type of queueing system under various conditions. When there are plural service windows, the queueing theory indicates that a fork-type queue, which collects people into a single queue, is more efficient than a parallel-type queue, i.e., queues for each service windows. However, in the walking-distance introduced queueing theory, we find that the parallel-type queue is more efficient when sufficiently many people are waiting in queues, and service time is shorter than walking time. We also consider the situation where there are two kinds of people, whose service time is short and long. The analytical result says that we can decrease people’s waiting time and their stress by setting up queues for each kind of people separately.


Service Time Cellular Automaton Service Rate Queueing System Throughput Rate 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Daichi Yanagisawa
    • 1
    • 2
  • Akiyasu Tomoeda
    • 1
  • Ayako Kimura
    • 1
  • Katsuhiro Nishinari
    • 1
    • 3
  1. 1.Department of Aeronautics and Astronautics, School of EngineeringThe University of Tokyo 
  2. 2.JSPS Research Fellow 
  3. 3.PRESTO, Japan Science and Technology Corporation TokyoJapan

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