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Tollbooth tandem queues with infinite homogeneous servers

  • Xiuli Chao (a1), Qi-Ming He (a2) and Sheldon Ross (a3)

Abstract

In this paper we analyze a tollbooth tandem queueing problem with an infinite number of servers. A customer starts service immediately upon arrival but cannot leave the system before all customers who arrived before him/her have left, i.e. customers depart the system in the same order as they arrive. Distributions of the total number of customers in the system, the number of departure-delayed customers in the system, and the number of customers in service at time t are obtained in closed form. Distributions of the sojourn times and departure delays of customers are also obtained explicitly. Both transient and steady state solutions are derived first for Poisson arrivals, and then extended to cases with batch Poisson and nonstationary Poisson arrival processes. Finally, we report several stochastic ordering results on how system performance measures are affected by arrival and service processes.

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Copyright

Corresponding author

Postal address: Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, MI 48109, USA. Email address: xchao@umich.edu
∗∗ Postal address: Department of Management Sciences, University of Waterloo, 200 University Avenue West, Waterloo, ON N2L 3G1, Canada. Email address: q7he@uwaterloo.ca
∗∗∗ Postal address: Daniel J. Epstein Department of Industrial and Systems Engineering, University of Southern California, Los Angeles, CA 90089, USA. Email address: smross@usc.edu

References

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Journal of Applied Probability
  • ISSN: 0021-9002
  • EISSN: 1475-6072
  • URL: /core/journals/journal-of-applied-probability
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