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Stochastic Models of Internal Mail Delivery Systems


  • Steven Nahmias

    (Department of Decision and Information Sciences, University of Santa Clara, Santa Clara, California 95053)

  • Michael H. Rothkopf

    (Energy Analysis Program, Lawrence Berkeley Laboratory, Berkeley, California 94720)


This paper develops two stochastic models of an internal mail delivery system in which a single clerk picks up, sorts and delivers mail to a closed loop of offices. The two models differ in whether deliveries are made at scheduled times or not. For a model in which all mail picked up each round is sorted before the next delivery, we assume that mail is generated in the system by a stationary Poisson process and derive an expression for the expected delay between generation of a letter and its ultimate delivery. These results are then extended to systems in which letters are generated according to a stationary compound Poisson process and to multiple clerk delivery systems. A second model in which mail is delivered at scheduled times only is shown to be equivalent to a classical storage process. For this model, we derive bounds on the expected number of letters left unsorted at the start of a scheduled delivery and the expected delivery delay. This model is also generalized to multiclerk systems.

Suggested Citation

  • Steven Nahmias & Michael H. Rothkopf, 1984. "Stochastic Models of Internal Mail Delivery Systems," Management Science, INFORMS, vol. 30(9), pages 1113-1120, September.
  • Handle: RePEc:inm:ormnsc:v:30:y:1984:i:9:p:1113-1120

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