Stochastic Models of Internal Mail Delivery Systems

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.

• 저널Management Science · 30(9) · 1113–1120
• 토픽Advanced Queuing Theory Analysis · Management Information Systems
• DOI10.1287/mnsc.30.9.1113
• 저자Steven Nahmias, Michael H. Rothkopf