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The shuttle dispatch problem with compound Poisson arrivals: Controls at two terminals. (English) Zbl 0715.90048
Summary: We consider the control of an infinite capacity shuttle which transports passengers between two terminals. The passengers arrive at each terminal according to a compound Poisson process and the travel time from one terminal to the other is a random variable following an arbitrary distribution. The following control limit policy is considered: dispatch the shuttle at terminal i, at the instant that the total number of passengers waiting at terminal i reaches or exceeds a predetermined control limit \(m_ i\). The objective of this paper is to obtain the mean waiting time of an arbitrary passenger at each terminal for given control values \(m_ 1\) and \(m_ 2\). We also discuss a search procedure to obtain the optimal control values which minimize the total expected cost per unit time under a linear cost structure.

MSC:
90B22 Queues and service in operations research
60K25 Queueing theory (aspects of probability theory)
93E20 Optimal stochastic control
90B06 Transportation, logistics and supply chain management
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