The shuttle dispatch problem with compound Poisson arrivals: Controls at two terminals.

*(English)*Zbl 0715.90048Summary: 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 |

##### Keywords:

batch service queues; bulk arrival queueing systems; mass-transit systems; infinite capacity shuttle; control limit policy; mean waiting time
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\textit{H.-S. Lee} and \textit{M. M. Srinivasan}, Queueing Syst. 6, No. 2, 207--221 (1990; Zbl 0715.90048)

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