The shuttle dispatch problem with compound Poisson arrivals: controls at two terminals
H. S. Lee,Mandyam M. Srinivasan +1 more
TL;DR: A search procedure is discussed to obtain the mean waiting time of an arbitrary passenger at each terminal for given control valuesm1 andm2 to minimize the total expected cost per unit time under a linear cost structure.
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Abstract: 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 terminali, at the instant that the total number of passengers waiting at terminali reaches or exceeds a predetermined control limitm
i
. The objective of this paper is to obtain the mean waiting time of an arbitrary passenger at each terminal for given control valuesm
1 andm
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.
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TL;DR: Under a linear cost structure, an explicit expression for the expected cost per unit time as a function of the control value, m, is provided and a simple and efficient method for computing the optimal control value is presented.
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