Approximate, Closed Form Moment Formulas for Bulk Arrival, Bulk Service Queues

Warren B. Powell
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Warren B. Powell: Princeton University, Princeton, New Jersey

Transportation Science, 1986, vol. 20, issue 1, 13-23

Abstract: Traditional analysis of bulk queues has relied on classical transform methods, which requires the determination of the complex zeroes of a given function, or iterative numerical techniques. In this research, transform results are used to help find approximate closed form expressions for the mean and variance of the length of the queue at departure instants. The moments of the length of the queue in continuous time and of the waiting time distribution are derived in closed form as a function of the new formulas. An approximate method for fitting a distribution for the length of the queue is provided and used to calculate the probability a customer will leave on a given outbound vehicle. Finally, approximate queueing and delay formulas are developed for bulk queues operating under a vehicle cancellation policy.

Date: 1986
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ortrsc:v:20:y:1986:i:1:p:13-23

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