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

Warren B. Powell

22 citations0/0 files storedTransportation Science

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Advanced Queuing Theory Analysis Transportation Planning and Optimization Traffic control and management

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.

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References

1983The Single Server Queue.1967A General Class of Bulk Queues with Poisson Input 1954On Queueing Processes with Bulk Service 1959Imbedded Markov Chain Analysis of a Waiting-Line Process in Continuous Time 1986The Bulk Service Queue with a General Control Strategy: Theoretical Analysis and a New Computational Procedure 1955Waiting Time in Bulk Service Queues 1985Analysis of Vehicle Holding and Cancellation Strategies in Bulk Arrival, Bulk Service Queues 1959A Contribution to the Theory of Bulk Queues

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