METAMODELS FOR ESTIMATING WATERWAY DELAYS THROUGH SERIES OF QUEUES

A numerical method has been developed for estimating delays on congest ed waterways. Analytic and numerical results are presented for series of G/G/1 queues, i.e. with generally distributed arrivals and service times and single chambers at each lock. One or two-way traffic operati ons are modelled. A metamodelling approach which develops simple formu las to approximate the results of simulation models is presented. The structure of the metamodels is developed from queueing theory while th eir coefficients are statistically estimated from simulation results. The numerical method consists of three modules: (1) delays, (2) arriva ls and (3) departures. The first estimates the average waiting time fo r each lock when the arrival and service time distributions at this lo ck are known. The second identifies the relations between the arrival distributions at one lock and the departure distributions from the ups tream and downstream locks. The third estimates the mean and variance of inter-departure times when the inter-arrival and service time distr ibutions are known. The method can be applied to systems with two-way traffic through common hi-directional servers as well as to one-way tr affic systems. Algorithms for both cases are presented. This numerical method is shown to produce results that are close to the simulation r esults. The metamodels developed for estimating delays and variances o f inter-departure times may be applied to waterways and other series o f G/G/1 queues. These metamodels for G/G/1 queues may provide key comp onents of algorithms for analyzing networks of queues. (C) 1998 Elsevi er Science Ltd.