On Observable Chaotic Maps for Queuing Analysis

Abstract

A queuing model based on chaotic mapping offers a number of distinct advantages over stochastic and constant deterministic models. Depending on the type of chaotic map used, such a queue can capture transient behavior, intermittency, steady state behavior, and complex distributions in arrival rates. These characteristics are especially desirable in many queuing applications in transportation. Earlier studies resulted in chaotic queuing models that cannot be estimated by using observed arrivals. An alternative queuing model is presented along with methods to specify the model, interpret its results, and estimate its parameters. The proposed queuing model used chaotic maps of interarrival times to generate arrivals so that parameters could be calibrated with observable data. A sample queue based on the ergodic logistic map is presented. For the calibration of the mapping on the basis of observed data, the method of successive averages was used with a joint parameter and state estimation algorithm. Two connected queues illustrated how a purely deterministic queuing network could still result in a joint invariant distribution. The results offer a positive view of this method and its applicability to queuing problems, particularly in the field of transportation and dynamic network loading.