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Distribution sensitivity in a highway flow model
Author(s) -
Ross Andrew M.
Publication year - 2009
Publication title -
applied stochastic models in business and industry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.413
H-Index - 40
eISSN - 1526-4025
pISSN - 1524-1904
DOI - 10.1002/asmb.761
Subject(s) - sensitivity (control systems) , clearance , queue , queueing theory , traffic flow (computer networking) , distribution (mathematics) , log normal distribution , mathematics , statistics , computer science , simulation , computer network , mathematical analysis , engineering , medicine , electronic engineering , urology
We examine a model of traffic flow on a highway segment, where traffic can be impaired by random incidents (usually, collisions). Using analytical and numerical methods, we show the degree of sensitivity that the model exhibits to the distributions of service times (in the queueing model) and incident clearance times. Its sensitivity to the distribution of time until an incident is much less pronounced. Our analytical methods include an M / G t /∞ analysis ( G t denotes a service process whose distribution changes with time) and a fluid approximation for an M / M / c queue with general distributions for the incident clearance times. Our numerical methods include M / PH 2 / c / K models with many servers and with phase‐type distributions for the time until an incident occurs or is cleared. We also investigate different time scalings for the rate of incident occurrence and clearance. Copyright © 2009 John Wiley & Sons, Ltd.