Transpn. zyxwvutsrqponmlkjihgfedcbaZYXWVUT Rex -A., Vol. 30, No. 4, pp. 287-305, 1996 Copyright G 1996 ElsevierScience Ltd Pergamon Printed~in Great Britain. All rights reserved 0965-8564/96 $15.00 + 0.00 ESTIMATION OF A TRIP TABLE AND THE 0 PARAMETER IN A STOCHASTIC NETWORK SHIHSIEN LIU Department of Transportation Management, Tamkang University, Taipei, Taiwan, R.O.C. and JON D. FRICKER School of Civil Engineering, Purdue University, West Lafayette, IN 47907-1284, U.S.A (Received I3 March 1995) Abstract-An origin-destination (O-D) table that accurately portrays a study area’s travel pat- terns is a valuable element in the modeling and analysis used to support public transportation investment decisions. The probabilistic approach to O-D table estimation involves a heuristic enumeration of link choice probabilities. The parameter 8, which reflects the variation in path choices among tripmakers, has not been discussed in the context of O-D table estimation, nor has an efficient way been demonstrated to determine the associated link use probabilities. This paper presents a method for O-D table estimation in a stochastic network. The “OD,Theta” method can not only estimate the O-D table, it also estimates the 8 parameter in the same process. The pro- posed method is illustrated using a sample test network. Finally, the method is applied to a real network, with the results compared to those from some well-known O-D estimation software. Copyright 0 1996 Elsevier Science Ltd INTRODUCTION The accuracy of an origin-destination (O-D) table estimated from link counts is affected by many factors, including the accuracy of the link counts and the assumed route choice behavior of the tripmakers. There are three main ways to approach this problem, all of which are based on explicit trip-making behavior. The Gravity Model assumes that each trip interchange value is based on the level of productions and attractions at the trip origin and destination, and on a function that represents the spatial separation of each origin-destination pair. Because trip impedance between each O-D pair affects the level of the trip production and attraction, the main drawback of the gravity model is that it cannot handle with accuracy external-external (or ‘through’) trips (Willumsen, 1981). A second approach uses mathematical programming techniques associated with equili- brium traffic assignment methods to estimate a trip matrix in a congested network. Based on the user equilibrium condition, Nguyen (1977) developed a bi-level programming structure to derive O-D tables from traffic counts via two models. By ‘bi-level program- ming problem’, we mean using two separate but interdependent optimization models to solve the problem iteratively. The major disadvantage of this approach is that a bi-level programming structure would pose computational difficulties for a large network. The third approach, entropy maximization (EM) and information minimization (IM), can make full use of the information contained in the observed flows. Actually, EM and IM are two similar but distinct model types. EM assumes that observed link counts follow the multinomial distribution. This assumption provides the basis for modeling O-D trip patterns if no more information is known about the network flows. The IM model, how- ever, adjusts the EM’s distribution assumption if given information about the degree to which O-D trips use each of the links in the network. Unfortunately, the link use infor- mation is usually derived from an outdated or artificially fabricated trip table. 287