A Modified Iogit Assignment Model Which Obviates Enumeration and Overlapping Problems
RUSSO F and VITE i i i A A, Universittt degli Studi di Reggio Calabria, Italy
A very significant body of literature dealing with assignment models for urban and extra-urban transport networks, both for road and transit systems, has been produced over the year.s..The most commonly used assignment models are based on route choice mod
A very significant body of literature dealing with assignment models for urban and extra-urban transport networks, both for road and transit systems, has been produced over the year.s..The most commonly used assignment models are based on route choice models (deterministic or stochastic) solved with implicit or explicit path enumeration algorithms. Recently, studies have been conducted to analyse the generation of path choice set subject to behavioural rules.
Assignment models (Cascetta, 1998) are used both for congested networks within equilibrium models or dynamic models and for non-congested networks within static or pseudo-dynamic network loading models, with specifications of path choice that allow the use of implicit path enumeration algorithms.
Stochastic User Equilibrium (SUE) assignment models take into account errors in user's generalised cost perceptions, and with the stochastic approach it is possible to model multi-class problems.
For SUE assignment, Logit dr Probit models are generally used. The Logit model has a closed analytical functional form and with Dial's specification (Dial, 1971) has the possibility of being solved with algorithms on the network but it has the problem of IIA (Independence of Irrelevant Alternative) which, in the case of paths with considerable overlaps, significantly affects the quality of the results. The Probit model proposed by Sheffi and Powell (1981) overcomes the path overlapping problem, by introducing a covariance proportional to the degree of path overlapping. Models in the Probit family cannot be expressed in closed analytical form and hence, to be solved, require Montecarlo techniques which, though based on implicit path enumeration algorithms, generally demand a large number of iterations.
On the other hand, explicit path enumeration allows greater modelling flexibility insomuch as it is possible to model both choice set generation and choice among alternatives, including path-related attributes.
Explicit enumeration allows path information to be obtained and hence the reconstruction of relevant attributes which define systematic utility, as well as the elements which contribute to forming the dispersion matrix concerning the hypotheses used to define the random errors. Dispersion matrixes may thus be specified with different structures and/or multiple decisional levels.
In the context of explicit path enumeration a C-Logit model has been proposed (Cascetta et aL, 1996) which, though retaining a closed analytical form, allows us to take account of path overlapping problems.
In this paper the C-Logii model and Dial algorithm are reconstructed in order to define a D-C-Legit path choice which "obviates path enumeration" and "Overcomes path overlapping problems". The model and its solution algorithm, based on a Dial structure, combine several positive features from models and algorithms found in the literature (Tab. 1).
The probability in the route choice model is evaluated in a closed form with a Legit model but a term depending on the path overlapping ratio is inserted. The Commonality Factor (C-Legit) proposed is used in an implicit Dial assignment. The modified algorithm simulates the overlapping effect among alternative paths, eliminates explicit enumeration and computes just one tree per origin.
The proposed formulation is verified on a test network and on a real transportation system. The model parameters are also calibrated in the real system using traffic flows" counted on links and the algorithm is compared with standard implicit Legit (Dial, 1971) and Montecarlo Probit (Sheffi and Powell, 1981) algorithms. The results, in term of real flows reproduction, are comparable with Probit and better than the results obtained with standard implicit Legit.
The paper is structured as follows: in section 2 notation and terminology are reported; section 3 treats the main features of the proposed model in terms of generating the choice set and choosing the alternative; in section 4 the solution algorithm is reported; lastly, in section 5 some numerical applications are presented.
Association for European Transport