The paper is in three sections: (1) the convergence of stochastic methods. The convergence of stochastic methods of road assignment such as BURRELL or DIAL are investigated in capacity-restrained networks where the cost of travel on any link depends on the flow of that link. A convergent solution is one where the costs assumed by the route-finding algorithm are identical to those corresponding to the resulting link flows. Both all-or-nothing and dial assignments are shown to be inherently non-convergent whereas under certain, quite reasonable, conditions the hypothesis underpinning BURRELL assignment should lead to convergent solutions. However, simplications made by BURRELL in the method of solution for a large network may make the point of convergence extremely difficult, if not impossible, to find. The authors conclude that the instability of these methods, reflected by severe oscillations in flows between interations, is generally an unaboidable feature of such models. (2) Equilibrium methods. This section reviews the equilibrium methods of assignment to capacity-restraint road networks, methods which are well-known theoretically but have not been used extensively in practice. Their major advantage over heuristic techniques is that they guarantee ultimate convergence to a solution which satisfies Wardrop's first principle of equal and minimum travel costs on all routes used. The principles of equilibrium assignment and a straightforward method based on iterative loading are presented. Results obtained by applying this method to a network of Leeds give better goodness of fit statistics with observed counts than conventional methods requiring comparable cpu times. In addition, the authors find that equilibrium methods are easy to incorporate into existing computer packages, require minimal user intervention, are stable in heavily-congested networks and avoid extreme misfits between predicted and observed flows. (3) Improved equilibrium methods. Two methods of improved solutions to equilibrium assignment models are described. The first, "quantal loading", is in fact based on a technique first used in Chicago over 20 years ago in which updates of the link times or costs are carried out at regular intervals within a single assignment rather than at the end. An extension which applies the same ideas as part of a series of iterative equilibrium assignments is developed. The major advantage of quantal loading is that it greatly accelerates the rate of convergence to Wardrop equilibrium, on a network of Leeds by a factor of 5 on the first iteration and factors of 2 thereafter. The potential reductions in cpu times are therefore considerable. The second technique is based on an improved method of combining or averaging different sets of link flows, again with the objective of accelerating convergences and reducing cpu. The results are less spectacular, but do show that the

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  • Corporate Authors:

    Printerhall Limited

    29 Newmart Street
    London W1P 3PE,   England 
  • Authors:
    • Vantagnetta
    • Dow, PDC
  • Publication Date: 1979-6

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  • Accession Number: 00310372
  • Record Type: Publication
  • Source Agency: Transport Research Laboratory
  • Files: ITRD, TRIS
  • Created Date: Aug 27 1980 12:00AM