Article:Maher, M.J., Zhang, X. and van Vliet, D. (2001) Abstract ⎯ This paper deals with two mathematically similar problems in transport network analysis: trip matrix estimation and traffic signal optimisation on congested road networks.These two problems are formulated as bi-level programming problems with stochastic user equilibrium assignment as the second-level programming problem. We differentiate two types of solutions in the combined matrix estimation and stochastic user equilibrium assignment problem (or, the combined signal optimisation and stochastic user equilibrium assignment problem): one is the solution to the bi-level programming problem and the other the mutually consistent solution where the two sub-problems in the combined problem are solved simultaneously. In this paper, we shall concentrate on the bi-level programming approach although we shall also consider mutually consistent solutions so as to contrast the two types of solutions. The purpose of the paper is to present a solution algorithm for the two bi-level programming problems and to test the algorithm on several networks.

9There has been rapid growth in interest in real-time transport strategies over the last decade, ranging 10 from automated highway systems and responsive traffic signal control to incident management and driver 11 information systems. The complexity of these strategies, in terms of the spatial and temporal interactions 12 within the transport system, has led to a parallel growth in the application of traffic microsimulation models 13 for the evaluation and design of such measures, as a remedy to the limitations faced by conventional static, 14 macroscopic approaches. However, while this naturally addresses the immediate impacts of the measure, a 15 difficulty that remains is the question of how the secondary impacts, specifically the effect on route and 16 departure time choice of subsequent trips, may be handled in a consistent manner within a microsimulation 17 framework. 18The paper describes a modelling approach to road network traffic, in which the emphasis is on the inte-19 grated microsimulation of individual trip-makersÕ decisions and individual vehicle movements across the 20 network. To achieve this it represents directly individual driversÕ choices and experiences as they evolve 21 from day-to-day, combined with a detailed within-day traffic simulation model of the space-time trajecto-22 ries of individual vehicles according to car-following and lane-changing rules and intersection regulations. 23 It therefore models both day-to-day and within-day variability in both demand and supply conditions, and 24 so, we believe, is particularly suited for the realistic modelling of real-time strategies such as those listed 25 above. The full model specification is given, along with details of its algorithmic implementation. A number 26 of representative numerical applications are presented, including: sensitivity studies of the impact of day-to-27 day variability; an application to the evaluation of alternative signal control policies; and the evaluation of 35Recent years have seen a massive increase in real-time advanced technological strategies 36 designed, for example, to reduce congestion, improve network efficiency, promote public trans-37 port use, decrease pollution and/or increase road safety. At the network-wide level, these include: 38 responsive, optimised traffic signal control, e.g. SCOOT (Hunt et al., 1981); congestion-based 39 road pricing (Oldridge, 1990); dynamic route guidance/information and variable message signs 40 (Emmerink and Nijkamp, 1999); congestion management strategies, e.g. freeway ramp-metering, 41 gating (Papageorgiou et al., 1989); public transport priority measures such as responsive bus sig-42 nal controls (Quinn, 1992), bus lanes and guided bus schemes (Liu et al., 1999). 43A general property of all these strategies is that they both respond to-and in turn influence-44 prevailing congestion levels, rather than being designed on the basis of long-term average condi-45 tions. That is to say, the variation in traffic conditions is just as important a consideration as t...

A computer program has been developed which follows the trajectories of fast ions in crystals, based on the assumption of classical dynamics and binary collisions. Initial work has been directed at various aspects of proton channeling in copper in the energy range 5-509 keV. The critical angle and distance of closest approach in a perfect lattice have been evaluated for both rows and planes and compare well with the predictions of the continuum mods1 as developed by Lindhard (1965). We also discuss the overlap of close-packed rows and planes, and the modifications necessary to the basic theory when thermal vibrations are introduced. Experiments have been simulated directly by obtaining a statistical analysis of the velocity distribution of protons reflected from a (1W) face of copper and transmitted through a thin (-1800 A) crystal. In reflection, distinct miniina were obtained along directions corresponding to close-packed rows and planes, in good agreement with experimental "blocking patterns" (Nelson 1967~). Transmission patterns also revealed 2 !ack of large-angle scattering parallel to close-packed planes, analogous to the white arms observed experimentally with thinner crystals.

We show that an essential step in the PARTAN variant of the Frank–Wolfe algorithm for equilibrium assignment, the calculation of a minimal step length for maintaining feasibility, can be accomplished using either analytical formulas or simple rules.

No abstract