Abstract: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… Show more
“…Allsop (1974), Gartner (1976), Smith (1979a, c), Bentley and Lambe (1980) and Dickson (1981) were among the first to point to the need to combine models of route choice and traffic signal control; in part so that optimal controls taking account of routeing reactions might be found. The study of traffic control and route choice has been pursued by Meneguzzer (1996Meneguzzer ( , 1997, Maher et al (2001), Wong et al (2001), and many others. Taale and van Zuylen (2001) provide an overview.…”
Section: A Brief Route Choice and Traffic Control Modelling Contextmentioning
This paper presents a novel idealised dynamical model of day to day traffic re-routeing (as traffic seeks cheaper routes) and proves a stability result for this dynamical model. (The dynamical model is based on swapping flow between paired alternative segments (these were introduced by Bar Gera (2010)) rather than between routes.) It is shown that under certain conditions the dynamical system enters a given connected set of approximate equilibria in a finite number of days or steps. This proof allows for saturation flows which act as potentially active flow constraints. The dynamical system involving paired alternative segment swaps is then combined with a novel green-time-swapping rule; this rule swaps green-time toward more pressurised signal stages. It is shown that if (i) the delay formulae have a simple form and (ii) the "pressure" formula fits the special control policy P 0 (see Smith, 1979a, b), then the combined flow-swapping / green-time-swapping dynamical model also enters a given connected set of approximate consistent equilibria in a finite number of steps. Computational results confirm, in a simple network, the positive P 0 result and also show, on the other hand, that such good behaviour may not arise if the equi-saturation control policy is utilized. The dynamical models described here do not represent blocking back effects.
“…Allsop (1974), Gartner (1976), Smith (1979a, c), Bentley and Lambe (1980) and Dickson (1981) were among the first to point to the need to combine models of route choice and traffic signal control; in part so that optimal controls taking account of routeing reactions might be found. The study of traffic control and route choice has been pursued by Meneguzzer (1996Meneguzzer ( , 1997, Maher et al (2001), Wong et al (2001), and many others. Taale and van Zuylen (2001) provide an overview.…”
Section: A Brief Route Choice and Traffic Control Modelling Contextmentioning
This paper presents a novel idealised dynamical model of day to day traffic re-routeing (as traffic seeks cheaper routes) and proves a stability result for this dynamical model. (The dynamical model is based on swapping flow between paired alternative segments (these were introduced by Bar Gera (2010)) rather than between routes.) It is shown that under certain conditions the dynamical system enters a given connected set of approximate equilibria in a finite number of days or steps. This proof allows for saturation flows which act as potentially active flow constraints. The dynamical system involving paired alternative segment swaps is then combined with a novel green-time-swapping rule; this rule swaps green-time toward more pressurised signal stages. It is shown that if (i) the delay formulae have a simple form and (ii) the "pressure" formula fits the special control policy P 0 (see Smith, 1979a, b), then the combined flow-swapping / green-time-swapping dynamical model also enters a given connected set of approximate consistent equilibria in a finite number of steps. Computational results confirm, in a simple network, the positive P 0 result and also show, on the other hand, that such good behaviour may not arise if the equi-saturation control policy is utilized. The dynamical models described here do not represent blocking back effects.
“…Far more common are iterated microsimulations that constrain themselves to the equilibration of route choice (and a strictly trip-based demand (van Zuylen and Willumsen, 1980), Bayesian estimation (Maher, 1983), generalized least squares (Bell, 1991;Bierlaire and Toint, 1995;Cascetta, 1984), and maximum likelihood estimation (Spiess, 1987) have been applied. These methods can be carried over at least approximately to congested networks (Maher et al, 2001;Yang, 1995;Yang et al, 1992;Bierlaire and Crittin, 2006;Cascetta and Posterino, 2001). The further addition of a time dimension, yielding various dynamic OD estimators, is also possible (Cascetta et al, 1993;Ashok, 1996;Bierlaire, 2002;Sherali and Park, 2001;Zhou, 2004).…”
This text describes the first application of a novel path flow and origin/destination (OD) matrix estimator for iterated dynamic traffic assignment (DTA) microsimulations. The presented approach, which operates on a trip-based demand representation, is derived from an agent-based DTA calibration methodology that relies on an activity-based demand model (Flötteröd et al., 2011a). The objective of this work is to demonstrate the transferability of the agent-based approach to the more widely used OD matrix-based demand representation.
2The calibration (i) operates at the same disaggregate level as the microsimulation and (ii) has drastic computational advantages over conventional OD matrix estimators in that the demand adjustments are conducted within the iterative loop of the DTA microsimulation, which results in a running time of the calibration that is in the same order of magnitude as a plain simulation. We describe an application of this methodology to the trip-based DRACULA microsimulation and present an illustrative example that clarifies its capabilities.
“…M(q) is the assignment map and/or link choice proportion, which relates the link flows v with the 0-D matrix q. In most of the aforementioned models, the linear relationship is used as below: Maher and Zhang;and Maher et al, 2001) have focused on formulating a bi-level programming problem for 0-D estimation of road traffic. Therefore, the bi-level programming approach, in which the lower level problem is a UE assignment and the upper level problem is a generalized least squares estimation, is used to ensure consistency in the link choice proportions (Yang et al, 1992).…”
Section: Introductionmentioning
confidence: 99%
“…It is because SUE assignment does consider the perceived error of travel time (Sheffi, 1985). Recently, Maher et al (2001) proposed a bi-level programming approach for ME and traffic count problems with SUE link flows. Based on the heuristic iterative algorithm (Maher et al, 2001), solution algorithm is developed for solving the proposed bi-level programming problem, The constrained generalized least squares (GLS) method (Bell, 1991) is used for solving the upper-level ME problem.…”
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