Traffic assignment and traffic control in general freeway-arterial corridor systems

We consider a general traffic corridor consisting of two subsystems of a freeway network and a surface street network. The two systems are coupled by access ramps to provide multiple alternative routes for drivers from their origins to destinations. Each ramp can be metered to influence flow distributions in such a way that some system performance index (e.g. total travel time) is optimized, provided that each driver chooses an individual minimum cost route in response to any given ramp control. In this article we first present a bilevel programming formulation of the traffic assignment and traffic control problem in the traffic corridor system. The lower-level problem represents a traffic equilibrium model involving explicitly ramp queuing, which predicts how drivers will react to any given on-ramp control pattern. The upper-level problem is to determine ramp metering rates that optimize a system performance criterion, taking into account drivers' route choice behavior. We also present a sensitivity analysis for the queuing network equilibrium problem. Explicit expression of the derivatives of equilibrium link flows and equilibrium ramp queuing times with respect to ramp metering rates is derived. A heuristic algorithm, using the derivative information from the sensitivity analysis, is developed to solve the proposed bilevel on-ramp traffic control problem. A numerical example is provided to illustrate the bilevel control model and the solution algorithm.

A procedure for real-time signal control that considers transit interference and priority

A rule-based procedure for determining real-time signals timings at a signalized intersection is described. It incorporates the effects of the traffic interference caused by on-line loading/ unloading of transit vehicles at the intersection. This procedure generates a number of short-term alternative real-time phase sequences for various levels of transit priority, based on a number of decision rules. It then evaluates these signal sequences and selects the one with the least overall cost to all traffic. The procedure is illustrated in terms of a simulated application to a critical intersection in Toronto's Queen Street corridor using real data. The preliminary simulation tests indicate the potential reduction in total compared to fixed-time operation, which results largely from selectively ushering transit vehicles to their loading positions at strategic times and serving cross-street traffic while the transit vehicles are loading.

Traffic assignment and signal control in saturated road networks

This article presents a model and a procedure for determining traffic assignment and optimizing signal timings in saturated road networks. Both queuing and congestion are explicitly taken into account in predicting equilibrium flows and setting signal split parameters for a fixed pattern of origin-to-destination trip demand. The model is formulated as a bilevel programming problem. The lower-level problem represents a network equilibrium model involving queuing explicitly on saturated links, which predicts how drivers will react to any given signal control pattern. The upper-level problem is to determine signal splits to optimize a system objective function, taking account of drivers' route choice behavior in response to signal split changes. Sensitivity analysis is implemented for the queuing network equilibrium problem to obtain the derivatives of equilibrium link flows and equilibrium queuing delays with respect to signal splits. The derivative information is then used to develop a gradient descent algorithm to solve the proposed bilevel traffic signal control problem. A numerical example is included to demonstrate the potential application of the assignment model and signal optimization procedure.

Simple algorithms for minimizing the sum of linear shipment costs and convex port costs

Several methods are discussed for minimizing the sum of linear collection/distribution costs from/to a number of zones, and non-linear costs at processing ports. The non-optimality and computational implications of approximating non-linear cost functions for use with the linear programming technique are discussed. A simple graphical technique is presented and two computational algorithms are developed which make use of the special structure of the problem. The algorithms are illustrated using a simple example. Both algorithms converge to global optima. One is more suitable for hand calculation and the other is easier to program, but both are easily programmed and are computationally efficient.

Traffic assignment in a congested discrete/ continuous transportation system

Consider a city where all workplaces are concentrated in a highly compact central business district (CBD) and the commuters' homes are continuously dispersed over the residential area surrounding the CBD. The transportation facilities in the city comprise a discrete freeway network and a two-dimensional continuum of dense surface streets. The freeway network is assumed to be superimposed on the continuum and connected with it at a limited number of points (freeway ramps). During the morning peak-hours, the commuters traveling to work have a choice between two routes to the CBD: traveling along the minor access roads to enter the freeways and then proceeding along the freeway to the CBD, or using only minor street roads straight to the CBD. Given this transportation system, it is important to estimate the total trips using each freeway ramp and their spatial distribution. In this paper, an optimization model is developed to deal with this traffic assignment problem, provided that each commuter seeks to minimize his individual congested travel time. The model is formulated by intergrating the conventional network and continuum equilibrium models and its dual formation is derived. A dual-based solution method is developed using the finite element technique, and illustrated with a numerical example for a hypothetical city.