Urban gridlock: Macroscopic modeling and mitigation approaches

Abstract

This paper describes an adaptive control approach to improve urban mobility and relieve congestion. The basic idea consists in monitoring and controlling aggregate vehicular accumulations at the neighborhood level. To do this, physical models of the gridlock phenomenon are presented both for single neighborhoods and for systems of inter-connected neighborhoods. The models are dynamic, aggregate and only require observable inputs. The latter can be obtained in real-time if the neighborhoods are properly instrumented. Therefore, the models can be used for adaptive control. Experiments should determine accuracy. Pareto-efficient strategies are shown to exist for the single-neighborhood case, and optimality principles are introduced for multi-neighborhood systems. The principles can be used without knowing the origin–destination table or the precise system dynamics.

Introduction

The current paradigm for the development and evaluation of transportation policies in cities all over the world relies heavily on forecasting models. Government agencies often stipulate by law the outputs that evaluation models must produce before a policy can be rolled out—even the kind of model in some cases. But the objective of these laws may not be achieved if the models and data used to produce the outputs are unreliable.

Unfortunately, this is almost always the case. The level of detail and complexity of available urban transportation models have steadily increased over decades: from the static and largely aggregate “four-step” models of the 1950s and 1960s; to the “disaggregate demand” and “network equilibrium” extensions of the 1970s and 1980s; and now the “dynamic simulation” models of the 1990s and 2000s. In theory, the most recent computer models can predict almost anything on a multi-modal transportation network in minute detail, but not in practice. Reasons are: (i) the models require too many inputs, such as dynamic origin–destination (O–D) matrices; (ii) driver navigation is an unpredictable gaming activity; and (iii) oversaturated networks behave chaotically.

Problem (i) is obvious; a model with reasonable spatio-temporal resolution for a large city could easily require more O–D entries than there are people in the city. Problem (ii) arises because, as pointed out in Addison and Heydecker (1993), “rational” drivers try to anticipate the congestion level along their possible paths, and to do this they need to know the decisions of “rational” drivers from other origins who may not have yet left but could arrive at the locations in question before them. These new drivers may face the same conundrum in reverse—simultaneously trying to guess the decisions of drivers from the first and other origins. Obviously then, drivers from all origins are engaged in a multi-sided double-guessing game akin to “poker”, unpredictable in nature. Problem (iii) has been pointed out in Daganzo, 1996, Daganzo, 1998; it is shown in these references that the output flows of congested networks are hypersensitive to the input demand; thus, the very networks that interest us are the least predictable.

Therefore, we propose here to manage congestion—and alleviate problem (iii)—by modeling city traffic at an aggregate level, focusing on control policies that perform equally well independent of the detailed inputs (i) and particular driver antics (ii). The basic idea consists in dividing the city into neighborhood-sized reservoirs (of dimensions comparable with a trip length) and to shift the modeling emphasis from microscopic predictions to macroscopic monitoring and control.

Some helpful work in this direction has already been done. A macroscopic model of steady state urban traffic was proposed in Herman and Prigogine (1979), further developed in Ardekani and Herman (1987) and fitted to data in Mahmassani et al. (1987). The latter two references propose that steady-state functions of a specific form exist between the number of vehicles in the network and each and every one of the following network-wide averages for: (i) vehicle speeds, (ii) flows, and (iii) fraction of stopped vehicles. The references explore the dependence of these functions on the structure of the network but not their sensitivity to the O–D demands. If insensitive, the functions could be viewed as properties of the network and be used to predict outflows in a dynamic environment. They could be an important element in a theory of macroscopic of network dynamics.

This paper pursues this idea, and also discusses the realism and need for validation of the insensitivity assumption. Its results should shed light on the development and control of urban gridlock. Section 2 below defines some terms and presents our basic aggregation hypothesis. Section 3 describes the behavior of a single reservoir (neighborhood), the gridlock phenomenon, and a control rule to optimize performance. Section 4 then discusses how to apply these ideas to city-wide settings. Section 5 suggests further work.