Stochastic cell transmission model (SCTM): A stochastic dynamic traffic model for traffic state surveillance and assignment

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Abstract

The paper proposes a first-order macroscopic stochastic dynamic traffic model, namely the stochastic cell transmission model (SCTM), to model traffic flow density on freeway segments with stochastic demand and supply. The SCTM consists of five operational modes corresponding to different congestion levels of the freeway segment. Each mode is formulated as a discrete time bilinear stochastic system. A set of probabilistic conditions is proposed to characterize the probability of occurrence of each mode. The overall effect of the five modes is estimated by the joint traffic density which is derived from the theory of finite mixture distribution. The SCTM captures not only the mean and standard deviation (SD) of density of the traffic flow, but also the propagation of SD over time and space. The SCTM is tested with a hypothetical freeway corridor simulation and an empirical study. The simulation results are compared against the means and SDs of traffic densities obtained from the Monte Carlo Simulation (MCS) of the modified cell transmission model (MCTM). An approximately two-miles freeway segment of Interstate 210 West (I-210W) in Los Ageles, Southern California, is chosen for the empirical study. Traffic data is obtained from the Performance Measurement System (PeMS). The stochastic parameters of the SCTM are calibrated against the flow–density empirical data of I-210W. Both the SCTM and the MCS of the MCTM are tested. A discussion of the computational efficiency and the accuracy issues of the two methods is provided based on the empirical results. Both the numerical simulation results and the empirical results confirm that the SCTM is capable of accurately estimating the means and SDs of the freeway densities as compared to the MCS.

Research highlights

► Parameters governing the fundamental diagram (speed–density relationship) are stochastic. This paper introduces the stochasticity of the fundamental diagram of traffic flow as stochastic parameters governing the sending and receiving functions of the cell transmission model (CTM). In addition, to enhance the future prediction the stochastic CTM (SCTM) also considers the stochasticity in travel demand. ► The SCTM can be formulated as a bilinear stochastic system in which the test with the empirical freeway data shows the consistency between the estimated mean and SD of the traffic densities by the SCTM and those from the empirical data. ► The test result also highlights the computational advantage of the SCTM over the application of Monte Carlo Simulation with CTM in terms of computational time and accuracy of estimated mean and SD of traffic densities.

Section snippets

Motivation and introduction

Dynamic traffic flow models are one of the key components of dynamic traffic assignment (DTA) as well as real-time traffic control and management. To model the complex freeway traffic, many efforts have been made to establish and validate both microscopic (e.g. car-following) and macroscopic (e.g. hydrodynamics-based) models. However, many of these models are too computationally demanding for online estimation of traffic states for a large-scale road network. A comparative study of the four

The MCTM and the SMM

The modified cell transmission model (MCTM) was developed by Muñoz et al. (2003). This model uses cell densities instead of cell occupancies which permits the CTM to adopt non-uniform cell lengths and leads to greater flexibility in partitioning freeways. In the MCTM, the density of cell i evolves according to the conservation of vehicles:ρi(k+1)=ρi(k)+Tsliqi,in(k)-qi,out(k),where ρi(k) is the vehicle density of cell i at time index k, qi,in(k) and qi,out(k) are the total flows (in vehicles per

The overall framework of the SCTM

As previously described, in Muñoz et al., 2003, Sun et al., 2003, the MCTM has been piecewise-linearized to obtain the SMM with five operational modes for a freeway segment based on Assumption 2.1. From the traffic control context, the linear structure of the SMM lends the advantage of simplifying control analysis, control design, and data-estimation design methods. From the traffic flow simulation context, Assumption 2.1 simplifies the traffic state of the freeway segment which increases the

Numerical example

To demonstrate the proposed method, we conduct the following numerical example. Consider a freeway segment consisting of four cells with neither on- nor off-ramp as depicted in Fig. 8. We assume that the first three cells of this freeway segment are of four lanes and the last cell consists of only 3 lanes. The cell length is set to be 100 m, and the time interval is T = 5 s.

It is assumed that the nominal flow–density relationships of all the four cells are characterized by triangular fundamental

An empirical study

In this section, we will validate the SCTM by two scenarios with empirical traffic data:

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    The first scenario is to test the proposed model against the supply uncertainty, i.e. only uncertain supply functions are considered. In this case, the demand pattern is chosen from a particular day. The utilized traffic flow data of 24 h were collected on April 22, 2008 from the Performance measurement system (PeMS).

Conclusions

In this paper, a stochastic cell transmission model (SCTM) is proposed for simulating the traffic density of a freeway section under stochastic demand and supply. The uncertainty terms are assumed to be wide-sense stationary, second-order processes consisting of uncorrelated random vectors with known means and variances. The stochasticities of the sending and receiving functions in the SCTM are governed by the random parameters of the fundamental flow–density diagrams, including the capacities,

Acknowledgments

This research is jointly sponsored by the project funded by University Research Grant A-PH65 from the Hong Kong Polytechnic University, and the project supported by the Research Grants Council of the Hong Kong Special Administration Region under Grant Project No. PolyU 5271/08E. The authors would like to thank Dr. Gabriel Gomes, Dr. Lyudmila Mihaylova, and the two anonymous referees for their constructive comments and suggestions, which led to improvements in the study. Special thanks should

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