Stochastic cell transmission model for traffic network with demand and supply uncertainties

Abstract

This article extends the stochastic cell transmission model (SCTM) to simulate traffic flows on networks with stochastic demand and supply. The SCTM divides a roadway segment into cells and accepts the means and variances of stochastic travel demand and supply functions as exogenous inputs, and produces the corresponding cell traffic densities over time. This article defines the rules of flow propagation for freeway corridors, traffic merges/diverges and signalised junctions based on a kind of link-node model. In the numerical studies, we simulate the proposed model with a hypothetical network. We apply the SCTM to estimate the queues and delays at signalised intersections. Compared with some well-known delay and queue estimation formulas, e.g. Webster, Beckmann, McNeil and Akcelik, the results show good consistency between the SCTM and these formulas. In addition, the SCTM describes the temporal behaviour of the queue and delay distributions at signalised junctions with stochastic supply functions and (non-stationary) arrivals.

Keywords:

• stochastic cell transmission model
• traffic density
• queue length
• signal delay
• probabilistic distribution
• spillback

Acknowledgements

The work described in this paper was jointly supported by the Research Grants Council of the Hong Kong Special Administration Region under grant project No. PolyU 5250/11E, and the Science and Technology Foundation of Beijing Jiaotong University under grant project No. 2010RC005.

Notes

Indeed, as commented by Sumalee et al. (2011a) that the definition of probabilities of occurrence of operational modes presented in the paper is only a feasible definition to the author, not a uniform definition of probabilities of occurrence of operational modes. One can revise the definition of probabilities of occurrence of operational modes to adapt to different traffic conditions and the desired accuracy.

The interconnected SCTM approach calculates the flow propagation by pairing up two neighbouring cells, which can be viewed as an extension of the approach used in the CTM. Consider the example depicted in Figure 3. First, two cells are chosen to form a basic SCTM subsystem. By the basic SCTM subsystem, random traffic state (including the traffic density and the possible wavefront in terms of probabilities of occurrence of operational modes) of the segment is calculated. Then, the last cell of the upstream subsystem and the first cell of the downstream subsystem is paired up to calculate the flow across these two subsystems.

The independency assumption is imposed to simplify the analysis and reduce the computational effort. In terms of traffic state estimation, the effect of this independency assumption is practically minor, as illustrated in Sumalee et al. (2011a) and Pan et al. (2011). However, due to the similar environmental conditions, human behaviours, flow propagation and congestion in traffic network, demand and supply uncertainties are correlated in both space and time domains. The uncorrelated or independent assumptions enforced explicitly or implicitly in the SCTM framework cause several limitations to the definitions of probabilities of occurrence of operational modes and their evaluations. These drawbacks render that the model may not perform very well when it is applied for short-term traffic flow prediction, especially under abnormal traffic conditions, e.g. incidents and adverse weather conditions due to the fact that the model does not consider the spatial-temporal correlations of the traffic flow fully and lacks of a proper prediction algorithm to forecast demand and supply profiles. Incorporating the spatial and temporal correlations with traffic dynamics can bring significant potential advantages for developing an efficient short-term traffic state predictor. Therefore, Pan et al. (2011), one of our recent work, extends the SCTM to consider the spatial and temporal correlations of demand and supply uncertainties. To retain the Markovian property of the SCTM, the spatial and temporal correlations are taken as exogenous inputs to a predictor to forecast the demand and supply information in the near future. The predicted demand and supply functions are then loaded into the SCTM for short-term traffic state forecasting.

This kind of link-node CTM representation of freeway segment, introduced by Kurzhanskiy (2007) and Muralidharan and Horowitz (2009), calculates the traffic flows in traffic networks (by flow conservation of a node) in a simpler manner. The simulation software Aurora, a simulation tool developed by the Tools for Operations Planning (TOPL) in University of California Berkeley, is based on this CTM implementation. A critical overview of macroscopic node models is provided by Tampère et al. (2011), wherein some shortcomings of state-of-the-art node models are summarised. It would be interesting for us to further extend our model following the generic class of first order macroscopic node models proposed by Tampère et al. (2011).