Modelling rain effects on risk-taking behaviours of multi-user classes in road networks with uncertainty

Journal of Advanced Transportation, Fall, 2008 by Shao Hu, William H.K. Lam, Lam Tam Mei, Yuan Xiao-Ming

This paper proposes a new travel time reliability-based traffic assignment model to investigate the rain effects on risk-taking behaviours of different road users in networks with day-to-day demand fluctuations and variations in travel time. A generalized link travel time function is used to capture the rain effects on vehicle travel times and road conditions. This function is further incorporated into daily demand variations to investigate those travel time variations arising from demand uncertainty and rain condition. In view of these rain effects, road users' perception errors on travel times and risk-taking behaviours on path choices are incorporated in the proposed model with the use of a logit-based stochastic user equilibrium framework. This new model is formulated as a variational inequality problem in terms of path flows. A numerical example is used to illustrate the application of the proposed model for assessment of the rain effects on road networks with uncertainty.

Introduction

With continuous growth of traffic demand over past decades, gaining a better understanding of road user's path choice behaviour in networks with uncertainty is important for alleviating traffic congestion problems under both recurrent and non-recurrent conditions. In view of travel time variations caused by network uncertainty, road users are becoming more sensitive to the reliability of path travel time which can be defined as the probability that a road user can arrive at a destination within a given travel time threshold (Asakura and Kashiwadani, 1991) rather than average path travel time in their path or route choice decision. Recent empirical studies support this contention and indicate that the reliability of path travel time plays an important role in road user's path choice behaviour (Lam and Small, 2001; de Palma and Picard, 2005). However, confronted with uncertain traffic conditions, different road users would have different risk-taking behaviours, namely; risk aversion, risk neutrality, and risk prone, on path choice problem. Such risk-taking behaviour in the context of path choice model has been investigated by some previous related studies (e.g. Bruinsma et al., 1999; Bates et al., 2001; Lam and Small, 2001; de Palma and Picard, 2005).

Recently, attention has been given to traffic assignment models with taking account the effects of road users' risk-taking behaviours in networks with uncertainty. Chen et al. (2002) found that different risk-taking path choice models would have different impacts on the estimation of travel time reliability measures. In general, these models can be grouped under the presence of supply and demand uncertainties. The supply uncertainty is caused by different disturbances on the roads with effects on the road capacities, which can be further categorized into predictable and expectable disturbances such as inclement weather and scheduled road works; and the unpredictable disturbances like traffic accidents, vehicle breakdown and signal failures. The former unpredictable disturbances in terms of capacity variations in road networks have been studied by Chen et al. (1999), Lo and Tung (2003) and Lo et al. (2006). On the other hand, the demand uncertainty which can be referred to day-to-day demand variation has also been examined by the previous works (Asakura and Kashiwadani, 1991; Clark and Watling, 2005).

In the literature, the well-known user equilibrium (UE) traffic assignment model (Wardrop, 1952) is based on the strong assumption that network travel times are deterministic. As discussed above, travel time varies from day to day due to uncertainty in demand and supply. In the absence of an alternative, road users learn path travel time variations from experience. Based on this assumption, existing studies have extended the UE principle from the deterministic case to the case with travel time variations. Considering the effect of unpredictable disturbances on supply uncertainty, Lo and Tung (2003) proposed the probabilistic user equilibrium (PUE) model based on link capacity variations. Subsequently, Lo et al. (2006) further extended the PUE model with the concept of travel time budget (TTB) to capture road user's attitude towards network uncertainty. This model is referred to as the TTB model. More recently, Shao et al. (2006) extended the TTB model and proposed a travel time reliability-based traffic assignment model to consider the effect of daily demand fluctuations. It should be pointed out that all the above studies mainly focused on either demand fluctuation or supply uncertainty. However, in reality, demand and supply uncertainties would simultaneously cause travel time variations and subsequently influence road user's path choice behaviour in networks with these uncertainties.

It is obvious that adverse weather conditions (e.g. rainfall or storms) would have significant impacts on the reliability of travel times. However, best to our knowledge, less attention has been given to examination of the causal relationships between travel time reliability and adverse weather (Aron et al., 1995; Kulmala, 1997). In view of this, this paper aims to investigate the road users' path choice problems in networks with both demand and supply certainties due to bad weather. When raining, visibility and pavement friction on roadways are reduced and hence cause a reduction in traffic parameters, i.e. lower free-flow speed and capacity (Federal Highway Administration, 2006). To study the rain effects, an extension of conventional modelling approaches for travel time variations is thus required. Rainfall information, which is freely available from weather forecasts, also affects traffic demand on networks as road users may change their travel modes, path or path choices or even postpone of making the trips. As a result, traffic demand will change and such uncertainty in demand would cause the variations of travel time. Therefore, investigation of road users with different risk-taking behaviours in response to these changes caused by supply and demand variations under rain condition is of importance in reality.