A micro-simulation model system of departure time using a perception updating model under travel time uncertainty

Abstract

Existing microscopic traffic models have often neglected departure time change as a possible response to congestion. In addition, they lack a formal model of how travellers base their daily travel decisions on the accumulated experience gathered from repetitively travelling through the transport network. This paper proposes an approach to account for these shortcomings. A micro-simulation approach is applied, in which individuals base their consecutive departure time decisions on a mental model. The mental model is the outcome of a continuous process of perception updating according to principles of reinforcement learning. Individuals’ daily travel decisions are linked to the traffic simulator SIAS-PARAMICS to create a simulation system in which both individual decision-making and system performance (and interactions between these two levels) are adequately represented. The model is applied in a case study that supports the feasibility of this approach.

Introduction

Congestion is a major problem in urban areas throughout the world, causing both economic and environmental damage. Congestion occurs when the demand for travel exceeds the capacity of the existing road infrastructure at a certain location and at a certain time. Policies that are typically applied in urban areas to resolve (or at least reduce) congestion problems are often aimed at increasing the capacity of the road infrastructure, by adding additional lanes or by optimising control systems (ramp metering, coordinated traffic signalling). In any case, the additional capacity is added to a complex traffic system, which is close to (or has already exceeded) system capacity. As a consequence, the behaviour of the system in response to minor changes in traffic demand or road capacity may be highly non-linear.

A suitable way of describing systems in such states is the use of micro-simulation models. Micro-simulation models describe the behaviour of individual decision makers, but also the interaction between the system level and the individual, e.g. due to limitations in the capacity of the system. Micro-simulation models are increasingly regarded as particularly suitable for modelling non-linearities in systems’ behaviour under critical situations (see Nagel and Raney, in press). In particular, the emergence of system-level phenomena such as congestion is more easily modelled in a bottom-up fashion. An additional advantage of micro-simulation models is that the behaviour of individual actors can be specified in accordance with behavioural principles, found in physiology, psychology or economic science, that go beyond the utility maximising assumptions used in analytical models. For example, existing analytical traffic allocation models assume that travellers have perfect information of travel times in the network, which is an unrealistic assumption. Applying learning-based algorithms may lead to different and probably more realistic assignments (Nakayama et al., 1999).

A drawback of micro-simulation models has long been their computational requirements, but this argument has lost its power in the light of improved computer technology. As a result, the last decade has shown the release of a considerable number of microscopic traffic simulators (e.g. Nagel and Raney, in press) that are often available as commercial software packages. Nowadays, microscopic traffic simulation is often used in many practical situations (e.g. Mahmassani and Jayakrishnan, 1991, Anderson and Souleyrette, 2002, Klügl and Bazzan, in press, Rossetti and Liu, in press).

Notwithstanding the usefulness of microscopic traffic simulators for applied traffic forecasting, their scope is often limited to route choice in a transport network, assuming an OD-matrix with fixed departure time profiles for each OD pair. This does not seem justified in settings with high congestion levels. Many publications (e.g. Jou et al., 1997, Mahmassani and Liu, 1999, Kroes et al., 1996) emphasize the importance of departure time choice as a potential response to congestion. Ignoring departure time as a response to policies aimed at the reduction of congestion (which is common practice in applied micro-simulation modelling) may therefore lead to biased results. In particular, it can be argued that individuals will try to maximize their trip utility by both minimizing travel time and arriving as close as possible in the vicinity of their preferred arrival time. In congested settings, this implies trade offs between travel time and arrival time, involving both route and departure time switches. Ignoring departure time switches and so-called schedule delays (diversions from someone’s preferred arrival time), will lead to wrong assessments of generalized travel costs (see de Palma and Marchal (2002) for a more elaborate discussion).

The scientific literature presents various micro-simulation models (or other assignment models) that include departure time choice (van der Mede and van Berkum, 1993, Hu and Mahmassani, 1997, Rossetti and Liu, in press). However, these models do not contain a number of aspects that we feel are crucial for modelling the response to congestion appropriately. First, existing assignment models do not account for the effect of travel time uncertainty on departure time choice. Uncertainty in travel times is in this study defined as the day-to-day variability in travel time that may arise, even if demand is stable, due to the stochastic nature of traffic flows as the outcome of individual driving behaviours in combination with signalling systems (Bonsall, 2004). This uncertainty, which is likely to increase with increasing congestion levels, may lead travellers to maintain safety margins in order to avoid late arrival. In general, travellers will balance the probabilities and consequences of both early and late arrival (Noland and Small, 1995). Ignoring the effect of travel time uncertainty will lead to a wrong assessment of the effect of congestion on departure time and the economic costs. In particular, Ettema and Timmermans (in press) demonstrate that the combination of stable average total travel time and increasing uncertainty leads to a shift towards earlier departure times and higher generalised travel costs.

Secondly, existing assignment models do not include a formal model of knowledge acquisition and cognition. This is crucial when analysing how departure time shifts take place in daily decision-making, which makes up a large percentage of traffic in congested settings. In particular, without a solid representation of how new experiences are integrated in a traveller’s cognitive system, his/her reaction to such experiences is hard to predict. In this respect, we assume that each new experience is interpreted in the context of previous knowledge to assess whether behaviour should be adjusted. For example, a single 10 min longer commute duration in a congested area may have a different impact on a traveller’s behaviour as compared to 100 consecutive events of this type. For instance, Avineri and Prashker (2003) demonstrate in a laboratory setting that travellers’ learning and route-switching behaviour depends on previously experienced travel time differences and travel time variance. In other words, to properly model departure time adjustments, travellers’ cognition of both mean travel conditions and their variance should be taken into account.

Based on a more general theoretical framework (Arentze and Timmermans, 2003), this paper presents a micro-simulation model accounting for departure time choice for routine trips under travel time uncertainty, applying a cognitive model of learning about the travel circumstances. In this model system, individual decision makers decide about the departure time for a routine trip, such as commuting, on consecutive days. Their decision-making is based on a mental model of traffic conditions, specifying the mean and variance of travel time for various departure times. This mental model is updated once new experiences become available. As the emphasis in this study is on departure time choice, route choice is not included in the model (a linear transport network is used). Including route choice into the mental model of learning and decision-making is considered an important next step. The departure time decisions are fed into a SIAS-PARAMICS micro-simulation model, simulating the resulting traffic flows, including delays due to congestion. This produces travel time experiences that are used again in the mental model of individual learning and decision-making. The paper provides further details and is organised as follows.

Section 2 provides further information regarding the architecture of the micro-simulation system. Section 3 provides more detail about the behavioural assumptions underlying the model. Both the information handling and storage and the decision-making mechanisms are described. Section 4 describes the case study in which the model was applied. Section 5 presents the results of the case study, in terms of the effects predicted for various policies. Section 6, finally, draws conclusions regarding the approach and addresses avenues for further research.