Simulation Results
The proposed multidimensional behavioural theory and models have been estimated and implemented in an agent-based simulation to demonstrate the capability. A toy network with one origin – destination pair, three alternative routes and three travel modes (auto, carpool and transit) is employed. The scenario that is analysed in this simulation is an assumed 10 per cent increase in travel demand which creates excessive travel time and cost for the simulated agents and stimulates them to start the multidimensional behaviour adjustments. 90,000 agents are generated in this microsimulation of extended morning peak hours (5:00—10:00 am). Agents' characteristics are synthesised based on Transportation Planning Board (TPB) – Baltimore Metropolitan Council (BMC) Household Travel Survey (2007/2008) data.
In the simulation, agents travel from origin to destination, accumulate experience, make behavioural adjustment on one or multiple dimensions, dynamically update beliefs and eventually satisfy on their decisions. The uniqueness of the model brings attention to each agent for whom the interplay of search gain and search cost is dynamically modelled in order to determine the behavioural dimension wherein the search and decision process occurs. Figure 10.4 illustrates the evolving gain/cost ratio for a particular agent.
On simulation day 1, the agent initially believes that all dimensions are rewarding (with all gain/cost ratios above one) while the most profitable dimension is the mode dimension. She/he then employs search rules and decision rules to identify and examine one alternative mode. While the subsequent search reveals further information, this agent's knowledge and subjective beliefs on the mode dimension evolve significantly. And on the second day, the departure time dimension emerges to be the one with the highest gain/cost ratio. A search for alternative departure
Figure 10.4: The evolving gain/cost ratios of multidimensional travel behaviour.
time is therefore performed. Iterating this process, the agent forms a time-dependent search path about choosing behavioural adjustment dimensions: mode-departure time-route-mode. On the fifth day, the gain/cost ratios of all dimensions drop down below 1, which indicates that this agent subjectively believes that no more searches are necessary. The agent is thus satisfied and stays dormant afterwards. Once a new turbulence emerges in the transport system, such as new policies and booming travel demand, the agent may be influenced in the way that the gain/cost ratios in certain dimensions grow. And the agent may seek further changes.
The convergence of the multidimensional behaviour is illustrated in Figure 10.5a. Overall, the model predicts active and reasonable agent behaviour along the three behavioural dimensions. The convergence processes are smooth. With the innate bounded rationality and satisficing behaviour, agents reach steady state and stop search within 25 search iterations. If each agent travels five days a week and all agents start search at the same time, it would take five weeks for the traffic to stabilise and equilibrate on the network. This is an interesting finding that on the one hand, it allows us to model the gradual behaviour adaptation to exogenous policies (e.g. pricing policy in Stockholm gradually nudge drivers to change behaviour, Borjesson, Eliasson, Hugosson, & Brundell-Freij, 2012). On the other hand, it suggests potential applicability of the proposed theory in large-scale planning models and simulation since it embeds multidimensional behavioural responses while maintaining a reasonable converging speed.
In response to the assumed demand increase, changing route and changing departure time are the most significant ways of behavioural adaptation. The initially high route searching frequency cools down rapidly since agents can hardly identify any better alternative routes under the assumed overall demand increase. Agents quickly learn the fact and update the subjective beliefs, which results in a decreasing search gain in the route dimension. Then agents turn to search alternative modes
Figure 10.5: Agent-based experiment of the multidimensional travel behaviour theory, (a) The convergence of the multidimensional behaviour, (b) Agents' mode search and switching behaviour, (c) Agents' departure time changes and peak
spreading, (d) Agents' payoff dynamics.
and departure times instead. Thus we can observe in the simulation an increasing number of agents searching for alternative departure times in the second and third simulation days. A few agents search for alternative modes. Agents' mode searching and switching behaviour is illustrated in Figure 10.5b. Agents' departure time changes are illustrated in Figure 10.5c.
By aggregating the individual behaviour into travel patterns, we can observe that the multidimensional learning and adaptation leads to a slight percentage decrease of auto drivers (Auto D in Figure 10.5b). Those agents switch to auto passengers (Auto P) or transit users. The aggregate mode share of auto drivers drops from 63.4% to 58.3%. After 6 simulation days, the mode share tends to be stabilized even though from the microscopic level, there still exist some 3000 travellers changing their travel modes. The active departure time changes lead to a significant peak spreading effect. The assumed demand increase results in more severe congestion and travel time unreliability especially during peak hours. The excessive travel time, cost and schedule delays make the departure time adjustments necessary in order for the agents to gain an acceptable payoff through search. The model predicts that the dominating behavioural responses to the stimulus are route changes and departure time changes, which are in consistency with the existing research (e.g. Arentze et al., 2004). Meanwhile, the model predicts the behavioural dynamics and adaptive processes, which advance our current understanding about multidimensional travel behaviour adjustments.
Travellers in the multidimensional agent-based model are not perfectly 'rational' in that they do not maximise their utility (or payoff). Instead, they are restrained by information acquisition cost, decision cost, computational limitation, time budget and deadlines. They are not perfectly rational also in the way that they follow different intuitives and heuristic behavioural rules. Figure 10.5d demonstrates that through multidimensional learning and adaptation, agents search and improve their relative searching payoff. This term is defined as the ratio of the cumulative actual search gain and the cumulative subjective search gain (i.e. subjectively believed maximum payoff from the search) for all the searchers. Judging by the curves, the departure time dimension turns out to be the most profitable dimension. Once searching in this dimension, agents are able to retrieve the highest relative searching payoff. However, this learning and adaptation does not ensure them to make decisions that result in maximum payoff. This example demonstrates the bounded rationality of the agents in search and changing their behaviour.
