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72 I N N O VAT I O N S I N T R AV E L D E M A N D M O D E L I N G , V O L U M E 2 activity-travel scheduling decisions, within-day reschedul- The functional form of utilities differs between activity ing, and learning processes in high resolutions of space and and travel episodes. For activity episodes, utility is time. It summarizes some concepts and discusses a series of defined as a continuous, S-shaped function of the dura- projects and activities that will be conducted to further the tion of the activity. This form reflects the notion that operational effectiveness of the models for Flanders. with increasing values duration is at first a limiting fac- tor in "producing" utility and after some point other fac- tors become limiting. In particular: AURORA max Ua Ua = (2) Key Characteristics 1 a 1 + ( a exp[ a ( a - v a )]) Aurora is an agent-based microsimulation system in where which each individual of the population is represented as va = duration of episode a, an agent. It is also an activity-based model in the sense Uamax = asymptotic maximum of the utility the that the model simulates the full pattern of activity and individual can derive from the activity, travel episodes of each agent and each day of the simu- and lated period. At the start of the day, the agent generates a a, a, and a = activity-specific parameters. schedule from scratch, and, during the day, the agent exe- cutes the schedule in space and time. It is also dynamic in The , , and parameters determine the duration, slope, that (a) perceived utilities of scheduling options depend and degree of symmetry at the inflection point, respec- on the state of the agent, and implementing a schedule tively. In turn, the asymptotic maximum is defined as a changes this state; (b) each time after having implemented function of schedule context, attributes, and history of a schedule, an agent updates his or her knowledge about the activity, as the transportation and land use system and develops habits for implementing activities, and (c) each time an Ux max Ua = f (t a ) * f (l a ) * f (qa ) * a (3) agent arrives at a node of the network or has completed 1 + exp[ x ( x - Ta )] an activity during execution of a schedule, the agent may a a where reconsider scheduling decisions for the remaining time of the day. This may happen because an agent's expectations ta, la, and qa = start time, location, and position in the may differ from reality. This may result from imperfect sequence of activity a, respectively, knowledge, but it may also be due to the nonstationarity 0 f(x) 1 = factors representing the impact of activity of the environment. As a result of the decisions of all other attributes on the maximum utility, agents, congestion may cause an increase in travel times Uxa = base level of the maximum utility, and on links or transaction times at activity locations. Fur- Ta = time elapsed since the last implementation thermore, random events may cause a discrepancy of activity a. between schedule and reality. The position variable, qa, takes into account possible carryover effects between activities leading to prefer- BASIC CONCEPTS ences about combinations or sequences of activities (e.g., shopping after a social activity). For this function, the Utility Function same functional form (an S-shape) is assumed as for the duration function (Equation 2). Thus, it can be assumed The model is based on a set of utility functions, in which that the urgency of an activity increases with an increas- the utility of a schedule is defined as the sum of utilities ing rate in the low range and a decreasing rate in the high across the sequence of travel and activity episodes it con- range of elapsed time (T). tains. Formally, The start-time factor of the maximum utility is a func- tion of attributes of the activity: A J t a - t1 U= Ua + U j (1) 2 1 a 1 2 if t a t a t a < t a a =1 J =1 ta - ta (4) where 0 2 if t a t a 3 ta < ta f (t a ) = 3 Ui = utility of episode i, ta - ta 3 4 3 4 if t a t a ta < ta A = number of activity episodes, and ta - ta J = number of travel episodes in the schedule. 1 otherwise