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M O D E L I N G S H O RT- T E R M D Y N A M I C S I N A C T I V I T Y- T R AV E L PAT T E R N S 73 where t a1 t 2 t 3 t 4 are the cutoff points dividing the possible to extend the heuristic with a limited number of a a a day into four intervals. The intervals define start times at simultaneous choices so as to reduce the risk of getting which the activity would not generate any utility (the trapped in a local optimum. first and last intervals), the utility is at a maximum (the Travel episodes are scheduled as part of activity third interval), and the utility is some fraction of the episodes. The trip to the location and the trip to home maximum. after having conducted the activity are considered attri- Traveling involves effort and sometimes monetary butes of an activity. The return-home trip is empty if the costs, depending on the transport mode used. If it is agent decides to travel to the next activity location assumed that travel time is not intrinsically rewarding, directly without first returning home (referred to as trip the utility of a travel episode is modeled as a negative chaining). Default settings are used for each activity function of duration. attribute when it is inserted in the schedule by an inser- tion or a substitution operation. Making the schedule consistent (Step 1b) is a subrou- Scheduling Method tine that implements minimal adaptations needed to make a schedule consistent with constraints, such as that The model assumes that individuals' abilities and priori- the individual should return home at the end of the day, ties to optimize a schedule are limited by cognitive con- start from home at the beginning of the day, use the same straints and the amount of mental effort that they are transport mode (if vehicle based) for trips that are willing to make. To find reasonable solutions within the chained, and so on. Travel times are initially set to constraints, the model uses a heuristic scheduling method. defaults and updated each time the destination location, The heuristic assumes an existing schedule (which may be origin location, or transport mode changes. empty) as given. The schedule should be consistent, and the result of the heuristic is again a consistent schedule with a higher or equal utility value. The heuristic searches Schedule Implementation for and implements improvements by considering one operation at a time. In the order in which they are consid- It is assumed that an activity schedule is implemented ered, these include (i) inserting activities, (ii) substituting sequentially during the day. To allow for possible resched- activities, (iii) repositioning activities, (iv) deleting activi- uling behavior, it is assumed that agents decide whether to ties, (v) changing locations, (vi) changing trip-chaining reschedule their activities at every node of the transporta- choices, and (vii) changing transport modes. A single oper- tion network and after completing each activity. Travel ation is repeated until no more improvement has been times on links are estimated as a function of the number of made. If the schedule has changed in any one of these agents using the link simultaneously for a given time step steps, the process is repeated. Each step in this procedure by means of the following well-known method: is in itself an iterative process that can be written as ti = tif [1 + (vi / ci ) ] (5) 1. For all options of , where a. Implement the option, b. Make the schedule consistent, ti = updated travel time on link i, c. Optimize durations, tif = free-floating travel time, d. Optimize start times, vi = traffic intensity, e. Evaluate the schedule's utility, and ci = capacity of the link, and f. Restore the schedule (i.e., undo Substep a). and = parameters. 2. If improves the schedule, then a. Implement and The estimates are used to determine actual travel b. Repeat from Step 1. times in that time step. Unexpected travel times and unforeseen events are two possible causes for a mismatch where denotes a specific operation consid- between a scheduled and actual end time of an episode. ered in Steps i through vii. As implied by this procedure, A time-surplus or time-lack situation at the moment of operations are always evaluated under conditions of con- completing an episode triggers rescheduling. sistency and optimal duration and timing decisions. The heuristic nature of this method is emphasized. In none of the steps is the evaluation of options exhaustive. By iter- Learning atively applying the search procedure, the method may still find good solutions. Some pairs of operations, such After having executed the schedule, an agent updates his as mode and location choices, may interact strongly. It is knowledge about choice sets, default settings of activi-