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Long-term dynamics

In some cases, it is possible that short-term changes do not seem to be effective enough in alleviating stress. Then, a long-term change may be considered. One of the main goals of the current study is to link those two time horizons (short and long-term) in one model of dynamic activity-travel behaviour.

Lowering aspirations

It is assumed that an individual will keep a record of how many consecutive times (s)he conducted an exploration for an activity type, under the same context c, without finding something satisfactory. As the exploration effort is built up, the probability that the individual will lower the conditional aspirations on the level of the dissatisfactory activity attributes increases. Lowering aspirations means that an individual lowers the conditional aspiration values of the attributes that caused dissatisfaction to the corresponding attribute values of the exploitation option. Specifically, the probability that an individual lowers the conditional aspiration level of an activity attribute of an activity type k, is:

(9.19)

where and are parameters of the logistic function.

Becoming 'awake'

After several decreases of the conditional aspiration values of an individual, it is possible that (s)he realises that (s)he needs to extent the possibilities and the universal choice set within which (s)he acts. In that case, the individual becomes 'awake' and realises that a long-term change needs to be considered.

In particular, the conditional aspiration value of an individual for activity type ะบ equals to:

(9.20)

where is the frequency of experiencing context c. In a similar way, the unconditional aspiration value of an individual for activity type is calculated, as well.

The mean value of the conditional aspiration values of the K total number of activity types included in an individual's agenda equals to the actually experienced utility of the current long-term decisions of that individual:

(9.21)

(9.18)

Similarly, the mean value of the unconditional aspirations of the K activity types equals to the aspiration of an individual, regarding his/her context of long-term decisions . Let be the stress tolerance threshold for the long-term level. We assume that if:

(9.22)

an individual does not consider making a long-term change, as (s)he does not suffer by stress on the long-term level. However, if this difference exceeds the long-term stress tolerance threshold, (s)he becomes 'awake' and considers conducting a long-term change. Predicting the point of time and the situation under which an individual becomes 'awake' is the boundary of this model. The process which led to a long-term change, the specific activity-type and context-condition which generated stress, and the effort of an individual to reduce it, can be predicted by the model. In this way, it gives a clear image of how the sequence of short to long-term adaptation efforts took place. Finally, the role that emotional responses played in this process, as well as the fluctuation of various conditional and unconditional aspiration values can also be traced.

Updating Phase

The decision-making process, which was described in the previous section, is followed by the implementation of the selected activity profile. Based on this experience, an individual updates the emotional value of the selected activity profiles, his/her beliefs and his/her aspiration values (as it was already explained). Moreover, the awareness and the activation level of the activity profiles are updated based on a learning/forgetting process (according to Eqs. (9.8) and (9.13)).

 
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