# Modeling Activity-Time to Build Realistic Plannings in Population Synthesis in a Suburban Area
## 1 Introduction  
Large-scale and complex mobility systems can be represented by simulating the behaviors and interactions of self-interested \"agents\". The simulation of mobility is particularly suitable for an agent-based design. Indeed, the objective in these simulations is to take into account human behaviors interacting in an open, dynamic, and complex environment [1]. This multi-agent paradigm provides a high level of details and allows representing non-linear phenomena and patterns that would be difficult to tackle with analytical approaches [2]. Among multi-agent models, there is a class called activity-based models, which specifically address the need for realistic representation of travel demand and the human behavior in a mobility context. The activity-based modeling (ABM) framework is capable of evaluating travel demand and transportation supply management strategies, such as road pricing and behavior modification programs (flexible scheduling, ride-sharing), in a more efficient way than the previous generation of aggregate flow models, which generally focus on evaluating network capacity improvement. Activity-based models describe in greater detail than traditional models the travel patterns related to activities of households throughout a period of time and for a specific studied region. In these models, detailed descriptions of individuals and the households in terms of socio-economic attributes is key to guaranteeing the behavioral aspects implied by the models [3]. In this context, population synthesis is the sub-model that ensures thespecification of an estimated population, whose complex configuration needs to be properly captured. A synthetic population is a representation of the actual population in a certain region and focuses only on a set of attributes of the actual population. This population exists only artificially (statistically) and is an approximation of the real population of the studied area [4]. The objective of an activity-based model is to predict, for each individual of the synthetic population, which activity is generated (activity-type), when it is executed (start-time), for how long (duration), where the activity takes part (location-choice), and the transport mode used (mode-choice). Most models struggle with the dynamic consistency due to the difficulty to capture the trade-off between activities scheduled throughout a traveller's daily path [5]. The choices depend on each other: the mode used depends on the activity location, the time-choice depends on the activity-type (typical duration, time-windows), and in the case of type of activity pattern (for a day, a week, etc. ), the activity order in the activity plan influences the choice of activity time and its duration. Some other dependencies (constraints) can be included, such as the travel time, which depend mainly on the mode-choice and location-choice. In this paper, we are interested in the activity time-choice. Given an activity plan, several approaches can be used to set the time-choice (mainly as part of the scheduling process). The objective is to find a realistic pattern for these activities by considering the activity-choice, location-choice, and mode-choice. It involves the introduction of several temporal-constraints related to the activity-duration and the activity-time distribution. The output of the proposed approach is an activity-plan with realistic times and correlated to the pre-defined time-distributions of the activities. Following their decision-making process (behavior-choice), activity-based models can be divided into two classes: econometric activity-based models and rule-based models. The econometric models use mainly utility maximization-based equations, with the aim to predict the probability of decision outcomes (based on the relationship between the travel and activity attributes). Several econometric models were developed, such as CEMDAP [6] and MORPC [7]. A rule-based model (also called computational process model), is a computer program built on a set of rules (a production system model).