Quasi-continuous dynamic equilibrium assignment with departure time choice in congested unidirectional pedestrian networks

Although walking has been considered as an important transport mode, pedestrian modelling has received little attention in either academic or practising circles. There is an increasing need for methods that can be used to help the planning, design and management of pedestrian traffic systems. This paper presents a nonlinear programming formulation of the dynamic pedestrian equilibrium assignment problem based on the following assumptions. The pedestrian traffic system in a congested urban area can be modelled as a capacitated network with alternative walkway sections. People in this pedestrian network make such decisions as selecting departure time and walking path between origins and destinations (OD). The study horizon is divided equally into shorter time intervals of 5-10 minutes each, for which the pedestrian departure time matrices are given by a logit formula. It is dependent on the predetermined departure time costs and the equilibrium OD walking costs. In the proposed model, a 'quasi-continuous' technique is adopted to smooth out the transitions of various variables between time intervals and to satisfy the first-in-first-out discipline. A heuristic algorithm that generates approximate solutions to the model is presented. The numerical results in a real network shows that the model and algorithm proposed in this paper are able to capture the main characteristics of the departure time and route choices in congested unidirectional pedestrian traffic systems.