Dijkstra's algorithm is one of the most well known algorithm to solve the shortest path problem (SPP). When applied to real situations, although the shortest path can be computed with Dijkstra's algorithm, it is not always the chosen one. In traffic situations, for example, the driver may not know the shortest path to follow. Even more, although the driver knows the shortest one, he/she may prefer choosing another path. There are different studies where extensions of Dijkstra's algorithm are used when the lengths of edges are no fixed. These extended versions of Dijkstra's algorithm can be adapted in order to simulate real situations in traffic. However, another approach consists of considering fixed lengths on edges and introducing some variations simulating the drivers' behaviours. In this work we present a modification on the Dijkstra's algorithm in order to simulate real situations in which the shortest path is not always chosen. As an example of application, we will extend the ATISMART model, introduced in FEMTEC 2013, where an accelerated-time simulation of car traffic in a smart city was described. In this previous work, all cars in the system used the Dijkstra's algorithm to choose the shortest path from their inputs to their exits. In this talk, the extended model ATISMART$^+$ for traffic flow simulation in smart cities is presented. This model includes more realistic situations considering different drivers' behaviours. As for the previous model, the implementation of ATISMART$^+$ is carried out using a Computer Algebra System (CAS), specifically Maxima, together with a graphic user interface, developed in Java.

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