The understanding of the pedestrian behavior in the crowd is indispensable for the assessment of urban layout and various approaches are reported for evaluating the safety of the social infrastructures. In this paper, a simulation model of pedestrian flow is introduced based on the Mixed Logical Dynamical (MLD) system approach. The effect of personal space is newly investigated from the viewpoint of the path-planning and an alternative pedestrian flow model is proposed based on the MLD system description. The feature of the proposed model is illustrated with typical simulations and the relation between the congestion and the effect of personal spaces is evaluated in the evacuation and bi-directional flows.
In this paper, we study the stability analysis of discrete-time interconnected positive systems by means of a weighted l1-induced norm, where the weighted l1-induced norm is computed from the l1 norm of the input and output signals evaluated with given weighting vectors. In the literature,it was shown that the weighted L1-induced norm of continuous-time LTI positive systems can be characterized by linear programming problem (LP). Moreover, the weighted L1-induced norm was proved to be useful for the stability analysis of interconnected positive systems. On the basis of these results, we first show that the weighted l1-induced norm of discrete-time LTI positive systems can be again characterized by LP. From this preliminary result, we can construct a transformation from a given discrete-time positive system to a continuous-time positive system, where the weighted L1-induced norm of the resulting system is equivalent to the weighted l1-induced norm of the original system. By means of this key transformation, we can readily extend the continuous-time case results to the stability analysis of discrete-time interconnected positive systems.
We propose a novel optimization problem for a vehicle delivery planning and its effective heuristics based on dynamic programming (DP). Novelty of the problem is that each delivery item has a designated delivery date with a certain relaxation window. Then, the minimum delivery cost can be decreased compared with the rigorous delivery date problem. The optimization of the actual delivery dates is formalized as 0-1 integer programming, which can be reduced to a resource allocation problem. DP is then applicable for the rigorous optimization, though the computational cost is large. Here we proposed a heuristic approach based on DP. First, the value function, which is obtained through recursive steps in DP, is approximated by a linear programming relaxation based on the method proposed by Bertsimas et al. Next, a search of the optimal solution at each recursive step is bounded by setting a threshold. Furthermore, the number of recursive steps can be shortened according to a characteristic time scale of a target problem. The proposed heuristics are applied to the target delivery problem, and detailed numerical calculations on various size problems with various parameter settings show the effectiveness with a largely reduced computational time.