A micro-macro hybrid model with application for material and pedestrian flow

Figures & data

Figure 1. Idea of the switch: from microscopic to macroscopic scale and vice versa.

Figure 2. Sketch of the conveyor belt.

Figure 3. Macroscopic to microscopic representation.

Figure 4. Switch from micro to macro for the material flow problem.

Figure 5. Switch from macro to micro for the material flow problem.

Figure 6. Evacuation of a room with one exit.

Figure 7. Switch from micro to macro for the pedestrian model.

Figure 8. Switch from macro to micro for the pedestrian model.

Table 1. Computing times [sec] for the material flow model

$N$	Micro $\to$ Macro	Macro $\to$ Micro
		Start solution	Optimization	Update alg.	$\sum$
50	0.0077	0.19	25.84	0.17	26.21
100	0.0076	0.34	135.24	0.61	136.19
150	0.0075	0.48	274.08	1.48	276.05
200	0.0074	0.81	727.16	3.03	731.00

Table 2. Computing times [sec] for the pedestrian model

$N$	Micro $\to$ Macro	Macro $\to$ Micro
		Start solution	Optimization	Update alg.	$\sum$
50	0.0109	1.37	57.17	0.05	58.59
100	0.0098	1.10	919.42	0.03	920.56
150	0.0163	1.21	255.69	0.07	256.97
200	0.0153	1.34	2939.13	0.12	2940.60