Mathematical model of single-source multi-destinations evacuation and optimization of emergency exits

doi:10.16265/j.cnki.issn1003-3033.2025.03.1994

Abstract

Abstract:

In order to improve the evacuation efficiency of public buildings and reduce casualties caused by emergencies, in view of the optimization problems of emergency exits and evacuation plans, a mathematical model and algorithm for the single-source multi-sink evacuation problem were proposed. Firstly, all evacuation paths were identified using path algorithm and sorted based on evacuation time. Then, the recursive formula for calculating evacuation time was derived based on the User Equilibrium (UE) principle and k-shortest path. The capacity allocation issues of each evacuation path at intersections were analyzed. After that then the optimization strategy for emergency exits is obtained. Finally, taking a building as an example, the evacuation network was established and calculated to validate the effectiveness of the algorithm and optimization strategy. The results show that the evacuation efficiency of the building network increases gradually with the increase in the number of evacuees, and the rate of change stabilizes after reaching a certain threshold value, Evacuation efficiency is closely associated with the total traffic capacity of specific emergency exits. Through the optimization of specific emergency exits, the evacuation efficiency of the network is enhanced, evacuation time can be reduced, and the optimization effect becomes more pronounced as the number of evacuees increases.

Key words: single-source multi-destinations, emergency exit, evacuation model, User Equilibrium principle, path algorithm

CLC Number:

X913.4安全系统工程

ZHOU Lingchang, LIANG Yin, LAI Yanping. Mathematical model of single-source multi-destinations evacuation and optimization of emergency exits[J]. China Safety Science Journal, 2025, 35(3): 187-193.

Figures/Tables 9

Fig.1

Fig.2

Fig.3

Table 1

Table 2

Evacuation paths and travel time before optimization

序号	通路编号	包含的疏散弧	运动时间
1	①	e₇、e₁₁、e₂₃、e₂₈	4
2	②	e₁₇、e₁₈、e₂₂、e₃₁	6
3	③	$e 14 、 e 15 、 e 26 、$ e₃₀	7
4	⑥	e₁₆、e₁₉、e₂₁、e₂₂、e₃₁	8
5	⑦	e₁、e₄、e₁₁、e₂₄、e₂₇	9
6	⑧	e₃、e₄、e₁₁、e₂₃、e₂₈	9
7	⑨	e₁₁、e₁₂、e₁₄、e₂₆、e₃₀	9
8	⑬	e₈、e₁₁、e₂₅、e₂₉	11

Table 2

Table 3

Table 4

Fig.4

Fig.5

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序号	人数	疏散时间 T/s		疏散效率/ (人·s^-1)		ΔN∶ΔT/ (人·s^-1)
序号	人数	优化前	优化后	优化前	优化后	优化前	优化后
1	0	4	4	—	—	—	—
2	5	6.2	6.2	0.81	0.81	2.27	2.27
3	10	7.14	7.14	1.4	1.4	5.32	5.32
4	15	7.86	7.86	1.9	1.9	6.94	6.94
5	20	8.5	8.44	2.35	2.37	7.81	8.62
6	25	9.07	9.0	2.76	2.78	8.77	8.93
7	30	9.46	9.31	3.17	3.22	12.82	16.00
8	35	9.85	9.63	3.55	3.64	12.82	16.00
9	40	10.23	9.94	3.91	4.03	13.16	16.00
10	45	10.61	10.24	4.24	4.4	13.16	16.79
11	50	11	10.53	4.54	4.75	12.82	17.00
12	55	11.33	10.82	4.8	5.08	15.02	16.97
13	60	11.67	11.12	5.14	5.4	14.97	17.01
14	65	12	11.41	5.4	5.7	15.02	17.01
15	70	12.33	11.7	5.68	5.98	15.02	17.01
16	75	12.67	12.0	5.92	6.25	14.97	17.01
17	80	13	12.29	6.15	6.51	15.02	17.01
18	85	13.33	12.59	6.38	6.75	15.02	17.01
19	90	13.67	12.88	6.58	6.99	14.98	16.99
20	95	14	13.18	6.79	7.21	15.00	17.00
21	100	14.33	13.47	6.98	7.42	15.02	17.00
22	105	14.67	13.77	7.16	7.63	14.97	16.98
23	110	15	14.06	7.33	7.82	15.02	17.02
24	115	15.33	14.35	7.5	8.01	15.02	17.00
25	120	15.67	14.65	7.66	8.196	14.97	17.01