iTEVAC: an enhanced trusted evacuation system leveraging fog computing and IoT

Figures & data

Figure 1. Fog node in TEVAC.

Table 1. Additional features of iTEVAC.

Feature	TEVAC	iTEVAC
System incorporates Fog computing and IoT devices.	x	x
System uses Dijkstra's algorithm to find the safest route.	x	x
System outputs safe movement directions from node locations to exits.	x	x
System controls isolated nodes (or nodes without exits) and automatically reports to the control centre for priority in rescue operations.		x
System continuously updates in real time when an incident occurs.		x

Figure 2. TEVAC based Fog computing.

Figure 3. Indoor escape scene context.

Figure 4. Graph based model.

Figure 5. Overall architecture of Trusted Evacuation system.

Figure 6. The iTEVAC process.

Table 2. Overall iTEVAC algorithm.

Step	Description
1	Calculate the execution time (time).
	Update the objective function values from the paths within the commercial centre based on M00:
	– For each element M00(i,j) in the grid matrix: – If M00(i,j) ≠ 0 and M00(i,j) ≠ Max: – Set M0(i,j) = M0(j,i) to a randomly generated value in the range [0, 100]. – Else: – Set M0(i,j) = M00(i,j).
2	Determine the grid information of the commercial centre before removing paths with objective function values exceeding the threshold:
	– Initialize G0 = I0 - F0 - K0 and G0_new = I0 - F0.
	– For each element M0(i,j) in the grid matrix:
	– If M0(i,j) ≠ 0 and M0(i,j) ≠ Max:
	– Set I0 = i, F0 = j, and K0 = M0(i,j).
3	Remove paths with objective function values exceeding the threshold:
	– Initialize M as an empty grid matrix.
	– For each element M0(i,j) in the grid matrix:
	– If M0(i,j) ≠ 0 and M0(i,j) ≠ Max and M0(i,j) > Thres:
	– Set M(i,j) = Max.
	– Else:
	– Set M(i,j) = M0(i,j).
4	Identify the isolated nodes within the commercial centre after removing paths with objective function values exceeding the threshold:
	– Initialize E as an empty matrix.
	– For each node i in the grid matrix:
	– If all elements in row M(i,:) are 0 or equal to Max and i ∉ Out:
	– Mark node i as isolated in matrix E.
5	Determine the grid information of the commercial centre after removing paths with objective function values exceeding the threshold:
	– Initialize G = I - F - K and G_new = I - F.
	– For each element M(i,j) in the grid matrix:
	– If M(i,j) ≠ 0 and M(i,j) ≠ Max:
	– Set I = i, F = j, and K = M(i,j).
6	Find all possible paths from the nodes requiring movement to all entrance/exit gates within the commercial centre:
	– Calculate the optimal paths using Dijkstra's algorithm and store them in the matrix outpath.
7	Find the safest path from the nodes requiring movement within the commercial centre to the entrance/exit gates:
	– Calculate the objective function value for each path in outpath.
	– For each node in Node:
	– Find the minimum objective function value among the paths in outpath connected to the corresponding gate in Out and store it in matrix optimal.
8	Conclude the execution time of the algorithm (time).

Table 3. Parameter values of the proposed algorithm.

Parameter	Value
x	100*rand(1)
Max	2*10^6
Note	[2 4 5 6 8 9 11 13 14 15 16 17 18 19 20]
Out	[1 3 7 10 12]
Threshold	80

Table 4. Scenario processing steps.

Step	Input	Output
1	M00, Note, Out, Max, Threshold	M1, E1, time1, optimal1, outpath1, G01, G1, G01_new, G1_new
2	M1, Note, Out, Max, Threshold	M2, E2, time2, optimal2, outpath2, G02, G2, G02_new, G2_new
3	M2, Note, Out, Max, Threshold	M3, E3, time3, optimal3, outpath3, G03, G3, G03_new, G3_new
4	M3, Note, Out, Max, Threshold	M4, E4, time4, optimal4, outpath4, G04, G4, G04_new, G4_new

Table 5. Grid matrix representation of the commercial center’ nodes.

	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20
1	0	x	Max	Max	Max	Max	Max	x	Max	Max	Max	Max	Max	Max	Max	Max	Max	Max	Max	Max
2	x	0	x	Max	Max	Max	Max	Max	x	Max	Max	Max	Max	Max	Max	Max	Max	Max	Max	Max
3	Max	x	0	x	Max	Max	Max	Max	Max	x	Max	Max	Max	Max	Max	Max	Max	Max	Max	Max
4	Max	Max	x	0	x	Max	Max	Max	Max	Max	x	Max	Max	Max	Max	Max	Max	Max	Max	Max
5	Max	Max	Max	x	0	x	Max	Max	Max	Max	Max	x	Max	Max	Max	Max	Max	Max	Max	Max
6	Max	Max	Max	Max	x	0	x	Max	Max	Max	Max	Max	x	Max	Max	Max	Max	Max	Max	Max
7	Max	Max	Max	Max	Max	x	0	Max	Max	Max	Max	Max	Max	x	Max	Max	Max	Max	Max	Max
8	x	Max	Max	Max	Max	Max	Max	0	x	Max	Max	Max	Max	Max	Max	Max	Max	Max	Max	Max
9	Max	x	Max	Max	Max	Max	Max	x	0	x	Max	Max	Max	Max	Max	Max	Max	Max	Max	Max
10	Max	Max	x	Max	Max	Max	Max	Max	x	0	x	Max	Max	Max	Max	Max	Max	Max	Max	Max
11	Max	Max	Max	x	Max	Max	Max	Max	Max	x	0	x	Max	Max	Max	Max	Max	Max	Max	Max
12	Max	Max	Max	Max	x	Max	Max	Max	Max	Max	x	0	x	Max	Max	Max	x	Max	Max	Max
13	Max	Max	Max	Max	Max	x	Max	Max	Max	Max	Max	x	0	x	Max	Max	x	Max	Max	Max
14	Max	Max	Max	Max	Max	Max	x	Max	Max	Max	Max	Max	x	0	Max	Max	Max	Max	Max	Max
15	Max	Max	Max	Max	Max	Max	Max	Max	Max	Max	Max	Max	Max	Max	0	x	Max	x	Max	Max
16	Max	Max	Max	Max	Max	Max	Max	Max	Max	Max	Max	Max	Max	Max	x	0	x	Max	x	Max
17	Max	Max	Max	Max	Max	Max	Max	Max	Max	Max	Max	x	x	Max	Max	x	0	Max	Max	x
18	Max	Max	Max	Max	Max	Max	Max	Max	Max	Max	Max	Max	Max	Max	x	Max	Max	0	x	Max
19	Max	Max	Max	Max	Max	Max	Max	Max	Max	Max	Max	Max	Max	Max	Max	x	Max	x	0	x
20	Max	Max	Max	Max	Max	Max	Max	Max	Max	Max	Max	Max	Max	Max	Max	Max	x	Max	x	0

Figure 7. Sensor values received by the intelligent system at time t1.

Table 6. Updated grid matrix reflecting changes in the network.

	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20
1	0	91.33	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	65.57	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6
2	91.33	0	27.84	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	84.91	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6
3	2e + 6	27.84	0	96.48	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	75.77	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6
4	2e + 6	2e + 6	96.48	0	95.71	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	65.54	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6
5	2e + 6	2e + 6	2e + 6	95.71	0	14.18	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	03.18	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6
6	2e + 6	2e + 6	2e + 6	2e + 6	14.18	0	79.22	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	82.34	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6
7	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	79.22	0	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	95.02	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6
8	65.57	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	0	93.39	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6
9	2e + 6	84.91	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	93.39	0	74.31	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6
10	2e + 6	2e + 6	75.77	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	74.31	0	17.11	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6
11	2e + 6	2e + 6	2e + 6	65.54	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	17.11	0	27.69	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6
12	2e + 6	2e + 6	2e + 6	2e + 6	03.18	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	27.69	0	69.48	2e + 6	2e + 6	2e + 6	09.71	2e + 6	2e + 6	2e + 6
13	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	82.34	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	69.48	0	03.44	2e + 6	2e + 6	48.97	2e + 6	2e + 6	2e + 6
14	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	95.02	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	03.44	0	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6
15	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	0	76.55	2e + 6	70.93	2e + 6	2e + 6
16	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	76.55	0	44.55	2e + 6	27.60	2e + 6
17	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	09.71	48.97	2e + 6	2e + 6	44.55	0	2e + 6	2e + 6	16.26
18	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	70.93	2e + 6	2e + 6	0	67.97	2e + 6
19	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	27.60	2e + 6	67.97	0	11.89
20	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	16.26	2e + 6	11.89	0

Table 7. Removing the hazardous paths in the grid matrix by replacing the values exceeding the threshold with the maximum value.

	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20
1	0	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	65.57	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6
2	2e + 6	0	27.84	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6
3	2e + 6	27.84	0	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	75.77	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6
4	2e + 6	2e + 6	2e + 6	0	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	65.54	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6
5	2e + 6	2e + 6	2e + 6	2e + 6	0	14.18	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	03.18	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6
6	2e + 6	2e + 6	2e + 6	2e + 6	14.18	0	79.22	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6
7	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	79.22	0	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6
8	65.57	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	0	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6
9	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	0	74.31	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6
10	2e + 6	2e + 6	75.77	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	74.31	0	17.11	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6
11	2e + 6	2e + 6	2e + 6	65.54	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	17.11	0	27.69	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6
12	2e + 6	2e + 6	2e + 6	2e + 6	03.18	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	27.69	0	69.48	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6
13	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	69.48	0	03.44	2e + 6	2e + 6	48.97	2e + 6	2e + 6	2e + 6
14	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	03.44	0	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6
15	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	0	76.55	2e + 6	70.93	2e + 6	2e + 6
16	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	76.55	0	44.55	2e + 6	27.60	2e + 6
17	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	48.97	2e + 6	2e + 6	44.55	0	2e + 6	2e + 6	16.26
18	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	70.93	2e + 6	2e + 6	0	67.97	2e + 6
19	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	27.60	2e + 6	67.97	0	11.89
20	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	16.26	2e + 6	11.89	0

Table

Algorithm 1 Remove Hazardous Paths
Inputs: Matrix M0 (Original grid matrix); Max (Maximum value); N (Size of the matrix)
Outputs: Matrix M (Updated grid matrix with hazardous paths removed)
Procedure:
1. Initialize M as M0.
2. For each element in M0:
a. If M0(i,j) > 80, set M(i,j) to Max.
b. Otherwise, keep the value of M0(i,j) in M(i,j).
3. Return the updated matrix M.

Table

Algorithm 2 Identify Isolated Nodes
Inputs: Matrix M (Updated grid matrix with hazardous paths removed); Note (List of nodes requiring movement within the commercial centre); Out (List of entrance/exit gates of the commercial centre)
Outputs: Matrix E (List of isolated nodes within the commercial centre)
Procedure:
1. Initialize an empty array E to store the isolated nodes.
2. For each node i in the list Note:
a. Initialize an array T with all elements set to 0.
b. For each node j in the range from 1 to N:
– If M(i, j) is equal to 0 or M(i, j) is equal to the maximum value Max, set T(j) to 0.
– Otherwise, set T(j) to 1.
c. Calculate the sum of all elements in array T and store it in R(i).
3. Initialize a variable r as 0 to keep track of the number of isolated nodes.
4. For each node i in the range from 1 to N:
– If R(i) is equal to 0, increment r by 1 and store the value of i in the r-th position of array E.

Figure 8. Separated grids.

Table

Algorithm 3 Convert Grid Matrix to Sub-Matrices
Inputs: Matrix M (Updated grid matrix with hazardous paths removed); N (Size of the matrix)
Outputs: Matrix I (Sub-matrix containing starting nodes for possible paths); Matrix F (Sub-matrix containing destination nodes for possible paths); Matrix K (Sub-matrix containing objective function values for possible paths)
Procedure:
1. Initialize a counter variable r to 0.
2. For each node i in the range from 1 to the total number of nodes:
– For each node j in the range from 1 to the total number of nodes:
– If j is greater than 1 and M(i,j) is not equal to Max:
– Increment the counter variable r by 1.
– Store the value of i in the corresponding position of matrix I.
– Store the value of j in the corresponding position of matrix F.
– Store the value of M(i,j) in the corresponding position of matrix K.
3. Return the sub-matrices I, F, and K.

Table 8. The value of optimal paths.

	1	2	3	4	5
1	1	[]	[]	[]	[]
2	[]	2	[2,3]	[2,3,10,11,4]	[2,3,10,11,12,5]
3	[]	[3,2]	3	[3,10,11,4]	[3,10,11,12,5]
4	[]	[4,11,10,3,2]	[4,11,10,3]	4	[4,11,12,5]
5	[]	[5,12,11,10,3,2]	[5,12,11,10,3]	[5,12,11,4]	5
6	[]	[6,5,12,11,10,3,2]	[6,5,12,11,10,3]	[6,5,12,11,4]	[6,5]
7	[]	[7,6,5,12,11,10,3,2]	[7,6,5,12,11,10,3]	[7,6,5,12,11,4]	[7,6,5]
8	[8,1]	[]	[]	[]	[]
9	[]	[9,10,3,2]	[9,10,3]	[9,10,11,4]	[9,10,11,12,5]
10	[]	[10,3,2]	[10,3]	[10,11,4]	[10,11,12,5]
11	[]	[11,10,3,2]	[11,10,3]	[11,4]	[11,12,5]
12	[]	[12,11,10,3,2]	[12,11,10,3]	[12,11,4]	[12,5]
13	[]	[13,17,12,11,10,3,2]	[13,17,12,11,10,3]	[13,17,12,11,4]	[13,17,12,5]
14	[]	[14,13,17,12,11,10,3,2]	[14,13,17,12,11,10,3]	[14,13,17,12,11,4]	[14,13,17,12,5]
15	[]	[15,16,17,12,11,10,3,2]	[15,16,17,12,11,10,3]	[15,16,17,12,11,4]	[15,16,17,12,5]
16	[]	[16,17,12,11,10,3,2]	[16,17,12,11,10,3]	[16,17,12,11,4]	[16,17,12,5]
17	[]	[17,12,11,10,3,2]	[17,12,11,10,3]	[17,12,11,4]	[17,12,5]
18	[]	[18,19,20,17,12,11,10,3,2]	[18,19,20,17,12,11,10,3]	[18,19,20,17,12,11,4]	[18,19,20,17,12,5]
19	[]	[19,20,17,12,11,10,3,2]	[19,20,17,12,11,10,3]	[19,20,17,12,11,4]	[19,20,17,12,5]
20	[]	[20,17,12,11,10,3,2]	[20,17,12,11,10,3]	[20,17,12,11,4]	[20,17,12,5]
	6	7	8	9	10
1	[]	[]	[1,8]	[]	[]
2	[2,3,10,11,12,5,6]	[2,3,10,11,12,5,6,7]	[]	[2,3,10,9]	[2,3,10]
3	[3,10,11,12,5,6]	[3,10,11,12,5,6,7]	[]	[3,10,9]	[3,10]
4	[4,11,12,5,6]	[4,11,12,5,6,7]	[]	[4,11,10,9]	[4,11,10]
5	[5,6]	[5,6,7]	[]	[5,12,11,10,9]	[5,12,11,10]
6	6	[6,7]	[]	[6,5,12,11,10,9]	[6,5,12,11,10]
7	[7,6]	7	[]	[7,6,5,12,11,10,9]	[7,6,5,12,11,10]
8	[]	[]	8	[]	[]
9	[9,10,11,12,5,6]	[9,10,11,12,5,6,7]	[]	9	[9,10]
10	[10,11,12,5,6]	[10,11,12,5,6,7]	[]	[10,9]	10
11	[11,12,5,6]	[11,12,5,6,7]	[]	[11,10,9]	[11,10]
12	[12,5,6]	[12,5,6,7]	[]	[12,11,10,9]	[12,11,10]
13	[13,17,12,5,6]	[13,17,12,5,6,7]	[]	[13,17,12,11,10,9]	[13,17,12,11,10]
14	[14,13,17,12,5,6]	[14,13,17,12,5,6,7]	[]	[14,13,17,12,11,10,9]	[14,13,17,12,11,10]
15	[15,16,17,12,5,6]	[15,16,17,12,5,6,7]	[]	[15,16,17,12,11,10,9]	[15,16,17,12,11,10]
16	[16,17,12,5,6]	[16,17,12,5,6,7]	[]	[16,17,12,11,10,9]	[16,17,12,11,10]
17	[17,12,5,6]	[17,12,5,6,7]	[]	[17,12,11,10,9]	[17,12,11,10]
18	[18,19,20,17,12,5,6]	[18,19,20,17,12,5,6,7]	[]	[18,19,20,17,12,11,10,9]	[18,19,20,17,12,11,10]
19	[19,20,17,12,5,6]	[19,20,17,12,5,6,7]	[]	[19,20,17,12,11,10,9]	[19,20,17,12,11,10]
20	[20,17,12,5,6]	[20,17,12,5,6,7]	[]	[20,17,12,11,10,9]	[20,17,12,11,10]
	11	12	13	14	15
1	[]	[]	[]	[]	[]
2	[2,3,10,11]	[2,3,10,11,12]	[2,3,10,11,12,17,13]	[2,3,10,11,12,17,13,14]	[2,3,10,11,12,17,16,15]
3	[3,10,11]	[3,10,11,12]	[3,10,11,12,17,13]	[3,10,11,12,17,13,14]	[3,10,11,12,17,16,15]
4	[4,11]	[4,11,12]	[4,11,12,17,13]	[4,11,12,17,13,14]	[4,11,12,17,16,15]
5	[5,12,11]	[5,12]	[5,12,17,13]	[5,12,17,13,14]	[5,12,17,16,15]
6	[6,5,12,11]	[6,5,12]	[6,5,12,17,13]	[6,5,12,17,13,14]	[6,5,12,17,16,15]
7	[7,6,5,12,11]	[7,6,5,12]	[7,6,5,12,17,13]	[7,6,5,12,17,13,14]	[7,6,5,12,17,16,15]
8	[]	[]	[]	[]	[]
9	[9,10,11]	[9,10,11,12]	[9,10,11,12,17,13]	[9,10,11,12,17,13,14]	[9,10,11,12,17,16,15]
10	[10,11]	[10,11,12]	[10,11,12,17,13]	[10,11,12,17,13,14]	[10,11,12,17,16,15]
11	11	[11,12]	[11,12,17,13]	[11,12,17,13,14]	[11,12,17,16,15]
12	[12,11]	12	[12,17,13]	[12,17,13,14]	[12,17,16,15]
13	[13,17,12,11]	[13,17,12]	13	[13,14]	[13,17,16,15]
14	[14,13,17,12,11]	[14,13,17,12]	[14,13]	14	[14,13,17,16,15]
15	[15,16,17,12,11]	[15,16,17,12]	[15,16,17,13]	[15,16,17,13,14]	15
16	[16,17,12,11]	[16,17,12]	[16,17,13]	[16,17,13,14]	[16,15]
17	[17,12,11]	[17,12]	[17,13]	[17,13,14]	[17,16,15]
18	[18,19,20,17,12,11]	[18,19,20,17,12]	[18,19,20,17,13]	[18,19,20,17,13,14]	[18,15]
19	[19,20,17,12,11]	[19,20,17,12]	[19,20,17,13]	[19,20,17,13,14]	[19,16,15]
20	[20,17,12,11]	[20,17,12]	[20,17,13]	[20,17,13,14]	[20,19,16,15]
	16	17	18	19	20
1	[]	[]	[]	[]	[]
2	[2,3,10,11,12,17,16]	[2,3,10,11,12,17]	[2,3,10,11,12,17,20,19,18]	[2,3,10,11,12,17,20,19]	[2,3,10,11,12,17,20]
3	[3,10,11,12,17,16]	[3,10,11,12,17]	[3,10,11,12,17,20,19,18]	[3,10,11,12,17,20,19]	[3,10,11,12,17,20]
4	[4,11,12,17,16]	[4,11,12,17]	[4,11,12,17,20,19,18]	[4,11,12,17,20,19]	[4,11,12,17,20]
5	[5,12,17,16]	[5,12,17]	[5,12,17,20,19,18]	[5,12,17,20,19]	[5,12,17,20]
6	[6,5,12,17,16]	[6,5,12,17]	[6,5,12,17,20,19,18]	[6,5,12,17,20,19]	[6,5,12,17,20]
7	[7,6,5,12,17,16]	[7,6,5,12,17]	[7,6,5,12,17,20,19,18]	[7,6,5,12,17,20,19]	[7,6,5,12,17,20]
8	[]	[]	[]	[]	[]
9	[9,10,11,12,17,16]	[9,10,11,12,17]	[9,10,11,12,17,20,19,18]	[9,10,11,12,17,20,19]	[9,10,11,12,17,20]
10	[10,11,12,17,16]	[10,11,12,17]	[10,11,12,17,20,19,18]	[10,11,12,17,20,19]	[10,11,12,17,20]
11	[11,12,17,16]	[11,12,17]	[11,12,17,20,19,18]	[11,12,17,20,19]	[11,12,17,20]
12	[12,17,16]	[12,17]	[12,17,20,19,18]	[12,17,20,19]	[12,17,20]
13	[13,17,16]	[13,17]	[13,17,20,19,18]	[13,17,20,19]	[13,17,20]
14	[14,13,17,16]	[14,13,17]	[14,13,17,20,19,18]	[14,13,17,20,19]	[14,13,17,20]
15	[15,16]	[15,16,17]	[15,18]	[15,16,19]	[15,16,19,20]
16	16	[16,17]	[16,19,18]	[16,19]	[16,19,20]
17	[17,16]	17	[17,20,19,18]	[17,20,19]	[17,20]
18	[18,19,16]	[18,19,20,17]	18	[18,19]	[18,19,20]
19	[19,16]	[19,20,17]	[19,18]	19	[19,20]
20	[20,19,16]	[20,17]	[20,19,18]	[20,19]	20

Table 9. The corresponding objective function values.

	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20
1	0	0	0	0	0	0	0	65.57	0	0	0	0	0	0	0	0	0	0	0	0
2	0	0	27.84	186.2	151.6	165.8	245.0	0	177.9	103.6	120.7	148.4	207.1	210.5	279.2	202.7	158.1	254.2	186.3	174.4
3	0	27.84	0	158.4	123.7	137.9	217.1	0	150.0	75.77	92.89	120.5	179.2	182.7	251.4	174.8	130.2	226.4	158.4	146.5
4	0	186.2	158.4	0	96.42	110.6	189.8	0	156.9	82.66	65.54	93.24	151.9	155.3	224.0	147.5	102.9	199.0	131.1	119.2
5	0	151.6	123.7	96.42	0	14.18	93.40	0	122.3	47.99	30.87	3.183	61.87	65.31	134.0	57.45	12.89	109.0	41.05	29.15
6	0	165.8	137.9	110.6	14.18	0	79.22	0	136.4	62.18	45.06	17.37	76.06	79.50	148.1	71.64	27.08	123.2	55.24	43.34
7	0	245.0	217.1	189.8	93.40	79.22	0	0	215.7	141.4	124.2	96.59	155.2	158.7	227.4	150.8	106.3	202.4	134.4	122.5
8	65.57	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
9	0	177.9	150.0	156.9	122.3	136.4	215.7	0	0	74.31	91.43	119.1	177.8	181.2	249.9	173.3	128.8	224.9	156.9	145.0
10	0	103.6	75.77	82.66	47.99	62.18	141.4	0	74.31	0	17.11	44.81	103.5	106.9	175.6	99.08	54.52	150.6	82.68	70.78
11	0	120.7	92.89	65.54	30.87	45.06	124.2	0	91.43	17.11	0	27.69	86.38	89.82	158.5	81.96	37.40	133.5	65.56	53.66
12	0	148.4	120.5	93.24	3.183	17.37	96.59	0	119.1	44.81	27.69	0	58.68	62.13	130.8	54.27	9.713	105.8	37.87	25.97
13	0	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	0	2e + 6	2e + 6	2e + 6	2e + 6	0	3.444	170.0	93.53	48.97	145.1	77.13	65.23
14	0	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	0	2e + 6	2e + 6	2e + 6	2e + 6	3.444	0	173.5	96.97	52.42	148.5	80.58	68.68
15	0	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	0	2e + 6	2e + 6	2e + 6	2e + 6	170.0	173.5	0	76.55	121.1	70.93	104.1	116.0
16	0	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	0	2e + 6	2e + 6	2e + 6	2e + 6	93.53	96.97	76.55	0	44.55	95.57	27.60	39.50
17	0	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	0	2e + 6	2e + 6	2e + 6	2e + 6	48.97	52.42	121.1	44.55	0	96.13	28.16	16.26
18	0	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	0	2e + 6	2e + 6	2e + 6	2e + 6	145.1	148.5	70.93	95.57	96.13	0	67.97	79.87
19	0	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	0	2e + 6	2e + 6	2e + 6	2e + 6	77.13	80.58	104.1	27.60	28.16	67.97	0	11.89
20	0	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	2e + 6	0	2e + 6	2e + 6	2e + 6	2e + 6	65.23	68.68	116.0	39.50	16.26	79.87	11.89	0

Table

Algorithm 4 Finding the Optimal Paths
Inputs: Matrix I (Sub-matrix containing starting nodes for possible paths); Matrix F (Sub-matrix containing destination nodes for possible paths); Matrix K (Sub-matrix containing objective function values for possible paths)
Outputs: Cell array outpath: Contains the optimal paths between each pair of nodes
Procedure:
1. Create a graph G using the sub-matrices I, F, and K.
2. For each node i in the range from 1 to N:
– For each node j in the range from 1 to N:
– Find the shortest path between node i and node j using the ‘shortestpath’ function.
– Store the obtained path in the cell array outpath at the position (i, j).
3. Return the cell array outpath.

Table

Algorithm 5 Calculating Objective Function Values for Optimal Paths
Inputs: Matrix M (Updated grid matrix with hazardous paths removed); Cell array outpath (Contains the optimal paths between each pair of nodes)
Outputs: Matrix Fitness (Contains the objective function values for the optimal paths)
Procedure:
1. Initialize the matrix Fitness with zeros.
2. For each node i in the range from 1 to N:
– For each node j in the range from 1 to N:
– Retrieve the optimal path H from the cell array outpath at position (i, j).
– Get the size of H and assign it to variables x and y.
– Initialize a vector HH with zeros of size (1, y-1).
– For each index k in the range from 1 to y-1:
– Assign the value M(H(k), H(k + 1)) to the k-th element of HH.
– Calculate the sum of the elements in HH and assign it to the (i, j)-th element of Fitness.
3. Return the matrix Fitness.

Table

Algorithm 6 Compute Optimal Evacuation Paths to Exit Gates
Inputs: Fitness (Matrix containing objective function values for optimal paths); Outpath (Matrix storing optimal paths between nodes); Note (Array of nodes requiring evacuation); Out (Array of designated exit gates); N (Dimension of the matrix)
Output: Optimal (A matrix containing the optimal evacuation paths for each node in Note to the nearest exit in Out)
Procedure:
Initialize FF as a matrix populated with large values (e.g. 10^10) to represent infinity.
Ascertain the dimensions of Note and assign them to variables x and y.
Ascertain the dimensions of Out and assign them to variables m and n.
For each node i in Note and each exit gate j in Out:
Assign Fitness(Note(i), Out(j)) to FF(Note(i), Out(j)).
For each node i in Note:
Identify the minimum value in the row FF(Note(i),:) and assign it to variables a and b.
Assign outpath{Note(i), b} to optimal{i}.
Output the matrix optimal containing the optimal paths.

Table 10. Title optimal evacuation paths for nodes to nearest exits.

Moving node	Optimal movement path	Direction and alert
2	[2,3]	Move to node 3
4	[4,11,10]	Move to node 11
5	[5,12]	Move to node 12
6	[6,5,12]	Move to node 5
8	[8,1]	Move to node 1
9	[9,10]	Move to node 10
11	[11,10]	Move to node 10
13	[13,17,12]	Move to node 17
14	[14,13,17,12]	Move to node 13
15	[15,16,17,12]	Move to node 16
16	[16,17,12]	Move to node 17
17	[17,12]	Move to node 12
18	[18,19,20,17,12]	Move to node 19
19	[19,20,17,12]	Move to node 20
20	[20,17,12]	Move to node 17

Figure 10. Comparison between iTEVAC and TEVAC.

Table 11. Algorithm processing time in comparison between iTEVAC and TEVAC.

Time Point	Processing Time (seconds)
	iTEVAC	TEVAC
t1	1.4414521	1.9657
t2	0.3509644	2.2393
t3	0.3719131	2.0694
t4	0.3177585	2.1549

Table 12. Isolated nodes and proposed solutions.

Time Point	Isolated nodes	Proposed solutions based on output [1 3 7 10 12]
t1	[0]	No rescue needed
t2	[1, 4, 7, 8]	Dispatch rescue to nodes 4–8 (1–7 are exits)
t3	[1, 4, 7, 8, 14, 18]	Dispatch rescue to nodes 4–8–14–18 (1–7 are exits)
t4	[1, 4, 7, 8, 14, 18]	Dispatch rescue to nodes 1–4–7–8–14–18

Table 13. Movement directions and alerts at time t2 for each node.

Moving node	Optimal movement path	Direction and alert
2	[2,3]	Move to node 3
4	[]	Call for rescue at node 4 as no exit path is found
5	[5,12]	Move to node 12
6	[6,5,12]	Move to node 5
8	[]	Call for rescue at node 8 as no exit path is found
9	[9,10]	Move to node 10
11	[11,10]	Move to node 10
13	[13,12]	Move to node 12
14	[14,13,12]	Move to node 13
15	[15,16,17,12]	Move to node 16
16	[16,17,12]	Move to node 17
17	[17,12]	Move to node 12
18	[18,19,16,17,12]	Move to node 19
19	[19,16,17,12]	Move to node 16
20	[20,19,16,17,12]	Move to node 19

Table 14. Movement directions and alerts at time t3 for each node.

Moving node	Optimal movement path	Direction and alert
2	[2,3]	Move to node 3
4	[]	Call for rescue at node 4 as no exit path is found
5	[5,12]	Move to node 12
6	[6,5,12]	Move to node 5
8	[]	Call for rescue at node 8 as no exit path is found
9	[9,10]	Move to node 10
11	[11,10]	Move to node 10
13	[13,12]	Move to node 12
14	[]	Call for rescue at node 14 as no exit path is found
15	[15,16,17,12]	Move to node 16
16	[16,17,12]	Move to node 17
17	[17,12]	Move to node 12
18	[]	Call for rescue at node 18 as no exit path is found
19	[19,16,17,12]	Move to node 16
20	[20,19,16,17,12]	Move to node 19

Table 15. Movement directions and alerts at time t4 for each node.

Moving node	Optimal movement path	Direction and alert
2	[2,3]	Move to node 3
4	[]	Call for rescue at node 4 as no exit path is found
5	[5,12]	Move to node 12
6	[6,5,12]	Move to node 5
8	[]	Call for rescue at node 8 as no exit path is found
9	[9,10]	Move to node 10
11	[11,10]	Move to node 10
13	[13,12]	Move to node 12
14	[]	Call for rescue at node 14 as no exit path is found
15	[15,16,17,13,12]	Move to node 16
16	[16,17,13,12]	Move to node 17
17	[17,13,12]	Move to node 13
18	[]	Call for rescue at node 18 as no exit path is found
19	[19,16,17,13,12]	Move to node 16
20	[20,19,16,17,13,12]	Move to node 19

Table 16. Comparative analysis of evacuation systems.

Aspect Feature	Integrated evacuation and rescue management system (IERM)	BIM and computer vision-based framework	iTEVAC
System Design	Agent-based simulation in AnyLogic	BIM model, IFC JAVA TOOLBOX, MatlabR2018b	Fog Computing, IoT
Methodology	Dynamic evacuation and rescue with priority assessment	Indoor positioning and path planning with computer vision	Smart evacuation leveraging IoT and Fog Computing
Simulation Environment	Pedestrian library for people flows simulation	Three-floor campus building model for testing	Commercial centre, old building with a network of path-nodes and exit-nodes
Key Features	Real-time data integration, risk-aware evacuation, dynamic rescue planning	GNM generation, indoor local positioning, BP neural network for path planning	Intelligent navigation systems, real-time situational analysis, decision-making speed < 1 s
Performance Metrics	Evacuation success rate, rescue success rate, total response time	Positioning accuracy, safety performance of rescue routes	Processing time, efficiency in identifying safe evacuation routes
Pros	High success rate, efficient resource allocation, adaptable to various scenarios	High accuracy in indoor positioning, considers local safety in route planning	Rapid decision-making, effective in complex environments, scalable
Cons	Complexity in implementation, requires extensive data	Relies on accurate BIM models, complex setup for indoor positioning	May require extensive IoT infrastructure, dependent on power and system connectivity