Positioning of ambulances of the SAMU system by Integer Programming and Queueing Theory

Barreto, Bruno; Alexandrino, Fernando; Coelho, Ormeu

doi:10.1590/0104-530X2100-16

Bruno Barreto

Departamento de Engenharia de Produção, Centro Federal de Educação Tecnológica Celso Suckow da Fonseca – CEFET/RJ, CEP 20271-110, Rio de Janeiro, RJ, Brazil, e-mail: brunobarreto7@gmail.com; fernando.hnd@gmail.com; ormeucoelho@gmail.com

Fernando Alexandrino

Departamento de Engenharia de Produção, Centro Federal de Educação Tecnológica Celso Suckow da Fonseca – CEFET/RJ, CEP 20271-110, Rio de Janeiro, RJ, Brazil, e-mail: brunobarreto7@gmail.com; fernando.hnd@gmail.com; ormeucoelho@gmail.com

Ormeu Coelho

Departamento de Engenharia de Produção, Centro Federal de Educação Tecnológica Celso Suckow da Fonseca – CEFET/RJ, CEP 20271-110, Rio de Janeiro, RJ, Brazil, e-mail: brunobarreto7@gmail.com; fernando.hnd@gmail.com; ormeucoelho@gmail.com

Facility	Address	ALS	BLS
Hospital Municipal Dr. Moacir R. do Carmo	3200 Washington Luiz Hwy., Beira Mar	2	2
Posto Médico Sanitário de Campos Elíseos	333 Actura St., Campos Elíseos	0	1
Posto Médico Sanitário Parque Equitativa	Automóvel Clube Ave., Parque Equitativa	0	1
Posto Médico Sanitário do Pilar	Carlos Alves St., Pilar	0	1
Posto Médico Sanitário Saracuruna	Presidente Roosevelt Ave., Saracuruna	0	1
Posto Médico Sanitário de Xerém	Nóbrega Ribeiro St., Xerém	0	1

Address	Node	Address	Node
Pam 404 Doutor Fernando Gil	01	Duque de Caxias, CEP 25250-400	25
Posto de Saúde Alaide Cunha	02	Duque de Caxias, CEP 25271-350	26
Duque de Caxias, CEP 25235-460	03	Duque de Caxias, CEP 25036-600	27
Duque de Caxias, CEP 25015-415	04	Duque de Caxias, CEP 25272-410	28
Duque de Caxias, CEP 25267-390	05	Duque de Caxias, CEP 25265-232	29
Posto Médico Sanitário de Campos Elíseos	06	Hospital Municipal Dr. Moacir R. do Carmo	30
Duque de Caxias, CEP 25220-570	07	Duque de Caxias, CEP 25240-650	31
Duque de Caxias, CEP 25245-230	08	Duque de Caxias, CEP 25046-380	32
Centro Municipal de Saúde de Duque de Caxias	09	Posto de Saúde Sarapuí	33
Hospital Infantil Ismélia Silveira	10	UPA Sarapuí	34
UPA Infantil Walter Garcia	11	Duque de Caxias, CEP 25025-300	35
UPA Duque de Caxias	12	Posto Médico Sanitário do Pilar	36
Duque de Caxias, CEP 25251-100	13	Posto Médico Sanitário Santa Cruz da Serra	37
Duque de Caxias, CEP 25243-150	14	Duque de Caxias, CEP 25271-430	38
Duque de Caxias, CEP 25237-030	15	Duque de Caxias, CEP 25040-060	39
Posto Médico Sanitário Parque Equitativa	16	Duque de Caxias, CEP 25045-040	40
Duque de Caxias, CEP 25060-190	17	Posto Médico Sanitário Saracuruna	41
Duque de Caxias, CEP 25231-180	18	Duque de Caxias, CEP 25270-450	42
Posto Médico Sanitário Dr. Jorge R. Pereira	19	Duque de Caxias, CEP 25030-180	43
Posto de Saúde Doutor José de Freitas	20	Duque de Caxias, CEP 25040-610	44
Posto de Saúde Edna Salles	21	Duque de Caxias, CEP 25065-162	45
Posto de Saúde José Camilo dos Santos	22	Hospital Municipal Maternidade de Xerém	46
Hospital Estadual Adão Pereira Nunes	23	Unidade Pré-Hospitalar Álvaro Figueira	47
Duque de Caxias, CEP 25250-130	24	Posto Médico Sanitário de Xerém	48

Node	District	LAT	LONG	$a_{i}$	Node	District	LAT	LONG	$a_{i}$
01	25 de Agosto	-22.793	-43.299	7,071	25	Mantiquira	-22.596	-43.302	10,616
02	25 de Agosto	-22.786	-43.297	7,071	26	Meio da Serra	-22.626	-43.206	2,344
03	Amapá	-22.676	-43.357	6,477	27	Olavo Bilac	-22.766	-43.328	34,770
04	Bar dos Cavaleiros	-22.795	-43.326	41,209	28	Parada Angélica	-22.629	-43.210	14,458
05	Barro Branco	-22.638	-43.244	15,700	29	Parada Morabi	-22.657	-43.230	4,444
06	Campos Elíseos	-22.660	-43.250	19,622	30	Parque Duque	-22.799	-43.289	44,983
07	Cangulo	-22.688	-43.236	13,053	31	Parque Eldorado	-22.635	-43.307	8,161
08	Capivari	-22.647	-43.328	1,489	32	Parque Fluminense	-22.725	-43.319	34,969
09	Centro	-22.787	-43.308	6,756	33	Parque Sarapuí	-22.751	-43.296	1,009
10	Centro	-22.788	-43.311	6,756	34	Parque Sarapuí	-22.751	-43.299	1,009
11	Centro	-22.793	-43.307	6,756	35	Periquitos	-22.779	-43.324	17,898
12	Centro	-22.786	-43.325	6,756	36	Pilar	-22.711	-43.306	33,525
13	Chácaras Arcampo	-22.657	-43.274	14,120	37	Santa Cruz da Serra	-22.645	-43.274	25,698
14	Chácaras Rio-Petrópolis	-22.665	-43.315	14,085	38	Santa Lúcia	-22.625	-43.210	16,732
15	Cidade dos Meninos	-22.630	-43.222	2,460	39	Santo Antônio	-22.745	-43.317	11,420
16	Cidade Parque Paulista	-22.635	-43.263	33,501	40	São Bento	-22.728	-43.305	22,062
17	Doutor Laureano	-22.764	-43.299	43,996	41	Saracuruna	-22.676	-43.254	46,660
18	Figueira	-22.680	-43.298	16,520	42	Taquara	-22.627	-43.236	12,191
19	Imbariê	-22.636	-43.217	34,332	43	Vila Centenário	-22.774	-43.313	21,922
20	Jardim Anhangá	-22.637	-43.231	12,867	44	Vila São José	-22.742	-43.317	31,009
21	Jardim Gramacho	-22.761	-43.278	53,731	45	Vila São Luís	-22.773	-43.298	30,420
22	Jardim Primavera	-22.695	-43.261	20,915	46	Xerém	-22.599	-43.302	7,466
23	Jardim Primavera	-22.670	-43.279	20,915	47	Xerém	-22.600	-43.292	7,466
24	Lamarão	-22.598	-43.293	192	48	Xerém	-22.601	-43.292	7,466

Node	01	02	06	09	10	11	12	16	19	20	21	22	23	30	33	34	36	37	41	46	47	48
01	2	4	24	3	8	5	13	23	24	23	12	20	16	7	11	12	16	22	23	23	22	22
02	4	4	22	5	8	7	10	21	22	21	10	18	14	9	9	10	14	20	21	22	20	20
03	27	26	28	25	23	24	27	23	28	27	27	29	20	28	19	19	15	22	29	16	16	16
04	10	11	27	8	6	8	4	26	27	26	16	23	19	13	15	16	19	25	26	26	25	25
05	27	26	9	29	29	30	33	6	10	5	22	22	13	23	24	25	23	8	14	17	15	15
06	18	18	29	20	20	21	25	13	18	18	14	11	10	15	15	16	15	12	5	13	12	11
07	27	26	30	29	29	30	34	24	30	29	22	10	23	23	24	25	23	23	10	25	23	23
08	26	26	20	28	29	29	33	15	20	19	21	21	13	23	23	25	19	14	21	13	13	12
09	4	5	26	3	8	7	10	25	26	25	14	22	19	9	13	13	19	25	25	26	25	24
10	7	8	28	5	1	4	6	27	28	27	16	24	21	12	13	13	19	26	27	28	26	26
11	9	11	25	7	4	2	9	24	25	24	14	21	18	10	13	14	17	23	24	25	23	23
12	9	9	29	8	5	8	7	28	29	28	17	25	21	14	15	15	22	27	28	28	27	27
13	18	18	12	20	20	21	25	7	12	11	14	14	4	15	15	17	15	3	13	12	10	10
14	25	25	19	27	27	28	32	14	19	18	21	20	11	22	22	23	18	13	20	15	13	13
15	26	26	8	28	28	29	33	9	2	6	22	20	16	23	23	24	23	11	13	20	18	18
16	25	24	11	27	27	28	32	5	10	6	20	20	12	21	22	23	21	6	16	15	14	13
17	12	8	21	9	11	11	13	20	21	20	9	17	14	10	6	6	14	19	20	21	19	19
18	21	21	15	23	25	26	29	14	15	14	17	16	7	18	18	19	13	13	16	15	13	13
19	25	24	6	27	26	27	31	11	4	5	20	18	18	21	22	23	21	13	11	19	18	18
20	25	24	6	27	26	27	31	7	5	4	20	18	14	21	22	23	21	9	11	18	16	16
21	12	11	21	14	14	14	19	20	22	21	3	17	14	8	8	9	14	20	21	21	20	20
22	21	20	24	23	22	23	27	20	24	23	16	9	16	17	18	19	16	19	8	21	19	19
23	17	16	9	19	19	20	24	11	9	8	13	13	16	14	14	15	13	7	11	13	11	11
24	25	25	19	27	27	28	32	13	19	19	21	20	12	22	22	23	22	13	20	3	2	2
25	26	26	21	29	28	29	33	14	21	20	22	22	13	23	24	25	23	14	21	2	3	3
26	27	26	8	29	28	29	33	12	4	8	22	20	19	23	24	25	23	14	13	21	20	20
27	15	14	33	14	11	14	8	32	33	32	22	29	25	20	14	14	21	31	32	32	31	31
28	26	25	8	28	28	29	33	12	3	7	21	19	19	22	23	24	22	14	13	20	19	19
29	23	22	5	25	25	26	30	13	6	7	18	16	15	20	20	21	19	15	10	18	16	16
30	5	8	22	7	8	8	13	21	22	21	11	18	15	6	10	11	14	20	21	22	20	20
31	27	27	22	29	29	30	34	13	22	18	23	23	14	24	25	26	25	12	22	8	7	7
32	15	15	22	14	12	13	16	21	23	22	16	23	15	17	8	8	8	20	23	21	20	20
33	13	13	18	11	10	10	14	17	18	17	8	14	11	9	2	2	11	17	18	18	17	16
34	13	13	20	11	9	10	14	19	21	20	9	16	13	10	2	1	13	19	20	20	19	19
35	11	10	30	10	7	10	4	29	30	29	18	26	23	16	16	16	24	29	30	30	29	28
36	20	20	18	19	17	17	21	16	18	17	20	20	11	21	13	13	5	16	19	17	16	16
37	21	20	13	23	22	24	27	5	13	11	16	16	7	17	18	19	17	2	15	12	11	10
38	27	27	9	29	29	30	34	11	4	9	22	20	19	24	24	25	23	14	14	22	21	21
39	14	13	25	13	10	11	15	24	25	24	14	21	18	15	7	7	14	24	24	25	24	23
40	16	15	25	14	13	13	16	23	25	24	16	23	17	17	8	8	10	22	25	23	22	22
41	21	20	21	23	23	24	28	15	21	20	16	8	13	17	18	19	17	14	6	15	14	14
42	28	28	13	30	30	31	35	7	8	7	24	23	15	25	25	26	25	10	17	18	17	17
43	9	6	27	6	5	6	7	26	27	26	15	23	20	13	11	11	18	25	26	27	25	25
44	15	15	28	13	12	13	16	26	28	27	15	22	20	16	8	8	13	25	26	27	25	25
45	9	5	21	6	8	9	11	20	21	20	9	17	13	9	8	9	13	19	20	21	19	19
46	26	26	20	28	28	29	33	14	20	20	21	21	13	23	23	24	22	13	21	1	3	3
47	25	24	19	27	27	28	32	13	19	18	20	20	11	21	22	23	21	13	19	3	4	1
48	24	24	18	26	26	27	31	12	18	18	20	19	11	21	21	22	20	11	19	3	1	4

Day	Interval (hours)	Day	Interval (hours)
1	0.56	12	5.92
2	1.84	13	1.08
3	2.10	14	1.65
4	3.21	15	0.18
5	6.40	16	2.63
6	0.36	17	5.03
7	0.59	18	5.84
8	1.75	19	0.14
9	0.15	20	2.59
10	2.96	21	1.31
11	3.86	Average	2.39

Node	Calls	$p_{i}$	$λ_{i}$	Node	Calls	$p_{i}$	$λ_{i}$
01	278	1.56%	0.007	25	274	1.53%	0.006
02	278	1.56%	0.007	26	274	1.53%	0.006
03	236	1.32%	0.006	27	706	3.95%	0.017
04	396	2.22%	0.009	28	336	1.88%	0.008
05	166	0.93%	0.004	29	256	1.43%	0.006
06	406	2.27%	0.010	30	376	2.11%	0.009
07	166	0.93%	0.004	31	136	0.76%	0.003
08	256	1.43%	0.006	32	506	2.83%	0.012
09	334	1.87%	0.008	33	248	1.39%	0.006
10	334	1.87%	0.008	34	248	1.39%	0.006
11	334	1.87%	0.008	35	146	0.82%	0.003
12	334	1.87%	0.008	36	496	2.78%	0.012
13	286	1.60%	0.007	37	746	4.18%	0.017
14	166	0.93%	0.004	38	386	2.16%	0.009
15	406	2.27%	0.010	39	186	1.04%	0.004
16	316	1.77%	0.007	40	356	1.99%	0.008
17	526	2.94%	0.012	41	666	3.73%	0.016
18	396	2.22%	0.009	42	316	1.77%	0.007
19	1186	6.64%	0.028	43	261	1.46%	0.006
20	686	3.84%	0.016	44	261	1.46%	0.006
21	536	3.00%	0.013	45	1126	6.30%	0.026
22	493	2.76%	0.012	46	91	0.51%	0.002
23	493	2.76%	0.012	47	91	0.51%	0.002
24	274	1.53%	0.006	48	91	0.51%	0.002

Server	Average service time	Standard deviation
1	59	41
2	95	67
3	81	65
4	156	94
5	18	14
6	86	77
7	43	30
8	114	68
9	29	23
ALS Average	77	54
BLS Average	75	53
Average	76	53

Case	Covered demand (%)	Average travel time (min)
Current	42.4	13.0
FLEET	66.3	11.4
PLMD ( $θ$ = 93%)	43.8	14.8
PLMD ( $θ$ = 88%)	62.6	10.9
PLMD ( $θ$ = 80%)	72.0	11.0

\begin{array}{l} P (i f a t l e a s t o n e s e r v e r i s w i t h i n c r i t i c a l d i s \tan c e S) \geq θ \\ = [1 - P (n o n e s e r v e r i s w i t h i n c r i t i c a l d i s \tan c e S)] \geq θ \\ = 1 - ρ^{\sum_{j \int J} c_{j i} y_{j}} \geq θ \end{array}

\bar{T_{i}} = (\frac{\sum_{n = 1}^{N} f_{n i}^{[1]} τ_{n i}}{\sum_{n = 1}^{N} f_{n i}^{[1]}}) (1 - p_{s}) + \sum_{j = 1}^{J} (\frac{λ_{i}}{λ}) t_{j i} p_{s}

[1] Source: Elaborated by the authors.

Brasil

Brasil

Positioning of ambulances of the SAMU system by Integer Programming and Queueing Theory

Node	01	02	06	09	10	11	12	16	19	20	21	22	23	30	33	34	36	37	41	46	47	48
01	2	4	24	3	8	5	13	23	24	23	12	20	16	7	11	12	16	22	23	23	22	22
02	4	4	22	5	8	7	10	21	22	21	10	18	14	9	9	10	14	20	21	22	20	20
03	27	26	28	25	23	24	27	23	28	27	27	29	20	28	19	19	15	22	29	16	16	16
04	10	11	27	8	6	8	4	26	27	26	16	23	19	13	15	16	19	25	26	26	25	25
05	27	26	9	29	29	30	33	6	10	5	22	22	13	23	24	25	23	8	14	17	15	15
06	18	18	29	20	20	21	25	13	18	18	14	11	10	15	15	16	15	12	5	13	12	11
07	27	26	30	29	29	30	34	24	30	29	22	10	23	23	24	25	23	23	10	25	23	23
08	26	26	20	28	29	29	33	15	20	19	21	21	13	23	23	25	19	14	21	13	13	12
09	4	5	26	3	8	7	10	25	26	25	14	22	19	9	13	13	19	25	25	26	25	24
10	7	8	28	5	1	4	6	27	28	27	16	24	21	12	13	13	19	26	27	28	26	26
11	9	11	25	7	4	2	9	24	25	24	14	21	18	10	13	14	17	23	24	25	23	23
12	9	9	29	8	5	8	7	28	29	28	17	25	21	14	15	15	22	27	28	28	27	27
13	18	18	12	20	20	21	25	7	12	11	14	14	4	15	15	17	15	3	13	12	10	10
14	25	25	19	27	27	28	32	14	19	18	21	20	11	22	22	23	18	13	20	15	13	13
15	26	26	8	28	28	29	33	9	2	6	22	20	16	23	23	24	23	11	13	20	18	18
16	25	24	11	27	27	28	32	5	10	6	20	20	12	21	22	23	21	6	16	15	14	13
17	12	8	21	9	11	11	13	20	21	20	9	17	14	10	6	6	14	19	20	21	19	19
18	21	21	15	23	25	26	29	14	15	14	17	16	7	18	18	19	13	13	16	15	13	13
19	25	24	6	27	26	27	31	11	4	5	20	18	18	21	22	23	21	13	11	19	18	18
20	25	24	6	27	26	27	31	7	5	4	20	18	14	21	22	23	21	9	11	18	16	16
21	12	11	21	14	14	14	19	20	22	21	3	17	14	8	8	9	14	20	21	21	20	20
22	21	20	24	23	22	23	27	20	24	23	16	9	16	17	18	19	16	19	8	21	19	19
23	17	16	9	19	19	20	24	11	9	8	13	13	16	14	14	15	13	7	11	13	11	11
24	25	25	19	27	27	28	32	13	19	19	21	20	12	22	22	23	22	13	20	3	2	2
25	26	26	21	29	28	29	33	14	21	20	22	22	13	23	24	25	23	14	21	2	3	3
26	27	26	8	29	28	29	33	12	4	8	22	20	19	23	24	25	23	14	13	21	20	20
27	15	14	33	14	11	14	8	32	33	32	22	29	25	20	14	14	21	31	32	32	31	31
28	26	25	8	28	28	29	33	12	3	7	21	19	19	22	23	24	22	14	13	20	19	19
29	23	22	5	25	25	26	30	13	6	7	18	16	15	20	20	21	19	15	10	18	16	16
30	5	8	22	7	8	8	13	21	22	21	11	18	15	6	10	11	14	20	21	22	20	20
31	27	27	22	29	29	30	34	13	22	18	23	23	14	24	25	26	25	12	22	8	7	7
32	15	15	22	14	12	13	16	21	23	22	16	23	15	17	8	8	8	20	23	21	20	20
33	13	13	18	11	10	10	14	17	18	17	8	14	11	9	2	2	11	17	18	18	17	16
34	13	13	20	11	9	10	14	19	21	20	9	16	13	10	2	1	13	19	20	20	19	19
35	11	10	30	10	7	10	4	29	30	29	18	26	23	16	16	16	24	29	30	30	29	28
36	20	20	18	19	17	17	21	16	18	17	20	20	11	21	13	13	5	16	19	17	16	16
37	21	20	13	23	22	24	27	5	13	11	16	16	7	17	18	19	17	2	15	12	11	10
38	27	27	9	29	29	30	34	11	4	9	22	20	19	24	24	25	23	14	14	22	21	21
39	14	13	25	13	10	11	15	24	25	24	14	21	18	15	7	7	14	24	24	25	24	23
40	16	15	25	14	13	13	16	23	25	24	16	23	17	17	8	8	10	22	25	23	22	22
41	21	20	21	23	23	24	28	15	21	20	16	8	13	17	18	19	17	14	6	15	14	14
42	28	28	13	30	30	31	35	7	8	7	24	23	15	25	25	26	25	10	17	18	17	17
43	9	6	27	6	5	6	7	26	27	26	15	23	20	13	11	11	18	25	26	27	25	25
44	15	15	28	13	12	13	16	26	28	27	15	22	20	16	8	8	13	25	26	27	25	25
45	9	5	21	6	8	9	11	20	21	20	9	17	13	9	8	9	13	19	20	21	19	19
46	26	26	20	28	28	29	33	14	20	20	21	21	13	23	23	24	22	13	21	1	3	3
47	25	24	19	27	27	28	32	13	19	18	20	20	11	21	22	23	21	13	19	3	4	1
48	24	24	18	26	26	27	31	12	18	18	20	19	11	21	21	22	20	11	19	3	1	4

Node	01	02	06	09	10	11	12	16	19	20	21	22	23	30	33	34	36	37	41	46	47	48
01	2	4	24	3	8	5	13	23	24	23	12	20	16	7	11	12	16	22	23	23	22	22
02	4	4	22	5	8	7	10	21	22	21	10	18	14	9	9	10	14	20	21	22	20	20
03	27	26	28	25	23	24	27	23	28	27	27	29	20	28	19	19	15	22	29	16	16	16
04	10	11	27	8	6	8	4	26	27	26	16	23	19	13	15	16	19	25	26	26	25	25
05	27	26	9	29	29	30	33	6	10	5	22	22	13	23	24	25	23	8	14	17	15	15
06	18	18	29	20	20	21	25	13	18	18	14	11	10	15	15	16	15	12	5	13	12	11
07	27	26	30	29	29	30	34	24	30	29	22	10	23	23	24	25	23	23	10	25	23	23
08	26	26	20	28	29	29	33	15	20	19	21	21	13	23	23	25	19	14	21	13	13	12
09	4	5	26	3	8	7	10	25	26	25	14	22	19	9	13	13	19	25	25	26	25	24
10	7	8	28	5	1	4	6	27	28	27	16	24	21	12	13	13	19	26	27	28	26	26
11	9	11	25	7	4	2	9	24	25	24	14	21	18	10	13	14	17	23	24	25	23	23
12	9	9	29	8	5	8	7	28	29	28	17	25	21	14	15	15	22	27	28	28	27	27
13	18	18	12	20	20	21	25	7	12	11	14	14	4	15	15	17	15	3	13	12	10	10
14	25	25	19	27	27	28	32	14	19	18	21	20	11	22	22	23	18	13	20	15	13	13
15	26	26	8	28	28	29	33	9	2	6	22	20	16	23	23	24	23	11	13	20	18	18
16	25	24	11	27	27	28	32	5	10	6	20	20	12	21	22	23	21	6	16	15	14	13
17	12	8	21	9	11	11	13	20	21	20	9	17	14	10	6	6	14	19	20	21	19	19
18	21	21	15	23	25	26	29	14	15	14	17	16	7	18	18	19	13	13	16	15	13	13
19	25	24	6	27	26	27	31	11	4	5	20	18	18	21	22	23	21	13	11	19	18	18
20	25	24	6	27	26	27	31	7	5	4	20	18	14	21	22	23	21	9	11	18	16	16
21	12	11	21	14	14	14	19	20	22	21	3	17	14	8	8	9	14	20	21	21	20	20
22	21	20	24	23	22	23	27	20	24	23	16	9	16	17	18	19	16	19	8	21	19	19
23	17	16	9	19	19	20	24	11	9	8	13	13	16	14	14	15	13	7	11	13	11	11
24	25	25	19	27	27	28	32	13	19	19	21	20	12	22	22	23	22	13	20	3	2	2
25	26	26	21	29	28	29	33	14	21	20	22	22	13	23	24	25	23	14	21	2	3	3
26	27	26	8	29	28	29	33	12	4	8	22	20	19	23	24	25	23	14	13	21	20	20
27	15	14	33	14	11	14	8	32	33	32	22	29	25	20	14	14	21	31	32	32	31	31
28	26	25	8	28	28	29	33	12	3	7	21	19	19	22	23	24	22	14	13	20	19	19
29	23	22	5	25	25	26	30	13	6	7	18	16	15	20	20	21	19	15	10	18	16	16
30	5	8	22	7	8	8	13	21	22	21	11	18	15	6	10	11	14	20	21	22	20	20
31	27	27	22	29	29	30	34	13	22	18	23	23	14	24	25	26	25	12	22	8	7	7
32	15	15	22	14	12	13	16	21	23	22	16	23	15	17	8	8	8	20	23	21	20	20
33	13	13	18	11	10	10	14	17	18	17	8	14	11	9	2	2	11	17	18	18	17	16
34	13	13	20	11	9	10	14	19	21	20	9	16	13	10	2	1	13	19	20	20	19	19
35	11	10	30	10	7	10	4	29	30	29	18	26	23	16	16	16	24	29	30	30	29	28
36	20	20	18	19	17	17	21	16	18	17	20	20	11	21	13	13	5	16	19	17	16	16
37	21	20	13	23	22	24	27	5	13	11	16	16	7	17	18	19	17	2	15	12	11	10
38	27	27	9	29	29	30	34	11	4	9	22	20	19	24	24	25	23	14	14	22	21	21
39	14	13	25	13	10	11	15	24	25	24	14	21	18	15	7	7	14	24	24	25	24	23
40	16	15	25	14	13	13	16	23	25	24	16	23	17	17	8	8	10	22	25	23	22	22
41	21	20	21	23	23	24	28	15	21	20	16	8	13	17	18	19	17	14	6	15	14	14
42	28	28	13	30	30	31	35	7	8	7	24	23	15	25	25	26	25	10	17	18	17	17
43	9	6	27	6	5	6	7	26	27	26	15	23	20	13	11	11	18	25	26	27	25	25
44	15	15	28	13	12	13	16	26	28	27	15	22	20	16	8	8	13	25	26	27	25	25
45	9	5	21	6	8	9	11	20	21	20	9	17	13	9	8	9	13	19	20	21	19	19
46	26	26	20	28	28	29	33	14	20	20	21	21	13	23	23	24	22	13	21	1	3	3
47	25	24	19	27	27	28	32	13	19	18	20	20	11	21	22	23	21	13	19	3	4	1
48	24	24	18	26	26	27	31	12	18	18	20	19	11	21	21	22	20	11	19	3	1	4

Node	01	02	06	09	10	11	12	16	19	20	21	22	23	30	33	34	36	37	41	46	47	48
01	2	4	24	3	8	5	13	23	24	23	12	20	16	7	11	12	16	22	23	23	22	22
02	4	4	22	5	8	7	10	21	22	21	10	18	14	9	9	10	14	20	21	22	20	20
03	27	26	28	25	23	24	27	23	28	27	27	29	20	28	19	19	15	22	29	16	16	16
04	10	11	27	8	6	8	4	26	27	26	16	23	19	13	15	16	19	25	26	26	25	25
05	27	26	9	29	29	30	33	6	10	5	22	22	13	23	24	25	23	8	14	17	15	15
06	18	18	29	20	20	21	25	13	18	18	14	11	10	15	15	16	15	12	5	13	12	11
07	27	26	30	29	29	30	34	24	30	29	22	10	23	23	24	25	23	23	10	25	23	23
08	26	26	20	28	29	29	33	15	20	19	21	21	13	23	23	25	19	14	21	13	13	12
09	4	5	26	3	8	7	10	25	26	25	14	22	19	9	13	13	19	25	25	26	25	24
10	7	8	28	5	1	4	6	27	28	27	16	24	21	12	13	13	19	26	27	28	26	26
11	9	11	25	7	4	2	9	24	25	24	14	21	18	10	13	14	17	23	24	25	23	23
12	9	9	29	8	5	8	7	28	29	28	17	25	21	14	15	15	22	27	28	28	27	27
13	18	18	12	20	20	21	25	7	12	11	14	14	4	15	15	17	15	3	13	12	10	10
14	25	25	19	27	27	28	32	14	19	18	21	20	11	22	22	23	18	13	20	15	13	13
15	26	26	8	28	28	29	33	9	2	6	22	20	16	23	23	24	23	11	13	20	18	18
16	25	24	11	27	27	28	32	5	10	6	20	20	12	21	22	23	21	6	16	15	14	13
17	12	8	21	9	11	11	13	20	21	20	9	17	14	10	6	6	14	19	20	21	19	19
18	21	21	15	23	25	26	29	14	15	14	17	16	7	18	18	19	13	13	16	15	13	13
19	25	24	6	27	26	27	31	11	4	5	20	18	18	21	22	23	21	13	11	19	18	18
20	25	24	6	27	26	27	31	7	5	4	20	18	14	21	22	23	21	9	11	18	16	16
21	12	11	21	14	14	14	19	20	22	21	3	17	14	8	8	9	14	20	21	21	20	20
22	21	20	24	23	22	23	27	20	24	23	16	9	16	17	18	19	16	19	8	21	19	19
23	17	16	9	19	19	20	24	11	9	8	13	13	16	14	14	15	13	7	11	13	11	11
24	25	25	19	27	27	28	32	13	19	19	21	20	12	22	22	23	22	13	20	3	2	2
25	26	26	21	29	28	29	33	14	21	20	22	22	13	23	24	25	23	14	21	2	3	3
26	27	26	8	29	28	29	33	12	4	8	22	20	19	23	24	25	23	14	13	21	20	20
27	15	14	33	14	11	14	8	32	33	32	22	29	25	20	14	14	21	31	32	32	31	31
28	26	25	8	28	28	29	33	12	3	7	21	19	19	22	23	24	22	14	13	20	19	19
29	23	22	5	25	25	26	30	13	6	7	18	16	15	20	20	21	19	15	10	18	16	16
30	5	8	22	7	8	8	13	21	22	21	11	18	15	6	10	11	14	20	21	22	20	20
31	27	27	22	29	29	30	34	13	22	18	23	23	14	24	25	26	25	12	22	8	7	7
32	15	15	22	14	12	13	16	21	23	22	16	23	15	17	8	8	8	20	23	21	20	20
33	13	13	18	11	10	10	14	17	18	17	8	14	11	9	2	2	11	17	18	18	17	16
34	13	13	20	11	9	10	14	19	21	20	9	16	13	10	2	1	13	19	20	20	19	19
35	11	10	30	10	7	10	4	29	30	29	18	26	23	16	16	16	24	29	30	30	29	28
36	20	20	18	19	17	17	21	16	18	17	20	20	11	21	13	13	5	16	19	17	16	16
37	21	20	13	23	22	24	27	5	13	11	16	16	7	17	18	19	17	2	15	12	11	10
38	27	27	9	29	29	30	34	11	4	9	22	20	19	24	24	25	23	14	14	22	21	21
39	14	13	25	13	10	11	15	24	25	24	14	21	18	15	7	7	14	24	24	25	24	23
40	16	15	25	14	13	13	16	23	25	24	16	23	17	17	8	8	10	22	25	23	22	22
41	21	20	21	23	23	24	28	15	21	20	16	8	13	17	18	19	17	14	6	15	14	14
42	28	28	13	30	30	31	35	7	8	7	24	23	15	25	25	26	25	10	17	18	17	17
43	9	6	27	6	5	6	7	26	27	26	15	23	20	13	11	11	18	25	26	27	25	25
44	15	15	28	13	12	13	16	26	28	27	15	22	20	16	8	8	13	25	26	27	25	25
45	9	5	21	6	8	9	11	20	21	20	9	17	13	9	8	9	13	19	20	21	19	19
46	26	26	20	28	28	29	33	14	20	20	21	21	13	23	23	24	22	13	21	1	3	3
47	25	24	19	27	27	28	32	13	19	18	20	20	11	21	22	23	21	13	19	3	4	1
48	24	24	18	26	26	27	31	12	18	18	20	19	11	21	21	22	20	11	19	3	1	4