STUDYING THE EFFECTS OF THE SKEWNESS OF INTER-ARRIVAL AND SERVICE TIMES ON THE PROBABILITY DISTRIBUTION OF WAITING TIMES

Romero-Silva, Rodrigo; Shaaban, Sabry; Marsillac, Erika; Hurtado-Hernandez, Margarita

doi:10.1590/0101-7438.2020.040.00223190

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ARTICLES • Pesqui. Oper. 40 • 2020 • https://doi.org/10.1590/0101-7438.2020.040.00223190 copy

STUDYING THE EFFECTS OF THE SKEWNESS OF INTER-ARRIVAL AND SERVICE TIMES ON THE PROBABILITY DISTRIBUTION OF WAITING TIMES

Authorship SCIMAGO INSTITUTIONS RANKINGS

ABSTRACT

Previous studies have shown that the mean queue length of a GI/G/1 system is significantly influenced by the skewness of inter-arrival times, but not by the skewness of service times. These results are limited because all the distributions considered in previous studies were positively skewed. To address this limitation, this paper investigates the effects of the skewness of inter-arrival and service times on the probability distribution of waiting times, when a negatively skewed distribution is used to model inter-arrival and service times. Subsequent to a series of experiments on a GI/G/1 queue using discrete-event simulation, results have shown that the lowest mean waiting time and the lowest variance of waiting times can be attained with a combination of positive inter-arrival skewness and negative service skewness. Results also show an interesting effect of the skewness of service times in the probability of no-delay in environments with a higher utilization factor.

Keywords:
queueing theory; skewness; GI/G/1 queue

Exp. factor	Abbrev.	Performance measures	Abbrev.	Exp. responses	Abbrev.
Inter-arrival time skewness	γ _A	Waiting time of customer j in replication i, experiment k	w _kij	Mean waiting time	W
Service time skewness	γ _S	Mean waiting time of all customers in replication i, experiment k	ẃ _ki	Waiting time variance	$σ_{W}^{2}$
Server’s utilization factor	ρ	Mean waiting time of all replications, experiment k	W _k	Waiting time skewness	γ _W
Inter-arrival time coefficient of variation	CV_A	Waiting time variance of all replications, experiment k	$σ_{W k}^{2}$	Intra-group mean waiting time	IGV_W
Service time coefficient of variation	CV_S	Waiting time skewness of all replications, experiment k	γ _Wk	Intra-group waiting time variance	IGV_σ 2
System’s coefficient of variation	CV	Probability of no-delay in replication i, experiment k	p0_ki	Intra-group waiting time skewness	IGV_γ
Experiment number	k	Average no-delay probability in all replications, experiment k	PW0_k	Intra-group probability of no-delay	IGV_PW0
Replication number	i	Intra-group variation for the mean waiting time, experiment k	IGV_Wk
Customer number	j
Number of replications	R
Number of customers per replication	N

	Factor levels
Factor	-1	0	+1
Skewness of inter-arrival times (γ _A)	-0.42 or -0.57	0	0.42
System’s CV	0.2318		0.3642
Server’s utilization (ρ)	0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.85, 0.90, 0.95, 0.97, 0.98, 0.99
Skewness of service times (γ _S)	-0.42 or -0.57	0	0.42 or 0.57

	Df	Sum Sq	Mean Sq	% Contribution	F value	Pr(>F)
CV	1	0.0	0.0	0.0%	0.0	0.9992
ρ	1	0.0	0.0	0.0%	0.0	0.9995
γ _A	1	454.3	454.3	37.4%	50603.9	0.0000
γ _S	1	32.4	32.4	2.7%	3610.7	0.0000
CV:ρ	1	0.0	0.0	0.0%	0.0	0.9999
CV:γ_A	1	73.6	73.6	6.1%	8202.4	0.0000
ρ:γ_A	1	527.5	527.5	43.5%	58759.0	0.0000
CV:γ_S	1	9.1	9.1	0.8%	1018.2	0.0000
ρ:γ_S	1	17.1	17.1	1.4%	1905.9	0.0000
γA:γ_S	1	0.2	0.2	0.0%	18.7	0.0000
CV:ρ:γ_A	1	91.7	91.7	7.6%	10216.6	0.0000
CV:ρ:γ_S	1	7.4	7.4	0.6%	826.0	0.0000
CV:γA:γ_S	1	0.1	0.1	0.0%	8.0	0.0046
ρ:γA:γ_S	1	0.4	0.4	0.0%	40.9	0.0000
CV:ρ:γA:γ_S	1	0.0	0.0	0.0%	0.0	0.8363
Residuals	25184	226.1	0.0	0.0%

	Df	Sum Sq	Mean Sq	% Contribution	F value	Pr(>F)
CV	1	0.0	0.0	0.0%	0.0	0.8293
ρ	1	0.0	0.0	0.0%	0.0	0.9643
γA	1	0.2	0.2	1.4%	9.2	0.0024
γS	1	5.4	5.4	37.1%	238.1	0.0000
CV:ρ	1	0.0	0.0	0.0%	0.0	0.9641
CV:γ_A	1	0.9	0.8	5.8%	37.4	0.0000
ρ:γ_A	1	1.8	1.8	12.3%	78.9	0.0000
CV:γ_S	1	0.1	0.1	0.4%	2.5	0.1165
ρ:γ_S	1	3.9	3.9	26.6%	170.5	0.0000
γA:γ_S	1	0.5	0.5	3.4%	21.6	0.0000
CV:ρ:γ_A	1	1.4	1.4	9.9%	63.7	0.0000
CV:ρ:γ_S	1	0.0	0.0	0.0%	0.1	0.7668
CV:γA:γ_S	1	0.1	0.1	0.8%	5.3	0.0213
ρ:γA:γ_S	1	0.2	0.2	1.5%	9.8	0.0017
CV:ρ:γA:γ_S	1	0.1	0.1	0.4%	2.8	0.0954
Residuals	35984	815.6	0.0	0.2%

Exp.	IG ID	a_A	m_A	b_A	γ _A	µ _A	σ _A	CV_A	ρ	µ _S	σ _S	CV_S	a_S	m_S	b_S	γ _S
1	A	1.26	4.87	4.87	-0.57	3.67	0.85	0.23	0.10	0.37	0.08	0.23	0.13	0.49	0.49	-0.57
2	A	1.26	4.87	4.87	-0.57	3.67	0.85	0.23	0.10	0.37	0.08	0.23	0.16	0.37	0.57	0.00
3	A	1.26	4.87	4.87	-0.57	3.67	0.85	0.23	0.10	0.37	0.08	0.23	0.25	0.25	0.61	0.57
4	A	1.59	3.67	5.75	0.00	3.67	0.85	0.23	0.10	0.37	0.08	0.23	0.13	0.49	0.49	-0.57
5	A	1.59	3.67	5.75	0.00	3.67	0.85	0.23	0.10	0.37	0.08	0.23	0.16	0.37	0.57	0.00
6	A	1.59	3.67	5.75	0.00	3.67	0.85	0.23	0.10	0.37	0.08	0.23	0.25	0.25	0.61	0.57
7	A	2.00	3.00	6.00	0.42	3.67	0.85	0.23	0.10	0.37	0.08	0.23	0.13	0.49	0.49	-0.57
8	A	2.00	3.00	6.00	0.42	3.67	0.85	0.23	0.10	0.37	0.08	0.23	0.16	0.37	0.57	0.00
9	A	2.00	3.00	6.00	0.42	3.67	0.85	0.23	0.10	0.37	0.08	0.23	0.25	0.25	0.61	0.57
10	B	1.26	4.87	4.87	-0.57	3.67	0.85	0.23	0.20	0.73	0.17	0.23	0.25	0.97	0.97	-0.57
11	B	1.26	4.87	4.87	-0.57	3.67	0.85	0.23	0.20	0.73	0.17	0.23	0.32	0.73	1.15	0.00
12	B	1.26	4.87	4.87	-0.57	3.67	0.85	0.23	0.20	0.73	0.17	0.23	0.49	0.49	1.21	0.57
13	B	1.59	3.67	5.75	0.00	3.67	0.85	0.23	0.20	0.73	0.17	0.23	0.25	0.97	0.97	-0.57
14	B	1.59	3.67	5.75	0.00	3.67	0.85	0.23	0.20	0.73	0.17	0.23	0.32	0.73	1.15	0.00
15	B	1.59	3.67	5.75	0.00	3.67	0.85	0.23	0.20	0.73	0.17	0.23	0.49	0.49	1.21	0.57
16	B	2.00	3.00	6.00	0.42	3.67	0.85	0.23	0.20	0.73	0.17	0.23	0.25	0.97	0.97	-0.57
17	B	2.00	3.00	6.00	0.42	3.67	0.85	0.23	0.20	0.73	0.17	0.23	0.32	0.73	1.15	0.00
18	B	2.00	3.00	6.00	0.42	3.67	0.85	0.23	0.20	0.73	0.17	0.23	0.49	0.49	1.21	0.57
19	C	1.26	4.87	4.87	-0.57	3.67	0.85	0.23	0.30	1.10	0.25	0.23	0.38	1.46	1.46	-0.57
20	C	1.26	4.87	4.87	-0.57	3.67	0.85	0.23	0.30	1.10	0.25	0.23	0.48	1.10	1.72	0.00
21	C	1.26	4.87	4.87	-0.57	3.67	0.85	0.23	0.30	1.10	0.25	0.23	0.74	0.74	1.82	0.57
22	C	1.59	3.67	5.75	0.00	3.67	0.85	0.23	0.30	1.10	0.25	0.23	0.38	1.46	1.46	-0.57
23	C	1.59	3.67	5.75	0.00	3.67	0.85	0.23	0.30	1.10	0.25	0.23	0.48	1.10	1.72	0.00
24	C	1.59	3.67	5.75	0.00	3.67	0.85	0.23	0.30	1.10	0.25	0.23	0.74	0.74	1.82	0.57
25	C	2.00	3.00	6.00	0.42	3.67	0.85	0.23	0.30	1.10	0.25	0.23	0.38	1.46	1.46	-0.57
26	C	2.00	3.00	6.00	0.42	3.67	0.85	0.23	0.30	1.10	0.25	0.23	0.48	1.10	1.72	0.00
27	C	2.00	3.00	6.00	0.42	3.67	0.85	0.23	0.30	1.10	0.25	0.23	0.74	0.74	1.82	0.57
28	D	1.26	4.87	4.87	-0.57	3.67	0.85	0.23	0.40	1.47	0.34	0.23	0.51	1.95	1.95	-0.57
29	D	1.26	4.87	4.87	-0.57	3.67	0.85	0.23	0.40	1.47	0.34	0.23	0.63	1.47	2.30	0.00
30	D	1.26	4.87	4.87	-0.57	3.67	0.85	0.23	0.40	1.47	0.34	0.23	0.99	0.99	2.43	0.57
31	D	1.59	3.67	5.75	0.00	3.67	0.85	0.23	0.40	1.47	0.34	0.23	0.51	1.95	1.95	-0.57
32	D	1.59	3.67	5.75	0.00	3.67	0.85	0.23	0.40	1.47	0.34	0.23	0.63	1.47	2.30	0.00
33	D	1.59	3.67	5.75	0.00	3.67	0.85	0.23	0.40	1.47	0.34	0.23	0.99	0.99	2.43	0.57
34	D	2.00	3.00	6.00	0.42	3.67	0.85	0.23	0.40	1.47	0.34	0.23	0.51	1.95	1.95	-0.57
35	D	2.00	3.00	6.00	0.42	3.67	0.85	0.23	0.40	1.47	0.34	0.23	0.63	1.47	2.30	0.00
36	D	2.00	3.00	6.00	0.42	3.67	0.85	0.23	0.40	1.47	0.34	0.23	0.99	0.99	2.43	0.57
37	E	1.26	4.87	4.87	-0.57	3.67	0.85	0.23	0.50	1.83	0.42	0.23	0.63	2.43	2.43	-0.57
38	E	1.26	4.87	4.87	-0.57	3.67	0.85	0.23	0.50	1.83	0.42	0.23	0.79	1.83	2.87	0.00
39	E	1.26	4.87	4.87	-0.57	3.67	0.85	0.23	0.50	1.83	0.42	0.23	1.23	1.23	3.04	0.57
40	E	1.59	3.67	5.75	0.00	3.67	0.85	0.23	0.50	1.83	0.42	0.23	0.63	2.43	2.43	-0.57
41	E	1.59	3.67	5.75	0.00	3.67	0.85	0.23	0.50	1.83	0.42	0.23	0.79	1.83	2.87	0.00
42	E	1.59	3.67	5.75	0.00	3.67	0.85	0.23	0.50	1.83	0.42	0.23	1.23	1.23	3.04	0.57
43	E	2.00	3.00	6.00	0.42	3.67	0.85	0.23	0.50	1.83	0.42	0.23	0.63	2.43	2.43	-0.57
44	E	2.00	3.00	6.00	0.42	3.67	0.85	0.23	0.50	1.83	0.42	0.23	0.79	1.83	2.87	0.00
45	E	2.00	3.00	6.00	0.42	3.67	0.85	0.23	0.50	1.83	0.42	0.23	1.23	1.23	3.04	0.57
46	F	1.26	4.87	4.87	-0.57	3.67	0.85	0.23	0.60	2.20	0.51	0.23	0.76	2.92	2.92	-0.57
47	F	1.26	4.87	4.87	-0.57	3.67	0.85	0.23	0.60	2.20	0.51	0.23	0.95	2.20	3.45	0.00
48	F	1.26	4.87	4.87	-0.57	3.67	0.85	0.23	0.60	2.20	0.51	0.23	1.48	1.48	3.64	0.57
49	F	1.59	3.67	5.75	0.00	3.67	0.85	0.23	0.60	2.20	0.51	0.23	0.76	2.92	2.92	-0.57
50	F	1.59	3.67	5.75	0.00	3.67	0.85	0.23	0.60	2.20	0.51	0.23	0.95	2.20	3.45	0.00
51	F	1.59	3.67	5.75	0.00	3.67	0.85	0.23	0.60	2.20	0.51	0.23	1.48	1.48	3.64	0.57
52	F	2.00	3.00	6.00	0.42	3.67	0.85	0.23	0.60	2.20	0.51	0.23	0.76	2.92	2.92	-0.57
53	F	2.00	3.00	6.00	0.42	3.67	0.85	0.23	0.60	2.20	0.51	0.23	0.95	2.20	3.45	0.00
54	F	2.00	3.00	6.00	0.42	3.67	0.85	0.23	0.60	2.20	0.51	0.23	1.48	1.48	3.64	0.57
55	G	1.26	4.87	4.87	-0.57	3.67	0.85	0.23	0.70	2.57	0.59	0.23	0.88	3.41	3.41	-0.57
56	G	1.26	4.87	4.87	-0.57	3.67	0.85	0.23	0.70	2.57	0.59	0.23	1.11	2.57	4.02	0.00
57	G	1.26	4.87	4.87	-0.57	3.67	0.85	0.23	0.70	2.57	0.59	0.23	1.73	1.73	4.25	0.57
58	G	1.59	3.67	5.75	0.00	3.67	0.85	0.23	0.70	2.57	0.59	0.23	0.88	3.41	3.41	-0.57
59	G	1.59	3.67	5.75	0.00	3.67	0.85	0.23	0.70	2.57	0.59	0.23	1.11	2.57	4.02	0.00
60	G	1.59	3.67	5.75	0.00	3.67	0.85	0.23	0.70	2.57	0.59	0.23	1.73	1.73	4.25	0.57
61	G	2.00	3.00	6.00	0.42	3.67	0.85	0.23	0.70	2.57	0.59	0.23	0.88	3.41	3.41	-0.57
62	G	2.00	3.00	6.00	0.42	3.67	0.85	0.23	0.70	2.57	0.59	0.23	1.11	2.57	4.02	0.00
63	G	2.00	3.00	6.00	0.42	3.67	0.85	0.23	0.70	2.57	0.59	0.23	1.73	1.73	4.25	0.57
64	H	1.26	4.87	4.87	-0.57	3.67	0.85	0.23	0.80	2.93	0.68	0.23	1.01	3.89	3.89	-0.57
65	H	1.26	4.87	4.87	-0.57	3.67	0.85	0.23	0.80	2.93	0.68	0.23	1.27	2.93	4.60	0.00
66	H	1.26	4.87	4.87	-0.57	3.67	0.85	0.23	0.80	2.93	0.68	0.23	1.97	1.97	4.86	0.57
67	H	1.59	3.67	5.75	0.00	3.67	0.85	0.23	0.80	2.93	0.68	0.23	1.01	3.89	3.89	-0.57
68	H	1.59	3.67	5.75	0.00	3.67	0.85	0.23	0.80	2.93	0.68	0.23	1.27	2.93	4.60	0.00
69	H	1.59	3.67	5.75	0.00	3.67	0.85	0.23	0.80	2.93	0.68	0.23	1.97	1.97	4.86	0.57
70	H	2.00	3.00	6.00	0.42	3.67	0.85	0.23	0.80	2.93	0.68	0.23	1.01	3.89	3.89	-0.57
71	H	2.00	3.00	6.00	0.42	3.67	0.85	0.23	0.80	2.93	0.68	0.23	1.27	2.93	4.60	0.00
72	H	2.00	3.00	6.00	0.42	3.67	0.85	0.23	0.80	2.93	0.68	0.23	1.97	1.97	4.86	0.57
73	I	1.26	4.87	4.87	-0.57	3.67	0.85	0.23	0.85	3.12	0.72	0.23	1.07	4.14	4.14	-0.57
74	I	1.26	4.87	4.87	-0.57	3.67	0.85	0.23	0.85	3.12	0.72	0.23	1.35	3.12	4.89	0.00
75	I	1.26	4.87	4.87	-0.57	3.67	0.85	0.23	0.85	3.12	0.72	0.23	2.10	2.10	5.16	0.57
76	I	1.59	3.67	5.75	0.00	3.67	0.85	0.23	0.85	3.12	0.72	0.23	1.07	4.14	4.14	-0.57
77	I	1.59	3.67	5.75	0.00	3.67	0.85	0.23	0.85	3.12	0.72	0.23	1.35	3.12	4.89	0.00
78	I	1.59	3.67	5.75	0.00	3.67	0.85	0.23	0.85	3.12	0.72	0.23	2.10	2.10	5.16	0.57
79	I	2.00	3.00	6.00	0.42	3.67	0.85	0.23	0.85	3.12	0.72	0.23	1.07	4.14	4.14	-0.57
80	I	2.00	3.00	6.00	0.42	3.67	0.85	0.23	0.85	3.12	0.72	0.23	1.35	3.12	4.89	0.00
81	I	2.00	3.00	6.00	0.42	3.67	0.85	0.23	0.85	3.12	0.72	0.23	2.10	2.10	5.16	0.57
82	J	1.26	4.87	4.87	-0.57	3.67	0.85	0.23	0.90	3.30	0.76	0.23	1.14	4.38	4.38	-0.57
83	J	1.26	4.87	4.87	-0.57	3.67	0.85	0.23	0.90	3.30	0.76	0.23	1.43	3.30	5.17	0.00
84	J	1.26	4.87	4.87	-0.57	3.67	0.85	0.23	0.90	3.30	0.76	0.23	2.22	2.22	5.46	0.57
85	J	1.59	3.67	5.75	0.00	3.67	0.85	0.23	0.90	3.30	0.76	0.23	1.14	4.38	4.38	-0.57
86	J	1.59	3.67	5.75	0.00	3.67	0.85	0.23	0.90	3.30	0.76	0.23	1.43	3.30	5.17	0.00
87	J	1.59	3.67	5.75	0.00	3.67	0.85	0.23	0.90	3.30	0.76	0.23	2.22	2.22	5.46	0.57
88	J	2.00	3.00	6.00	0.42	3.67	0.85	0.23	0.90	3.30	0.76	0.23	1.14	4.38	4.38	-0.57
89	J	2.00	3.00	6.00	0.42	3.67	0.85	0.23	0.90	3.30	0.76	0.23	1.43	3.30	5.17	0.00
90	J	2.00	3.00	6.00	0.42	3.67	0.85	0.23	0.90	3.30	0.76	0.23	2.22	2.22	5.46	0.57
91	K	1.26	4.87	4.87	-0.57	3.67	0.85	0.23	0.95	3.48	0.81	0.23	1.20	4.63	4.63	-0.57
92	K	1.26	4.87	4.87	-0.57	3.67	0.85	0.23	0.95	3.48	0.81	0.23	1.51	3.48	5.46	0.00
93	K	1.26	4.87	4.87	-0.57	3.67	0.85	0.23	0.95	3.48	0.81	0.23	2.34	2.34	5.77	0.57
94	K	1.59	3.67	5.75	0.00	3.67	0.85	0.23	0.95	3.48	0.81	0.23	1.20	4.63	4.63	-0.57
95	K	1.59	3.67	5.75	0.00	3.67	0.85	0.23	0.95	3.48	0.81	0.23	1.51	3.48	5.46	0.00
96	K	1.59	3.67	5.75	0.00	3.67	0.85	0.23	0.95	3.48	0.81	0.23	2.34	2.34	5.77	0.57
97	K	2.00	3.00	6.00	0.42	3.67	0.85	0.23	0.95	3.48	0.81	0.23	1.20	4.63	4.63	-0.57
98	K	2.00	3.00	6.00	0.42	3.67	0.85	0.23	0.95	3.48	0.81	0.23	1.51	3.48	5.46	0.00
99	K	2.00	3.00	6.00	0.42	3.67	0.85	0.23	0.95	3.48	0.81	0.23	2.34	2.34	5.77	0.57
100	L	1.26	4.87	4.87	-0.57	3.67	0.85	0.23	0.97	3.56	0.82	0.23	1.23	4.72	4.72	-0.57
101	L	1.26	4.87	4.87	-0.57	3.67	0.85	0.23	0.97	3.56	0.82	0.23	1.54	3.56	5.58	0.00
102	L	1.26	4.87	4.87	-0.57	3.67	0.85	0.23	0.97	3.56	0.82	0.23	2.39	2.39	5.89	0.57
103	L	1.59	3.67	5.75	0.00	3.67	0.85	0.23	0.97	3.56	0.82	0.23	1.23	4.72	4.72	-0.57
104	L	1.59	3.67	5.75	0.00	3.67	0.85	0.23	0.97	3.56	0.82	0.23	1.54	3.56	5.58	0.00
105	L	1.59	3.67	5.75	0.00	3.67	0.85	0.23	0.97	3.56	0.82	0.23	2.39	2.39	5.89	0.57
106	L	2.00	3.00	6.00	0.42	3.67	0.85	0.23	0.97	3.56	0.82	0.23	1.23	4.72	4.72	-0.57
107	L	2.00	3.00	6.00	0.42	3.67	0.85	0.23	0.97	3.56	0.82	0.23	1.54	3.56	5.58	0.00
108	L	2.00	3.00	6.00	0.42	3.67	0.85	0.23	0.97	3.56	0.82	0.23	2.39	2.39	5.89	0.57
109	M	1.26	4.87	4.87	-0.57	3.67	0.85	0.23	0.99	3.63	0.84	0.23	1.25	4.82	4.82	-0.57
110	M	1.26	4.87	4.87	-0.57	3.67	0.85	0.23	0.99	3.63	0.84	0.23	1.57	3.63	5.69	0.00
111	M	1.26	4.87	4.87	-0.57	3.67	0.85	0.23	0.99	3.63	0.84	0.23	2.44	2.44	6.01	0.57
112	M	1.59	3.67	5.75	0.00	3.67	0.85	0.23	0.99	3.63	0.84	0.23	1.25	4.82	4.82	-0.57
113	M	1.59	3.67	5.75	0.00	3.67	0.85	0.23	0.99	3.63	0.84	0.23	1.57	3.63	5.69	0.00
114	M	1.59	3.67	5.75	0.00	3.67	0.85	0.23	0.99	3.63	0.84	0.23	2.44	2.44	6.01	0.57
115	M	2.00	3.00	6.00	0.42	3.67	0.85	0.23	0.99	3.63	0.84	0.23	1.25	4.82	4.82	-0.57
116	M	2.00	3.00	6.00	0.42	3.67	0.85	0.23	0.99	3.63	0.84	0.23	1.57	3.63	5.69	0.00
117	M	2.00	3.00	6.00	0.42	3.67	0.85	0.23	0.99	3.63	0.84	0.23	2.44	2.44	6.01	0.57
118	N	1.26	4.87	4.87	-0.57	3.67	0.85	0.23	0.98	3.59	0.83	0.23	1.24	4.77	4.77	-0.57
119	N	1.26	4.87	4.87	-0.57	3.67	0.85	0.23	0.98	3.59	0.83	0.23	1.55	3.59	5.63	0.00
120	N	1.26	4.87	4.87	-0.57	3.67	0.85	0.23	0.98	3.59	0.83	0.23	2.42	2.42	5.95	0.57
121	N	1.59	3.67	5.75	0.00	3.67	0.85	0.23	0.98	3.59	0.83	0.23	1.24	4.77	4.77	-0.57
122	N	1.59	3.67	5.75	0.00	3.67	0.85	0.23	0.98	3.59	0.83	0.23	1.55	3.59	5.63	0.00
123	N	1.59	3.67	5.75	0.00	3.67	0.85	0.23	0.98	3.59	0.83	0.23	2.42	2.42	5.95	0.57
124	N	2.00	3.00	6.00	0.42	3.67	0.85	0.23	0.98	3.59	0.83	0.23	1.24	4.77	4.77	-0.57
125	N	2.00	3.00	6.00	0.42	3.67	0.85	0.23	0.98	3.59	0.83	0.23	1.55	3.59	5.63	0.00
126	N	2.00	3.00	6.00	0.42	3.67	0.85	0.23	0.98	3.59	0.83	0.23	2.42	2.42	5.95	0.57
127	O	0.00	3.00	4.00	-0.42	2.33	0.85	0.36	0.10	0.23	0.08	0.36	0.00	0.30	0.40	-0.42
128	O	0.00	3.00	4.00	-0.42	2.33	0.85	0.36	0.10	0.23	0.08	0.36	0.03	0.23	0.44	0.00
129	O	0.00	3.00	4.00	-0.42	2.33	0.85	0.36	0.10	0.23	0.08	0.36	0.07	0.17	0.47	0.42
130	O	0.25	2.33	4.41	0.00	2.33	0.85	0.36	0.10	0.23	0.08	0.36	0.00	0.30	0.40	-0.42
131	O	0.25	2.33	4.41	0.00	2.33	0.85	0.36	0.10	0.23	0.08	0.36	0.03	0.23	0.44	0.00
132	O	0.25	2.33	4.41	0.00	2.33	0.85	0.36	0.10	0.23	0.08	0.36	0.07	0.17	0.47	0.42
133	O	0.67	1.67	4.67	0.42	2.33	0.85	0.36	0.10	0.23	0.08	0.36	0.00	0.30	0.40	-0.42
134	O	0.67	1.67	4.67	0.42	2.33	0.85	0.36	0.10	0.23	0.08	0.36	0.03	0.23	0.44	0.00
135	O	0.67	1.67	4.67	0.42	2.33	0.85	0.36	0.10	0.23	0.08	0.36	0.07	0.17	0.47	0.42
136	P	0.00	3.00	4.00	-0.42	2.33	0.85	0.36	0.20	0.47	0.17	0.36	0.00	0.60	0.80	-0.42
137	P	0.00	3.00	4.00	-0.42	2.33	0.85	0.36	0.20	0.47	0.17	0.36	0.05	0.47	0.88	0.00
138	P	0.00	3.00	4.00	-0.42	2.33	0.85	0.36	0.20	0.47	0.17	0.36	0.13	0.33	0.93	0.42
139	P	0.25	2.33	4.41	0.00	2.33	0.85	0.36	0.20	0.47	0.17	0.36	0.00	0.60	0.80	-0.42
140	P	0.25	2.33	4.41	0.00	2.33	0.85	0.36	0.20	0.47	0.17	0.36	0.05	0.47	0.88	0.00
141	P	0.25	2.33	4.41	0.00	2.33	0.85	0.36	0.20	0.47	0.17	0.36	0.13	0.33	0.93	0.42
142	P	0.67	1.67	4.67	0.42	2.33	0.85	0.36	0.20	0.47	0.17	0.36	0.00	0.60	0.80	-0.42
143	P	0.67	1.67	4.67	0.42	2.33	0.85	0.36	0.20	0.47	0.17	0.36	0.05	0.47	0.88	0.00
144	P	0.67	1.67	4.67	0.42	2.33	0.85	0.36	0.20	0.47	0.17	0.36	0.13	0.33	0.93	0.42
145	Q	0.00	3.00	4.00	-0.42	2.33	0.85	0.36	0.30	0.70	0.25	0.36	0.00	0.90	1.20	-0.42
146	Q	0.00	3.00	4.00	-0.42	2.33	0.85	0.36	0.30	0.70	0.25	0.36	0.08	0.70	1.32	0.00
147	Q	0.00	3.00	4.00	-0.42	2.33	0.85	0.36	0.30	0.70	0.25	0.36	0.20	0.50	1.40	0.42
148	Q	0.25	2.33	4.41	0.00	2.33	0.85	0.36	0.30	0.70	0.25	0.36	0.00	0.90	1.20	-0.42
149	Q	0.25	2.33	4.41	0.00	2.33	0.85	0.36	0.30	0.70	0.25	0.36	0.08	0.70	1.32	0.00
150	Q	0.25	2.33	4.41	0.00	2.33	0.85	0.36	0.30	0.70	0.25	0.36	0.20	0.50	1.40	0.42
151	Q	0.67	1.67	4.67	0.42	2.33	0.85	0.36	0.30	0.70	0.25	0.36	0.00	0.90	1.20	-0.42
152	Q	0.67	1.67	4.67	0.42	2.33	0.85	0.36	0.30	0.70	0.25	0.36	0.08	0.70	1.32	0.00
153	Q	0.67	1.67	4.67	0.42	2.33	0.85	0.36	0.30	0.70	0.25	0.36	0.20	0.50	1.40	0.42
154	R	0.00	3.00	4.00	-0.42	2.33	0.85	0.36	0.40	0.93	0.34	0.36	0.00	1.20	1.60	-0.42
155	R	0.00	3.00	4.00	-0.42	2.33	0.85	0.36	0.40	0.93	0.34	0.36	0.10	0.93	1.77	0.00
156	R	0.00	3.00	4.00	-0.42	2.33	0.85	0.36	0.40	0.93	0.34	0.36	0.27	0.67	1.87	0.42
157	R	0.25	2.33	4.41	0.00	2.33	0.85	0.36	0.40	0.93	0.34	0.36	0.00	1.20	1.60	-0.42
158	R	0.25	2.33	4.41	0.00	2.33	0.85	0.36	0.40	0.93	0.34	0.36	0.10	0.93	1.77	0.00
159	R	0.25	2.33	4.41	0.00	2.33	0.85	0.36	0.40	0.93	0.34	0.36	0.27	0.67	1.87	0.42
160	R	0.67	1.67	4.67	0.42	2.33	0.85	0.36	0.40	0.93	0.34	0.36	0.00	1.20	1.60	-0.42
161	R	0.67	1.67	4.67	0.42	2.33	0.85	0.36	0.40	0.93	0.34	0.36	0.10	0.93	1.77	0.00
162	R	0.67	1.67	4.67	0.42	2.33	0.85	0.36	0.40	0.93	0.34	0.36	0.27	0.67	1.87	0.42
163	S	0.00	3.00	4.00	-0.42	2.33	0.85	0.36	0.50	1.17	0.42	0.36	0.00	1.50	2.00	-0.42
164	S	0.00	3.00	4.00	-0.42	2.33	0.85	0.36	0.50	1.17	0.42	0.36	0.13	1.17	2.21	0.00
165	S	0.00	3.00	4.00	-0.42	2.33	0.85	0.36	0.50	1.17	0.42	0.36	0.33	0.83	2.33	0.42
166	S	0.25	2.33	4.41	0.00	2.33	0.85	0.36	0.50	1.17	0.42	0.36	0.00	1.50	2.00	-0.42
167	S	0.25	2.33	4.41	0.00	2.33	0.85	0.36	0.50	1.17	0.42	0.36	0.13	1.17	2.21	0.00
168	S	0.25	2.33	4.41	0.00	2.33	0.85	0.36	0.50	1.17	0.42	0.36	0.33	0.83	2.33	0.42
169	S	0.67	1.67	4.67	0.42	2.33	0.85	0.36	0.50	1.17	0.42	0.36	0.00	1.50	2.00	-0.42
170	S	0.67	1.67	4.67	0.42	2.33	0.85	0.36	0.50	1.17	0.42	0.36	0.13	1.17	2.21	0.00
171	S	0.67	1.67	4.67	0.42	2.33	0.85	0.36	0.50	1.17	0.42	0.36	0.33	0.83	2.33	0.42
172	T	0.00	3.00	4.00	-0.42	2.33	0.85	0.36	0.60	1.40	0.51	0.36	0.00	1.80	2.40	-0.42
173	T	0.00	3.00	4.00	-0.42	2.33	0.85	0.36	0.60	1.40	0.51	0.36	0.15	1.40	2.65	0.00
174	T	0.00	3.00	4.00	-0.42	2.33	0.85	0.36	0.60	1.40	0.51	0.36	0.40	1.00	2.80	0.42
175	T	0.25	2.33	4.41	0.00	2.33	0.85	0.36	0.60	1.40	0.51	0.36	0.00	1.80	2.40	-0.42
176	T	0.25	2.33	4.41	0.00	2.33	0.85	0.36	0.60	1.40	0.51	0.36	0.15	1.40	2.65	0.00
177	T	0.25	2.33	4.41	0.00	2.33	0.85	0.36	0.60	1.40	0.51	0.36	0.40	1.00	2.80	0.42
178	T	0.67	1.67	4.67	0.42	2.33	0.85	0.36	0.60	1.40	0.51	0.36	0.00	1.80	2.40	-0.42
179	T	0.67	1.67	4.67	0.42	2.33	0.85	0.36	0.60	1.40	0.51	0.36	0.15	1.40	2.65	0.00
180	T	0.67	1.67	4.67	0.42	2.33	0.85	0.36	0.60	1.40	0.51	0.36	0.40	1.00	2.80	0.42
181	U	0.00	3.00	4.00	-0.42	2.33	0.85	0.36	0.70	1.63	0.59	0.36	0.00	2.10	2.80	-0.42
182	U	0.00	3.00	4.00	-0.42	2.33	0.85	0.36	0.70	1.63	0.59	0.36	0.18	1.63	3.09	0.00
183	U	0.00	3.00	4.00	-0.42	2.33	0.85	0.36	0.70	1.63	0.59	0.36	0.47	1.17	3.27	0.42
184	U	0.25	2.33	4.41	0.00	2.33	0.85	0.36	0.70	1.63	0.59	0.36	0.00	2.10	2.80	-0.42
185	U	0.25	2.33	4.41	0.00	2.33	0.85	0.36	0.70	1.63	0.59	0.36	0.18	1.63	3.09	0.00
186	U	0.25	2.33	4.41	0.00	2.33	0.85	0.36	0.70	1.63	0.59	0.36	0.47	1.17	3.27	0.42
187	U	0.67	1.67	4.67	0.42	2.33	0.85	0.36	0.70	1.63	0.59	0.36	0.00	2.10	2.80	-0.42
188	U	0.67	1.67	4.67	0.42	2.33	0.85	0.36	0.70	1.63	0.59	0.36	0.18	1.63	3.09	0.00
189	U	0.67	1.67	4.67	0.42	2.33	0.85	0.36	0.70	1.63	0.59	0.36	0.47	1.17	3.27	0.42
190	V	0.00	3.00	4.00	-0.42	2.33	0.85	0.36	0.80	1.87	0.68	0.36	0.00	2.40	3.20	-0.42
191	V	0.00	3.00	4.00	-0.42	2.33	0.85	0.36	0.80	1.87	0.68	0.36	0.20	1.87	3.53	0.00
192	V	0.00	3.00	4.00	-0.42	2.33	0.85	0.36	0.80	1.87	0.68	0.36	0.53	1.33	3.73	0.42
193	V	0.25	2.33	4.41	0.00	2.33	0.85	0.36	0.80	1.87	0.68	0.36	0.00	2.40	3.20	-0.42
194	V	0.25	2.33	4.41	0.00	2.33	0.85	0.36	0.80	1.87	0.68	0.36	0.20	1.87	3.53	0.00
195	V	0.25	2.33	4.41	0.00	2.33	0.85	0.36	0.80	1.87	0.68	0.36	0.53	1.33	3.73	0.42
196	V	0.67	1.67	4.67	0.42	2.33	0.85	0.36	0.80	1.87	0.68	0.36	0.00	2.40	3.20	-0.42
197	V	0.67	1.67	4.67	0.42	2.33	0.85	0.36	0.80	1.87	0.68	0.36	0.20	1.87	3.53	0.00
198	V	0.67	1.67	4.67	0.42	2.33	0.85	0.36	0.80	1.87	0.68	0.36	0.53	1.33	3.73	0.42
199	W	0.00	3.00	4.00	-0.42	2.33	0.85	0.36	0.85	1.98	0.72	0.36	0.00	2.55	3.40	-0.42
200	W	0.00	3.00	4.00	-0.42	2.33	0.85	0.36	0.85	1.98	0.72	0.36	0.21	1.98	3.75	0.00
201	W	0.00	3.00	4.00	-0.42	2.33	0.85	0.36	0.85	1.98	0.72	0.36	0.57	1.42	3.97	0.42
202	W	0.25	2.33	4.41	0.00	2.33	0.85	0.36	0.85	1.98	0.72	0.36	0.00	2.55	3.40	-0.42
203	W	0.25	2.33	4.41	0.00	2.33	0.85	0.36	0.85	1.98	0.72	0.36	0.21	1.98	3.75	0.00
204	W	0.25	2.33	4.41	0.00	2.33	0.85	0.36	0.85	1.98	0.72	0.36	0.57	1.42	3.97	0.42
205	W	0.67	1.67	4.67	0.42	2.33	0.85	0.36	0.85	1.98	0.72	0.36	0.00	2.55	3.40	-0.42
206	W	0.67	1.67	4.67	0.42	2.33	0.85	0.36	0.85	1.98	0.72	0.36	0.21	1.98	3.75	0.00
207	W	0.67	1.67	4.67	0.42	2.33	0.85	0.36	0.85	1.98	0.72	0.36	0.57	1.42	3.97	0.42
208	X	0.00	3.00	4.00	-0.42	2.33	0.85	0.36	0.90	2.10	0.76	0.36	0.00	2.70	3.60	-0.42
209	X	0.00	3.00	4.00	-0.42	2.33	0.85	0.36	0.90	2.10	0.76	0.36	0.23	2.10	3.97	0.00
210	X	0.00	3.00	4.00	-0.42	2.33	0.85	0.36	0.90	2.10	0.76	0.36	0.60	1.50	4.20	0.42
211	X	0.25	2.33	4.41	0.00	2.33	0.85	0.36	0.90	2.10	0.76	0.36	0.00	2.70	3.60	-0.42
212	X	0.25	2.33	4.41	0.00	2.33	0.85	0.36	0.90	2.10	0.76	0.36	0.23	2.10	3.97	0.00
213	X	0.25	2.33	4.41	0.00	2.33	0.85	0.36	0.90	2.10	0.76	0.36	0.60	1.50	4.20	0.42
214	X	0.67	1.67	4.67	0.42	2.33	0.85	0.36	0.90	2.10	0.76	0.36	0.00	2.70	3.60	-0.42
215	X	0.67	1.67	4.67	0.42	2.33	0.85	0.36	0.90	2.10	0.76	0.36	0.23	2.10	3.97	0.00
216	X	0.67	1.67	4.67	0.42	2.33	0.85	0.36	0.90	2.10	0.76	0.36	0.60	1.50	4.20	0.42
217	Y	0.00	3.00	4.00	-0.42	2.33	0.85	0.36	0.95	2.22	0.81	0.36	0.00	2.85	3.80	-0.42
218	Y	0.00	3.00	4.00	-0.42	2.33	0.85	0.36	0.95	2.22	0.81	0.36	0.24	2.22	4.19	0.00
219	Y	0.00	3.00	4.00	-0.42	2.33	0.85	0.36	0.95	2.22	0.81	0.36	0.63	1.58	4.43	0.42
220	Y	0.25	2.33	4.41	0.00	2.33	0.85	0.36	0.95	2.22	0.81	0.36	0.00	2.85	3.80	-0.42
221	Y	0.25	2.33	4.41	0.00	2.33	0.85	0.36	0.95	2.22	0.81	0.36	0.24	2.22	4.19	0.00
222	Y	0.25	2.33	4.41	0.00	2.33	0.85	0.36	0.95	2.22	0.81	0.36	0.63	1.58	4.43	0.42
223	Y	0.67	1.67	4.67	0.42	2.33	0.85	0.36	0.95	2.22	0.81	0.36	0.00	2.85	3.80	-0.42
224	Y	0.67	1.67	4.67	0.42	2.33	0.85	0.36	0.95	2.22	0.81	0.36	0.24	2.22	4.19	0.00
225	Y	0.67	1.67	4.67	0.42	2.33	0.85	0.36	0.95	2.22	0.81	0.36	0.63	1.58	4.43	0.42
226	Z	0.00	3.00	4.00	-0.42	2.33	0.85	0.36	0.97	2.26	0.82	0.36	0.00	2.91	3.88	-0.42
227	Z	0.00	3.00	4.00	-0.42	2.33	0.85	0.36	0.97	2.26	0.82	0.36	0.24	2.26	4.28	0.00
228	Z	0.00	3.00	4.00	-0.42	2.33	0.85	0.36	0.97	2.26	0.82	0.36	0.65	1.62	4.53	0.42
229	Z	0.25	2.33	4.41	0.00	2.33	0.85	0.36	0.97	2.26	0.82	0.36	0.00	2.91	3.88	-0.42
230	Z	0.25	2.33	4.41	0.00	2.33	0.85	0.36	0.97	2.26	0.82	0.36	0.24	2.26	4.28	0.00
231	Z	0.25	2.33	4.41	0.00	2.33	0.85	0.36	0.97	2.26	0.82	0.36	0.65	1.62	4.53	0.42
232	Z	0.67	1.67	4.67	0.42	2.33	0.85	0.36	0.97	2.26	0.82	0.36	0.00	2.91	3.88	-0.42
233	Z	0.67	1.67	4.67	0.42	2.33	0.85	0.36	0.97	2.26	0.82	0.36	0.24	2.26	4.28	0.00
234	Z	0.67	1.67	4.67	0.42	2.33	0.85	0.36	0.97	2.26	0.82	0.36	0.65	1.62	4.53	0.42
235	ZA	0.00	3.00	4.00	-0.42	2.33	0.85	0.36	0.98	2.29	0.83	0.36	0.00	2.94	3.92	-0.42
236	ZA	0.00	3.00	4.00	-0.42	2.33	0.85	0.36	0.98	2.29	0.83	0.36	0.25	2.29	4.33	0.00
237	ZA	0.00	3.00	4.00	-0.42	2.33	0.85	0.36	0.98	2.29	0.83	0.36	0.65	1.63	4.57	0.42
238	ZA	0.25	2.33	4.41	0.00	2.33	0.85	0.36	0.98	2.29	0.83	0.36	0.00	2.94	3.92	-0.42
239	ZA	0.25	2.33	4.41	0.00	2.33	0.85	0.36	0.98	2.29	0.83	0.36	0.25	2.29	4.33	0.00
240	ZA	0.25	2.33	4.41	0.00	2.33	0.85	0.36	0.98	2.29	0.83	0.36	0.65	1.63	4.57	0.42
241	ZA	0.67	1.67	4.67	0.42	2.33	0.85	0.36	0.98	2.29	0.83	0.36	0.00	2.94	3.92	-0.42
242	ZA	0.67	1.67	4.67	0.42	2.33	0.85	0.36	0.98	2.29	0.83	0.36	0.25	2.29	4.33	0.00
243	ZA	0.67	1.67	4.67	0.42	2.33	0.85	0.36	0.98	2.29	0.83	0.36	0.65	1.63	4.57	0.42
244	ZB	0.00	3.00	4.00	-0.42	2.33	0.85	0.36	0.99	2.31	0.84	0.36	0.00	2.97	3.96	-0.42
245	ZB	0.00	3.00	4.00	-0.42	2.33	0.85	0.36	0.99	2.31	0.84	0.36	0.25	2.31	4.37	0.00
246	ZB	0.00	3.00	4.00	-0.42	2.33	0.85	0.36	0.99	2.31	0.84	0.36	0.66	1.65	4.62	0.42
247	ZB	0.25	2.33	4.41	0.00	2.33	0.85	0.36	0.99	2.31	0.84	0.36	0.00	2.97	3.96	-0.42
248	ZB	0.25	2.33	4.41	0.00	2.33	0.85	0.36	0.99	2.31	0.84	0.36	0.25	2.31	4.37	0.00
249	ZB	0.25	2.33	4.41	0.00	2.33	0.85	0.36	0.99	2.31	0.84	0.36	0.66	1.65	4.62	0.42
250	ZB	0.67	1.67	4.67	0.42	2.33	0.85	0.36	0.99	2.31	0.84	0.36	0.00	2.97	3.96	-0.42
251	ZB	0.67	1.67	4.67	0.42	2.33	0.85	0.36	0.99	2.31	0.84	0.36	0.25	2.31	4.37	0.00
252	ZB	0.67	1.67	4.67	0.42	2.33	0.85	0.36	0.99	2.31	0.84	0.36	0.66	1.65	4.62	0.42

Abbreviation	Variable	Abbreviation	Variable
Exp.	Experiment number	ρ	Utilization of the server
IG ID	Intra-group identification	µ _S	Mean service time
a_A	Minimum value in the triangular distribution of inter-arrival times	σ _S	Service time variance
m_A	Mode in the triangular distribution of inter-arrival times	CV_S	Service time coefficient of variation
b_A	Maximum value in the triangular distribution of inter-arrival times	a_S	Minimum value in the triangular distribution of service times
γ _A	Inter-arrival time skewness	m_S	Mode in the triangular distribution of service times
µ _A	Mean inter-arrival time	b_S	Maximum value in the triangular distribution of service times
σ _A	Inter-arrival time variance	γ _S	Service time skewness
CV_A	Inter-arrival time coefficient of variation

				ρ
Response	CV	γ _A	γ _S	0.50	0.60	0.70	0.80	0.85	0.90	0.95	0.97	0.98	0.99
W	0.2318	-1	1	0.0151	0.0509	0.1416	0.3875	0.6716	1.2898	3.2088	5.8111	9.0307	18.7106
W	0.2318	-1	0	0.0138	0.0481	0.1354	0.3728	0.6504	1.2585	3.1835	5.7978	8.9753	18.5740
W	0.2318	-1	-1	0.0126	0.0454	0.1290	0.3583	0.6284	1.2189	3.1366	5.7874	8.9392	18.5673
W	0.2318	0	1	0.0081	0.0359	0.1176	0.3550	0.6362	1.2383	3.1182	5.7672	8.9376	18.5593
W	0.2318	0	0	0.0067	0.0323	0.1096	0.3386	0.6160	1.2164	3.1028	5.7036	8.9306	18.5553
W	0.2318	0	-1	0.0053	0.0287	0.1014	0.3291	0.5914	1.1876	3.1267	5.6976	8.9284	18.3799
W	0.2318	1	1	0.0032	0.0241	0.0989	0.3217	0.6091	1.2118	3.1041	5.6958	8.8984	17.9690
W	0.2318	1	0	0.0020	0.0193	0.0884	0.3115	0.5869	1.1896	3.1068	5.6622	8.8592	17.8611
W	0.2318	1	-1	0.0008	0.0141	0.0779	0.2959	0.5669	1.1634	3.0541	5.6017	8.7935	17.8563
W	0.3642	-1	1	0.0835	0.1729	0.3583	0.7931	1.2686	2.2656	5.3181	9.4550	14.6379	28.4957
W	0.3642	-1	0	0.0819	0.1693	0.3506	0.7785	1.2470	2.2381	5.3968	9.4286	14.5772	28.2157
W	0.3642	-1	-1	0.0802	0.1653	0.3421	0.7622	1.2339	2.1976	5.1869	9.4020	14.5024	27.7617
W	0.3642	0	1	0.0649	0.1489	0.3312	0.7617	1.2464	2.2206	5.2080	9.3660	14.4305	27.4010
W	0.3642	0	0	0.0628	0.1445	0.3218	0.7475	1.2243	2.2078	5.2466	9.3278	14.3473	27.3867
W	0.3642	0	-1	0.0609	0.1400	0.3126	0.7333	1.2099	2.1941	5.2099	9.2846	14.3320	26.6839
W	0.3642	1	1	0.0443	0.1230	0.3015	0.7326	1.2072	2.1874	5.1856	9.2485	14.3163	26.4135
W	0.3642	1	0	0.0411	0.1174	0.2922	0.7211	1.1937	2.1694	5.2029	9.2420	13.9344	26.0665
W	0.3642	1	-1	0.0378	0.1117	0.2839	0.7058	1.1825	2.1450	5.1511	9.1872	13.8578	25.3369
γ _W	0.2318	1	-1	18.3392	6.6158	3.7333	2.6100	2.3284	2.1151	1.8588	1.6433	1.4570	1.0597
γ _W	0.2318	1	0	15.3695	6.6370	3.8928	2.7020	2.3862	2.1021	1.8438	1.6393	1.4493	1.0469
γ _W	0.2318	1	1	13.4282	6.3375	3.8832	2.7642	2.4036	2.1050	1.8252	1.6384	1.4046	1.0453
γ _W	0.2318	0	-1	10.1765	5.6561	3.7423	2.6987	2.3893	2.1050	1.8162	1.6242	1.4031	1.0220
γ _W	0.2318	0	0	10.3953	5.8710	3.8422	2.7762	2.4184	2.1511	1.8131	1.6014	1.4018	1.0194
γ _W	0.2318	0	1	10.0456	5.8431	3.8714	2.7950	2.4366	2.1583	1.8023	1.5929	1.3979	1.0162
γ _W	0.2318	-1	-1	7.8316	5.0776	3.6342	2.7491	2.3826	2.1196	1.7985	1.5870	1.3976	1.0092
γ _W	0.2318	-1	0	8.1641	5.2423	3.7109	2.7752	2.4180	2.1523	1.7982	1.5862	1.3954	1.0083
γ _W	0.2318	-1	1	8.2116	5.3073	3.7493	2.8247	2.4624	2.1763	1.7858	1.5832	1.3764	0.9843
γ _W	0.3642	1	-1	4.7035	3.3753	2.6407	2.2302	2.0948	1.9478	1.6718	1.4045	1.1885	0.8111
γ _W	0.3642	1	0	4.8006	3.4622	2.6945	2.2696	2.0881	1.9310	1.6656	1.3894	1.1667	0.7973
γ _W	0.3642	1	1	4.8089	3.4944	2.7333	2.2832	2.1076	1.9306	1.6627	1.3863	1.1660	0.7890
γ _W	0.3642	0	-1	4.3426	3.3719	2.7303	2.3116	2.0674	1.9034	1.6567	1.3758	1.1568	0.7733
γ _W	0.3642	0	0	4.4250	3.4169	2.7451	2.3080	2.1664	1.9020	1.6469	1.3707	1.1452	0.7468
γ _W	0.3642	0	1	4.4965	3.4506	2.7823	2.3241	2.1097	1.8987	1.6444	1.3689	1.1310	0.7443
γ _W	0.3642	-1	-1	4.1015	3.3213	2.7414	2.2925	2.0987	1.8925	1.6434	1.3676	1.1299	0.7405
γ _W	0.3642	-1	0	4.1735	3.3508	2.7577	2.3025	2.1071	1.8869	1.6039	1.3651	1.1289	0.7263
γ _W	0.3642	-1	1	4.2102	3.3762	2.7977	2.3023	2.1199	1.8711	1.5984	1.3393	1.1169	0.7016
PW0	0.2318	1	-1	0.9928	0.9428	0.8219	0.6291	0.5044	0.3583	0.1907	0.1176	0.0790	0.0408
PW0	0.2318	1	0	0.9885	0.9373	0.8234	0.6361	0.5116	0.3651	0.1946	0.1209	0.0825	0.0420
PW0	0.2318	1	1	0.9849	0.9319	0.8227	0.6424	0.5196	0.3735	0.2014	0.1241	0.0848	0.0437
PW0	0.2318	0	-1	0.9763	0.9221	0.8179	0.6375	0.5136	0.3660	0.1934	0.1213	0.0808	0.0421
PW0	0.2318	0	0	0.9747	0.9202	0.8155	0.6391	0.5176	0.3721	0.2004	0.1252	0.0853	0.0441
PW0	0.2318	0	1	0.9728	0.9184	0.8137	0.6403	0.5212	0.3775	0.2059	0.1271	0.0882	0.0448
PW0	0.2318	-1	-1	0.9599	0.9033	0.8064	0.6421	0.5249	0.3790	0.2020	0.1236	0.0852	0.0425
PW0	0.2318	-1	0	0.9594	0.9024	0.8046	0.6407	0.5243	0.3797	0.2055	0.1274	0.0866	0.0436
PW0	0.2318	-1	1	0.9589	0.9016	0.8030	0.6394	0.5239	0.3816	0.2099	0.1310	0.0879	0.0458
PW0	0.3642	1	-1	0.8845	0.7751	0.6326	0.4577	0.3559	0.2467	0.1289	0.0793	0.0539	0.0287
PW0	0.3642	1	0	0.8830	0.7775	0.6373	0.4623	0.3642	0.2513	0.1323	0.0851	0.0531	0.0317
PW0	0.3642	1	1	0.8843	0.7795	0.6395	0.4702	0.3640	0.2569	0.1400	0.0789	0.0624	0.0333
PW0	0.3642	0	-1	0.8642	0.7701	0.6368	0.4626	0.3579	0.2464	0.1252	0.0748	0.0483	0.0244
PW0	0.3642	0	0	0.8628	0.7690	0.6377	0.4658	0.3659	0.2504	0.1282	0.0809	0.0466	0.0261
PW0	0.3642	0	1	0.8639	0.7685	0.6360	0.4709	0.3638	0.2538	0.1345	0.0750	0.0560	0.0257
PW0	0.3642	-1	-1	0.8503	0.7641	0.6413	0.4735	0.3702	0.2566	0.1331	0.0801	0.0542	0.0284
PW0	0.3642	-1	0	0.8489	0.7632	0.6404	0.4740	0.3753	0.2589	0.1346	0.0858	0.0518	0.0289
PW0	0.3642	-1	1	0.8502	0.7624	0.6380	0.4769	0.3712	0.2617	0.1403	0.0794	0.0606	0.0280

				ρ
Response	CV	γ _A	γ _S	0.50	0.60	0.70	0.80	0.85	0.90	0.95	0.97	0.98	0.99
W	0.2318	-1	1	a	a	a	a	a	a	a	a	a	a
W	0.2318	-1	0	b	b	b	b	b	b	ab	a	a	a
W	0.2318	-1	-1	c	c	c	c	d	d	bc	a	a	a
W	0.2318	0	1	d	d	d	d	c	c	bcd	a	a	a
W	0.2318	0	0	e	e	e	e	e	d	cd	a	a	a
W	0.2318	0	-1	f	f	f	f	g	e	bcd	a	a	a
W	0.2318	1	1	g	g	g	g	f	d	cd	a	a	a
W	0.2318	1	0	h	h	h	h	g	e	cd	a	a	a
W	0.2318	1	-1	i	i	i	i	h	f	d	a	a	a
W	0.3642	-1	1	a	a	a	a	a	a	ab	a	a	a
W	0.3642	-1	0	b	b	b	b	b	ab	a	a	a	a
W	0.3642	-1	-1	c	c	c	c	bc	bcd	b	a	a	a
W	0.3642	0	1	d	d	d	c	b	bc	b	a	a	a
W	0.3642	0	0	e	e	e	d	cd	bcd	ab	a	a	a
W	0.3642	0	-1	f	f	f	e	de	cd	b	a	a	a
W	0.3642	1	1	g	g	g	e	ef	cd	b	a	a	a
W	0.3642	1	0	h	h	h	f	fg	de	b	a	a	a
W	0.3642	1	-1	i	i	i	g	g	e	b	a	a	a
γ _W	0.2318	1	-1	a	a	c	d	c	ab	a	a	a	a
γ _W	0.2318	1	0	b	a	a	c	b	b	a	a	a	a
γ _W	0.2318	1	1	c	b	ab	b	b	ab	a	a	a	a
γ _W	0.2318	0	-1	e	d	c	c	b	ab	a	a	a	a
γ _W	0.2318	0	0	d	c	b	b	ab	ab	a	a	a	a
γ _W	0.2318	0	1	e	c	ab	ab	ab	ab	a	a	a	a
γ _W	0.2318	-1	-1	g	g	d	b	b	ab	a	a	a	a
γ _W	0.2318	-1	0	f	f	c	b	ab	ab	a	a	a	a
γ _W	0.2318	-1	1	f	e	c	a	a	a	a	a	a	a
γ _W	0.3642	1	-1	b	d	d	b	b	a	a	a	a	a
γ _W	0.3642	1	0	a	ab	c	ab	b	a	a	a	a	a
γ _W	0.3642	1	1	a	a	bc	ab	ab	a	a	a	a	a
γ _W	0.3642	0	-1	e	d	bc	a	b	a	a	a	a	a
γ _W	0.3642	0	0	d	c	bc	a	a	a	a	a	a	a
γ _W	0.3642	0	1	c	bc	ab	a	ab	a	a	a	a	a
γ _W	0.3642	-1	-1	g	e	bc	a	ab	a	a	a	a	a
γ _W	0.3642	-1	0	f	de	ab	a	ab	a	a	a	a	a
γ _W	0.3642	-1	1	f	d	a	a	ab	a	a	a	a	a
PW0	0.2318	1	-1	a	a	b	f	f	f	e	f	f	c
PW0	0.2318	1	0	b	b	a	e	e	e	d	e	de	bc
PW0	0.2318	1	1	c	c	ab	a	b	d	c	c	cd	abc
PW0	0.2318	0	-1	d	d	c	e	d	e	d	de	ef	bc
PW0	0.2318	0	0	e	e	d	d	c	d	c	bc	bcd	ab
PW0	0.2318	0	1	f	f	e	cd	b	c	b	b	a	ab
PW0	0.2318	-1	-1	g	g	f	ab	a	bc	c	cd	bcd	bc
PW0	0.2318	-1	0	h	h	g	bc	a	ab	b	b	abc	abc
PW0	0.2318	-1	1	i	i	h	cd	a	a	a	a	ab	a
PW0	0.3642	1	-1	a	c	e	f	d	e	c	b	bc	bc
PW0	0.3642	1	0	b	b	cd	e	c	d	b	a	bc	a
PW0	0.3642	1	1	a	a	b	c	c	b	a	b	a	a
PW0	0.3642	0	-1	c	d	cd	e	d	e	d	c	d	e
PW0	0.3642	0	0	d	e	c	d	c	d	c	b	d	cde
PW0	0.3642	0	1	c	e	d	c	c	c	b	c	b	de
PW0	0.3642	-1	-1	e	f	a	b	b	b	b	b	bc	bc
PW0	0.3642	-1	0	f	fg	ab	b	a	b	b	a	c	b
PW0	0.3642	-1	1	e	g	c	a	b	a	a	b	a	bcd

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