Stochastic hierarchical multiobjective routing model in MPLS networks with two service classes: an experimental study on imprecision and uncertainty issues

Girão-Silva, Rita; Craveirinha, José; Clímaco, João

doi:10.1186/2195-5468-2-3

Journal of Uncertainty Analysis and Applications

Table 7 Average o.f. values for simulation of the static and the dynamic routing model

From: Stochastic hierarchical multiobjective routing model in MPLS networks with two service classes: an experimental study on imprecision and uncertainty issues

α	O.f.	Initial	Analytical	Static routing	Dynamic routing model results
		solution	results	model results	τ=10 m	τ=20 m	τ=30 m
	W _Q	20,859.85	21,690.16 ^a	21,690.52 ± 37.22	21,688.67 ± 37.15	21,693.07 ± 37.19	21,693.46 ± 37.81
	B _{M m\|Q}	0.110	0.00545	0.00619 ± 0.00119	0.00713 ± 0.000937	0.00591 ± 0.000643	0.00574 ± 0.00133
	B _{m 1\|Q}	0.110	0.00545	0.00619 ± 0.00119	0.00713 ± 0.000937	0.00591 ± 0.000643	0.00574 ± 0.00133
	B _{m 2\|Q}	0.0689	0.000465	0.000828 ± 0.000124	0.000944 ± 0.000213	0.000849 ± 0.000140	0.000816 ± 0.000193
0.0	B _{m 3\|Q}	0.00308	0.000275	0.000288 ± 2.64·10⁻⁵	0.000141 ± 2.11·10⁻⁵	0.000125 ± 2.68·10⁻⁵	0.000155 ± 2.85·10⁻⁵
	B _{M 1\|Q}	0.555	0.0613	0.0771 ± 0.0117	0.0723 ± 0.0282	0.0520 ± 0.00627	0.0509 ± 0.0214
	B _{M 2\|Q}	0.378	0.00699	0.00794 ± 0.00174	0.00522 ± 0.00139	0.00475 ± 0.00129	0.00430 ± 0.000795
	B _{M 3\|Q}	0.0190	0.00287	0.00288 ± 0.000312	0.00126 ± 0.000142	0.00103 ± 0.000274	0.000909 ± 0.000228
	W _B	6,738.68	7,158.14	7,161.10 ± 11.67	7,205.94 ± 19.96	7,172.37 ± 16.34	7,173.99 ± 11.71
	W _Q	17,611.81	17,685.89 ^b	17,683.53 ± 15.54	17,683.54 ± 15.54	17,683.51 ± 15.56	17,683.51 ± 15.47
	B _{M m\|Q}	0.0160	1.04 ·10⁻⁵	8.59 ·10⁻⁷ ± 8.23·10⁻⁷	0	2.15 ·10⁻⁵ ± 5.52·10⁻⁵	2.09 ·10⁻⁵ ± 5.36·10⁻⁵
	B _{m 1\|Q}	0.0160	1.04 ·10⁻⁵	0	0	2.15 ·10⁻⁵ ± 5.52·10⁻⁵	2.09 ·10⁻⁵ ± 5.36·10⁻⁵
	B _{m 2\|Q}	0.00926	7.2 ·10⁻⁹	0	0	0	0
0.5	B _{m 3\|Q}	0.000371	6.25 ·10⁻⁷	8.59 ·10⁻⁷ ± 8.23·10⁻⁷	0	5.64 ·10⁻⁸ ± 1.27·10⁻⁷	1.38 ·10⁻⁷ ± 3.00·10⁻⁷
	B _{M 1\|Q}	0.147	0.000128	0	0	0.00292 ± 0.00751	0.000891 ± 0.00229
	B _{M 2\|Q}	0.0866	4.45 ·10⁻⁷	0	0	0	0
	B _{M 3\|Q}	0.00353	4.46 ·10⁻⁶	2.24 ·10⁻⁵ ± 1.72·10⁻⁵	0	2.26 ·10⁻⁶ ± 4.94·10⁻⁶	5.68 ·10⁻⁶ ± 9.32·10⁻⁶
	W _B	5,247.65	5,296.57	5,297.18 ± 12.84	5,297.31 ± 12.80	5,297.33 ± 12.79	5,297.23 ± 12.86
	W _Q	16,025.69	16,028.14 ^c	16,077.61 ± 15.03	16,077.61 ± 15.03	16,077.61 ± 15.03	16,077.61 ± 15.03
	B _{M m\|Q}	0.000577	5 ·10⁻¹⁰	0	0	0	0
	B _{m 1\|Q}	0.000577	5 ·10⁻¹⁰	0	0	0	0
	B _{m 2\|Q}	0.000334	<1·10⁻¹⁰	0	0	0	0
1.0	B _{m 3\|Q}	1.16 ·10⁻⁵	<1·10⁻¹⁰	0	0	0	0
	B _{M 1\|Q}	0.00650	1.27 ·10⁻⁸	0	0	0	0
	B _{M 2\|Q}	0.00347	<1·10⁻¹⁰	0	0	0	0
	B _{M 3\|Q}	0.000123	2 ·10⁻¹⁰	0	0	0	0
	W _B	3,354.76	3,355.88	3,350.97 ± 24.92	3,350.97 ± 24.92	3,350.97 ± 24.92	3,350.97 ± 24.92

Average o.f. values, and 95% confidence intervals, for simulation of the static (with a warm-up time of 8 h) and the dynamic routing model (with t₀ = t₁ = 4 h, update period τ and b = 0.3), a total simulation time of 48 h on the test network $G$ , for different values of α, when the HMOR-S2 is used to update the routing plan. ^a99.90%; ^b100%; ^c99.75% of the approximate ideal values for the QoS flows revenue, W_Q^ideal, from the data in [25].

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