Graph Notations

Definition

$G\left(V,E\right)$

VSP core network

B

Set of all border (PE) nodes of the core network

$C_u,P_u$

Set of CE/PE nodes of VPN u, here $P_u\subseteq B$

$C_{u,b}$

Set of VPNs hosted by border node b

$G_{u,\mathcal{l}}\left(V_u,E_u\right)$

Abstract topology of VPN u of topology type ℓ

$T{S}_u$

TA SLA parameter set for VPN u

$T_u/R_u$

Abstract topology type subscription/Refresh interval of TA for VPN u

$S\left(V_u,E_u\right)$

Partition subgraph for VPN u

$t_{ij}$ (or $t\left(e\right)$ )

Total capacity of edge $\left(i,j\right)$ or e

$r_{ij}$ (or $r\left(e\right)$ )

Residual capacity of edge $\left(i,j\right)$ or e

U

Set of all VPNs provided TA service

$U_b$

Set of VPNs hosted on node b

$Z\left(x,y\right)$

Set of VPNs common to border nodes x and y

K

Set of all commodities in a multicommodity formulation

$K_v$

Set of all source-destination border node pair commodity of VPN v

$f_{mc}\left(k\right)$

Flow of commodity k corresponding to multicommodity flow (MMCF) formulation

$x_{ij}^{uk}$

Resource partitioned on edge $\left(i,j\right)$ for VPN u for source-destination commodity k

$D\left(s_k,d_k\right)$

Demand corresponding to source-destination commodity k