Graph Notations


G ( V , E )

VSP core network


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 B

C u , b

Set of VPNs hosted by border node b

G u , l ( V u , E u )

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 ( V u , E u )

Partition subgraph for VPN u

t i j (or t ( e ) )

Total capacity of edge ( i , j ) or e

r i j (or r ( e ) )

Residual capacity of edge ( i , j ) or e


Set of all VPNs provided TA service

U b

Set of VPNs hosted on node b

Z ( x , y )

Set of VPNs common to border nodes x and y


Set of all commodities in a multicommodity formulation

K v

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

f m c ( k )

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

x i j u k

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

D ( s k , d k )

Demand corresponding to source-destination commodity k