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Table 1 The used notations

From: A distributed controller for a virtualized router

Symbol

Description

\(S\)

Set of hosted slices, e.g., \(S={s_{1}, s_{2}, s_{3}, s_{4}}\)

\({\text{ LR}}_{s}\)

Set of line-rates in the slice \(s\)

\(C\)

Set of cards with controlled resources, e.g., \(C=\{{\text{ LC}}_{1},{\text{ LC}}_{2}, {\text{ LC}}_{3}, SF\}\)

\(T_{s}\)

Tier of slice \(s \in S\), e.g., \(T_{s}=\{LC_{1},LC_{2}, SF\}\)

\(R\)

Set of all controlled resource types, e.g., \(R = \{{\text{ NP,} \text{ Memory}}\}\)

\(L_{c}\)

Set of slices sharing the resources of card \(c\), e.g., \(L_{1}=\{s_{1}, s_{2}\}\)

\({xr}_{s,r,c}^{l}\)

Requested fraction of resource type \(r\) in card \(c\) to be allocated to line-rate \(l\) in slice \(s\), \(0\le {xr}_{s,r,c}^{l}(k)\le 1\)

\({xr}_{s,r,c}\)

Requested fraction of resource type \(r\) in card \(c\) to be allocated to slice \(s\) (from all its line-rates), \(0\le {xr}_{s,r,c}(k)\le 1\)

\(xa_{s,r,c}\)

Actual fraction of resource type \(r\) in card \(c\) allocated to slice \(s\), \(0\le xa_{s,r,c}(k)\le 1\)

\(\tau _{s}\)

Target packet latency for slice \(s\) for a given time interval

\(t{s}\)

Measured average packet latency for slice \(s\) for a given time interval

\(y_{s}\)

Performance for slice \(s\) for a given time interval, where \({y}_{s}=\frac{\tau _{s}}{ t_{s}}\)

\(w_{s}\)

Priority weight for slice \(s\)

\(q\)

Stability factor in the slice controller