Skip to main content

Table 2 Formulation of ILP

From: SLA-constrained service selection for minimizing costs of providing composite cloud services under stochastic runtime performance

Goal

\(\hbox{min} \left( {\sum\nolimits_{{i \in I_{s} }} {\sum\nolimits_{{j \in J_{s} }} {{\text{c}}_{ij} x_{ij} } + \sum\nolimits_{{l \in L_{AND} }} {\sum\nolimits_{{i \in I_{l} }} {\sum\nolimits_{{j \in J_{si} }} {c_{ij} x_{ij} + cost} } } } } \right)\)

Conditions

\(\sum\nolimits_{{i \in I_{s} }} {\sum\nolimits_{{j \in J_{s} }} {t_{ij} x_{ij} + tim{\text{e}}1 + {\text{time}}2 \le {\text{SLA}}} }\)

\(\forall {\text{l}} \in L_{AND} \sum\nolimits_{{i \in I_{l} }} {\sum\nolimits_{{j \in J_{si} }} {t_{ij} x_{ij} \le time1} }\)

\(\forall {\text{l}} \in L_{XOR} \sum\nolimits_{{i \in I_{l} }} {\sum\nolimits_{{j \in J_{si} }} {t_{ij} x_{ij} \le time2} }\)

\(\forall {\text{l}} \in L_{XOR} \sum\nolimits_{{i \in I_{l} }} {\sum\nolimits_{{j \in J_{si} }} {C_{ij} x_{ij} \le cost} }\)

\(\sum\nolimits_{{j \in J_{i} }} {x_{ij} = 1}\)