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

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Table 4 Formulation of nonlinear programming

Goal	\({ \hbox{min} }\left( {\sum\nolimits_{{i \in I_{s} }} {\sum\nolimits_{{j \in J_{s} }} {{\text{c}}_{ij} x_{ij} } } + \sum\nolimits_{{l \in L_{AND} }} {\sum\nolimits_{{i \in I_{l} }} {\sum\nolimits_{{j \in J_{si} }} {c_{ij} x_{ij} } } } + \mathop {\hbox{max} }\limits_{{l \in L_{XOR} }} \sum\nolimits_{{i \in I_{l} }} {\sum\nolimits_{{j \in J_{si} }} {c_{ij} x_{ij} } } } \right)\)
Conditions	μ = mean response time of the entire composite cloud service calculated based on t _i,j and x _i,j
	σ = standard deviation of response time of the entire composite cloud service calculated based on ti,j and xi,j
	bound = the limit on response time specified in SLA
	\(k = \frac{bound - \mu }{\sigma }\)
	\(\frac{1}{{2k^{2} }} \le r\%\)
	\(\sum\nolimits_{{j \in J_{i} }} {x_{ij} = 1}\)