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

SpringerPlus

Table 3 Worst-case aggregation functions for response time and costs

	Sequence	AND-block	XOR-block
Response time	\(\sum\nolimits_{{i \in I_{s} }} {\sum\nolimits_{{j \in J_{s} }} {t_{ij} x_{ij} } }\)	\(\mathop {\hbox{max} }\limits_{{l \in L_{AND} }} \sum\nolimits_{{i \in I_{l} }} {\sum\nolimits_{{j \in J_{si} }} {t_{ij} x_{ij} } }\)	\(\mathop {\hbox{max} }\limits_{{l \in L_{XOR} }} \mathop \sum \limits_{{i \in I_{l} }} \mathop \sum \limits_{{j \in J_{si} }} t_{ij} x_{ij}\)
Cost	\(\sum\nolimits_{{i \in I_{s} }} {\sum\nolimits_{{j \in J_{s} }} {c_{ij} x_{ij} } }\)	\(\sum\nolimits_{{l \in L_{AND} }} {\sum\nolimits_{{i \in I_{l} }} {\sum\nolimits_{{j \in J_{si} }} {c_{ij} x_{ij} } } }\)	\(\mathop {\hbox{max} }\limits_{{l \in L_{XOR} }} \sum\nolimits_{{i \in I_{l} }} {\sum\nolimits_{{j \in J_{si} }} {c_{ij} x_{ij} } }\)