Table 1: Nomenclature.

Sets and indicesDescription

,, and Number of applications/demands, DCs, and time slot sets
m, iIndex of applications, data centers,

ParametersDescription

Positive weighting factors for real-time/elastic applications
Static power consumption for data center i
,Maximum delay for app. m in , maximum number of user demand in data center i
I, TNumber of data centers, time slots
Mean service time for application m in data center i
Positive weighting parameters
Real-time/elastic probability distribution function
Penalty function

VariablesDescription

Number of real-time/elastic connections for application m at time slot t
Number of real-time/elastic application m connections served by at time slot t
Power amount bought/sold from/to electrical grid at slot t
Power price bought/sold from/to electrical grid at slot t
Amount of renewable generation at slot t
Mean power amount bought/sold from/to electrical grid at slot t
Mean power price bought/sold from/to electrical grid at slot t
Mean renewable generation at slot t
Arrival/departure processes for queue at slot t
th queue backlog at time slot t
Virtual queue j backlog at time slot t,