Table 1 Terminology definition

V

Total number of task types

N

Number of task arrivals

n _i

Number of type-i task arrivals, where 0≤i≤V

M

Number of active servers in data center

S _j

Server j, where 1≤j≤M

B _i,j

Capacity of S _j to store type-i tasks

x _i,j

Number of task i assigned to S _j

μ _i,j

Average processing time of type-i task by S _j

τ _i,j

Average queueing delay of type-i tasks on S _j

w _i,j

Queue occupancy of type-i tasks at S _j

T _w

Average task response time

X _j

Schedule in which tasks are processed by S _j

ω

Weight vector

P _i,j

Power consumed by S _j to process a type-i task

E _i,j

Energy consumed by S _j to process a type-i task

E

Total server energy consumption in a data center