Table 1 Major notations

I

# of cloud clusters

T

# of time slots

L_i

# of cloudlets in cluster i

J_i

# of tasks in cluster i

D_i

Amount of electricity that i purchased from the grid

c_i

Asking price of E_i

E_i

Electricity reduction that cluster i can offer

P_i

Cluster i’s reward earned from the smart grid

z_i

Cluster i’s bid is accepted (1) or not (0)

E_all

EDR target

b_ij

Value of task j in cluster i

a_ij

The arrival time of task j in cluster i

d_ij

The deadline of task j in cluster i

w_ij

# of time slots required for task j in cluster i

λ_ij

The workload of task j in cluster i in one slot

τ_ij

# of slots that pass the deadline for task j in i

Z_l(t)

Marginal price of unit workload at cloudlet l at t

R_l(t)

The amount of allocated resources in cloudlet l at t

θ_i

Maintenance cost for cluster i

p

Local generation cost per unit

\(e_{l}^{t}\)

Energy consumption of cloudlet l at t

u_g

Total local generation

x_ij

Task j in cluster i is accepted (1) or not (0)

y_ijl(t)

Task j is allocated in cluster i’s l at t (1) or not (0)