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Table 8 Annotation of sets and indexes used in mathematical model

From: Impact of service rates and base station switching granularity on energy consumption of cellular networks

Set description

Set index

Set structure

Maximum number of set elements

Set of all CSs: J

j

j∈J = {1, …, m}

m

Set of all test points (TCs): I

i

i∈I = {1, …, n}

n

Set of all Tx power levels: K

k

k∈K = {1, …, l}

l

Set of all time periods: H

t

t∈H = {1, …, p}

p

Set of all service types (voice/data) offered to users

z

z∈Z = {1, …, q}

q

Set of all measurement points (MPs): S

s

s∈S = {1, …, u}

u

Subsets of Tx power levels detected for (i,j) combination: K(ij)

k

k∈K = {1,…,l i,j }

l i,j

Subsets of TCs covered with (j,k) combination: I(jk)

i

i∈I(jk) = {1, …, n j,k }

n j,k

Subsets of TCs covered with (j,k,r) combination: I(jkr)

i

i∈I(jkr) = {1, …, n j,k,r }

n j,k,r

Subset of CSs allocated at points of basic grid (BG): J*

j

j∈J*= {1, …, m BG }

m BG

Sets of CS-configuration pairs covering TC i: JK(i) Indexing of JK(i) set members (pairs): b(i)

j b ,k b h

j b ,k b ∈JK(i) = {(j 1 ,k 1 ),…,(j B(i) ,k B(i) )} h∈b(i) = {1,…, B(i)}

j B(i) , k B(i) B(i)

Subsets of TCs covered with (j,k) combination in time period t: I(jkt)

i

i∈I(jkt) = {1, …, n j,k,t }

n j,k,t

Subsets of TCs covered with (j,k,r) combination in time period t: I(jkrt)

i

i∈I(jkrt) = {1, …, n j,k,r,t }

n j,k,r,t