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Table 1 Basic notations used in the paper

From: Resource allocation in a generalized LTE air interface virtualization framework exploiting user behavior

v

VO index

V

total VO number

\(\mathcal {S}\)

cooperative VO set

\(\mathcal {V}\)

total VO set

n

data BS index

N

total data BS number

k

PRB index

K v

allocated PRBs number of VO#v

m

user index

M v

user number of VO#v

\({\mathcal {M}}_{v}\)

user set of VO#v

d v

average user traffic rate demand of VO#v

b v

minimum PRB number to operate VO#v

c v

additional claimed PRB number of VO#v

Y

estimated total PRB number to support the whole service area

Φ

Shapley value

y

characteristic function of coalition

\({K_{n}^{\max }}\)

total PRB number of BS n

\(P_{n}^{\max }\)

transmission power budget of BS n

\(R_{{k,n}}^{{m,v}}\)

data rate on PRB k in VO#v of BS n

\(g_{{k,n}}^{{m,v}}\)

user channel condition on PRB k in VO#v of BS n

\(a_{{k,n}}^{{m,v}}\)

PRB allocation indicator

\(p_{{k,n}}^{{m,v}}\)

transmit power on PRB k in VO#v of BS n

P cn

circuit power of BS n

η

power amplifier inefficiency

R tot

total data rate

P tot

total power assumption