\({\mathcal {S}}\) | Set of base stations (BSs), with index \(s \in \left \{1,..., \mathbf {s} \stackrel {\triangle }{=} |{\mathcal {S}}| \right \}\) |
\({\mathcal {P}}\) | Set of power levels (PLs), with index \(p \in \left \{1,..., \mathbf {p} \stackrel {\triangle }{=} |{\mathcal {P}}|\right \}\) |
\({\mathcal {U}}\) | Set of user equipments (UEs), with index \(u \in \left \{1,..., \mathbf {u} \stackrel {\triangle }{=} |{\mathcal {U}}|\right \}\) |
\({\mathcal {C}}\) | Set of component carriers (CCs), with index \(c \in \left \{1,..., \mathbf {c} \stackrel {\triangle }{=} |{\mathcal {C}}|\right \}\) |
\({\mathcal {B}}\) | Set of resource blocks (RBs) per CC, with index \(b \in \left \{1,..., \mathbf {b} \stackrel {\triangle }{=} |{\mathcal {B}}|\right \}\) |
\({\mathcal {L}}\) | Set of modulation and coding schemes (MCSs) per RB, with index \(l \in \left \{1,..., \mathbf {l} \stackrel {\triangle }{=} |{\mathcal {L}}| \right \}\) |
\({\mathcal {N}}_{s}\) | Set of neighboring cells of cell s, which may interfere with s when given the same RBs |
f _{ s} | Maximum number of CCs able to be used by cell s |
k _{ u} | Maximum number of CCs able to be assigned to UE u |
W | Balance weight |
Ψ _{ u,c,b,s,p} | Index of the highest-rate MCS used by UE u on RB b of CC c at PL p of cell s |
r _{ l} | Achieved transmission rate of an RB on MCS l |
\(\underline {e}_{{u,c,b,l,s,p}}\) | Binary variable showing if RB b of CC c on MCS l at PL p of cell s is assigned to UE u |
\(v(\underline {e})\) | Achieved transmission rate with the allocation indicated by \(\underline {e}\) |
\(\hat {\underline {e}}, \hat {\underline {e}}_{1},..., \hat {\underline {e}}_{10}\) and \(\tilde {\underline {e}}_{4}, \tilde {\underline {e}}_{5}\) | Binary variables similar to \(\underline {e}\) with certain elements to be varied while fixing the others, for the different scenarios shown in Section 3.2 and Eqs. (5)–(12), (14), (16), and (18)–(21) |
\(\hat {\underline {y}}_{1},..., \hat {\underline {y}}_{5}\) | Auxiliary variables for the different scenarios shown in Eqs. (13), (15), (17), and (18)–(21) |
\(P_{\text {tot}}(t), \overline {P}_{\text {tot}}, P_{\text {max}}\) | Total power consumption at time t, its limit of the time-average expectation, and the maximum transmit power |
\(R_{\text {tot}}(t), \overline {R}_{\text {tot}}\) | Total data rate at time t, and its limit of the time-average expectation |
\(Q(t), \overline {Q}\) | Data queue length at time t, and its limit of the time-average expectation |
Z_{u}(t),H_{u}(t) | Virtual queue lengths at time t corresponding to (27-C5) and (27-C6), respectively, for UE u |
\(A_{u}(t), A_{u}^{\text {max}}, \lambda _{u}\) | Traffic arrival of UE u at time t, its maximum value allowed, and arrival rate of UE u |
R_{u}(t),μ_{u}(t) | Admitted traffic of UE u, and link (service) rate of UE u, at time t |
\(\overline {r}_{u}\) | Time-average throughput of UE u |
η_{EE},ηEEreq | Energy efficiency and its requirement |