Table 2 Notation Summary
Notation | Description |
|---|---|
\(\mathcal {N}, N\) | Set and total number of subchannels, respectively |
\(\mathcal {M}, M\) | Set and total number of relays, respectively |
\(\mathcal {K}, K\) | Set and total number of users, respectively |
\(\mathcal {B}\) | Set of all the serving nodes, including the BS and relays |
\(\mathcal {K}_{m}\) | Set of users connected to node m |
\(\mathcal {Q}_{m}\) | Set of users that have a buffer in node m |
m(k) | Serving node of user k |
T | Duration of a time slot |
B | Bandwidth of a subchannel |
Γ k | SNR gap for user k |
\(e^{m}_{\textit {kn}}(t), x^{m}_{\textit {kn}}(t)\) | Channel gain-to-noise ratio and subchannel allocation indicator of subchannel n in time slot t, respectively, for the link of user k from node m |
\(r^{m}_{\textit {kn}}(t), \tilde {r}^{m}_{\textit {kn}}(t)\) | Achievable transmission rate and estimated achievable transmission rate on subchannel n in time slot t, respectively, for the link of user k from node m |
\({r^{m}_{k}}(t)\) | Total transmission rate on the link of user k from node m in time slot t |
\({p^{m}_{n}}(t)\) | Power used by node m on subchannel n in time slot t |
\(P_{m}(t), \hat {P}_{m}, P^{av}_{m}\) | Total power to be used in time slot t, peak power constraint and average power constraint, respectively, for node m |
\({L^{m}_{k}}, {Q^{m}_{k}}(t)\) | Capacity of MAC layer buffer of user k in node m and the queue size in it in time slot t, respectively |
\({a^{m}_{k}}(t)\) | Size of data arrived at the MAC layer buffer of user k in node m in time slot t |
\(\hat {a}\) | Upper bound of data admission into a buffer in the MAC layer of the BS |
J k ,Y k (t),A k (t) | Capacity, queue size and the arrived data size in time slot t, respectively, in the top layer buffer of user k in the BS |
\(\mathcal {U}(.), V\) | Utility function and the value coefficient for it, respectively |
γ k (t),G k (t) | Auxiliary variable corresponding to data admission of user k and its corresponding virtual queue size, respectively, in time slot t |
Z m (t),I | Virtual power queue size of node m in time slot t and the importance factor, respectively, corresponding to average power constraints |
\({\rho ^{m}_{k}},W_{e}\) | Indicator variable for the link of user k from node m and the extra weight, respectively, for providing fair data admission |
\(\tilde {N}_{m}, \hat {N}_{m}\) | Estimation of node m for its number of subchannels and the upper bound considered by the BS on the number of subchannels for node m, respectively |
\({D^{m}_{n}}, D^{m}\) | Average demand of relay m on subchannel n and average total demand of node m, respectively |
\(D^{0a}_{n}, D^{0a}\) | Average demand of the BS on subchannel n and average total demand of the BS, respectively, for type A time slot |
\(D^{0b}_{n}, D^{0b}\) | Average demand of the BS on subchannel n and average total demand of the BS, respectively, for type B time slot |
D A,D B | Total demand for type A and type B time slots, respectively |