## 5 Congestion Mitigation for Bottlenecked Secondary User  
We have shown that the bottlenecked SU is a little more inclined to be a congested SU node during the slot \(\tau_{rp}\) due to its buffer overflow under the scenario of the hop-by-hop fluid flows of the data sequence of the SSR injected from \(|\mathcal{N}_{IT}|+|\mathcal{N}_{ET}|\) IT and MT SSNs to this bottlenecked SU. We use the buffer size \(B_{b}\) to denote the buffer saturation value of bottlenecked SU \(b\). Recall that the amount of data traffic \(\vartheta_{b}(t_{0}^{\prime})\) in buffer of SU \(b\) at time \(t_{0}^{\prime}\) evolves according to Equation (2) for the given slot \(\tau_{rp}\). As depicted in Figure 2(a), the buffer of bottlenecked SU \(b\) is composed of two buffer segments, i.e., the forward buffer that holds data traffic injected from upstream SUs denoted by \(\vartheta_{b}^{F}\big{(}\tau_{rp}\big{)}\), and the internal buffer that stores the data sequence of SSR transmitted from IT and MT SSNs denoted by \(\vartheta_{b}^{I}\big{(}\tau_{rp}\big{)}\). Normally, there exist idle segments within the forward buffer or the internal buffer of bottlenecked SU \(b\) when \(\vartheta_{b}\big{(}t_{0}^{\prime}+\tau_{rp}\big{)}<B_{b}\). This phenomenon is referred to the normal status where the offered data load does not exceed available buffer capacity of bottleneck SU \(b\) because of its higher data rate to deliver the amount of data traffic to other SUs and remove the amount of the data sequence of SSR during the slot \(\tau_{rp}\). However, congestion in bottlenecked SU \(b\) will occur when the offered data load exceeds its available buffer capacity due to buffer overflow imposed by the data load involving the data sequence of the SSR injected from IT and MT SSNs together with the data traffic from upstream SUs. We assume that the congestion detection information of bottlenecked SU \(b\) can be transferred back to the \(m\)-th SSN by means of a hop-by-hop backpressure signal via the CCC form bottlenecked SU \(b\) to the \(m\)-th SSN. As a result, bottlenecked SU \(b\) is said to be a congested SU if and only if the amount of its current data traffic \(\vartheta_{b}\big{(}t_{0}^{\prime}+\tau_{rp}\big{)}\geq B_{b}\) during the slot \(\tau_{rp}\), as shown in Figure 3b. We further assume that the \(m\)-th SSN has the data sequence of the SSR with \(\Xi_{m}\) bits to transmit at time \(t\in\big{[}t_{0}^{\prime},t_{0}^{\prime}+\tau_{rp}\big{]}\). According to [24], the data sequence of SSR with \(\Xi_{m}\) bits to transmit from the \(m\)-th SSN to bottlenecked SU \(b\) during the slot \(\tau_{rp}\) under the transmit power \(p_{m}(t)\) can be approximately expressed as follows based on channel capacity \(C_{m\to b}\) given by Equation (4):  
\[\Xi_{m}=\tau_{rp}W\log_{2}\Bigg{(}1+\frac{p_{m}(t)K|h_{m\to b}|^{2}}{N_{0}W} \Bigg{)} \tag{38}\]  
Clearly, \(\Xi_{m}\) depends on channel capacity \(C_{m\to b}\) and is also a function of the transmit power \(p_{m}(t)\). For ease of exposition, we use \(\Xi_{m}(p_{m}(t))\) to denote the amount of bits of the data sequence of SSR transmitted from the \(m\)-th SSN to bottlenecked SU \(b\) under transmit power \(p_{m}(t)\). Therefore, the aggregated amount of bits of the data sequence of SSR from all \(|\mathcal{N}_{IT}|+|\mathcal{N}_{ET}|\) IT and MT SSNs to bottleneck SU \(b\) during the slot \(\tau_{rp}\) under transmit power \(p_{m}(t)\) is given as \(\sum_{m\in\mathcal{N}}\Xi_{m}(p_{m}(t))\), for \(\mathcal{N}=\mathcal{N}_{IT}\cup\mathcal{N}_{MT}\). Recall that the internal buffer of bottlenecked SU \(b\) is used to store the amount of the data sequence of SSR transmitted from SSNs denoted by \(\vartheta_{b}^{l}\big{(}\tau_{rp}\big{)}\) during the slot \(\tau_{rp}\) by using  
Figure 3: Illustration of buffer based congestion detection at bottlenecked secondary user (SU) \(b\). (a) Normal status without buffer overflow; (b) Congestion occurrence due to buffer overflow. Equation (2).