# QoS-Aware Downlink Traffic Scheduling for Cellular Networks with Dual Connectivity
## 5 Proposed QoS eNB Scheduling (QED) Method  
In this section, we introduce the proposed MAC scheduling method, named QED, which aims to prevent GBR packets to be dropped. The basic idea of QED is that if a GBR packet satisfies the designed criteria (described later), this packet will be moved to a _guarantee to transmit_ (_GTT_) set. For those packets in the GTT set, the QED will decide their transmit sequences. Then, when assigning RBs, the QED first allocates RBs to serve packets in GTT. After processing packets in GTT, if there are remaining RBs, the QED allocates RBs to the other data flows in the system. In the following, we describe the designed QED method in detail. In every TTI, the QED first discards the expired packets and then removes them from the system. The QED then checks the existing GBR data flows. For a GBR data flow, the QED first selects the packets whose remaining transmission times are less than \(\hat{T}_{n}\) TTIs. For each of the selected packets, the QED performs the following operations: (Assume that the QED is now processing the packet \(p\), which belongs to UE \(u_{i}\) and the corresponding bearer \(b_{i}\).) First, the QED calculates \(p\)'s needed transmission time and remaining transmission time as follows. * \(p\)'s needed transmission time \(\mathcal{E}(p)\): Let the packet length of \(p\) be \(L_{p}\) and \(\hat{O}(u)\) be the estimated transmission capability (defined in Section 4). The QED estimates \(p\)'s needed transmission time as: \[\mathcal{E}(p)=\frac{L_{p}}{\hat{O}(u_{i})}.\]
* \(p\)'s remaining transmission time \(\mathcal{R}(p)\): Let \(\mathcal{W}(p)\) be the \(p\)'s waiting time in the system. Recall that \(\mathcal{Q}_{d}(b_{i})\) is the corresponding delay constraint of the bearer \(b_{i}\) (defined in Section 3). The QED calculates \(p\)'s remaining transmission time as: \[\mathcal{R}(p)=\mathcal{Q}_{d}(b_{i})-\mathcal{W}(p).\]  
Note that \(\mathcal{W}(p)\) can be derived by subtracting the current time with the time instant that the packet \(p\) arrived at the PDCP layer of the MeNB. Based on the definitions of \(\mathcal{E}(p)\) and \(\mathcal{R}(p)\), if \(\mathcal{E}(p)<\mathcal{R}(p)\), this implies that the packet \(p\) cannot be processed on time and \(p\) will not be scheduled. Otherwise, the packet \(p\) will be put into the GTT set if the packet \(p\) satisfies the following inequality:  
\[\frac{\mathcal{R}(p)}{\mathcal{Q}_{d}(b_{i})}\times\frac{1}{-\log \mathcal{Q}_{l}(b_{i})}\leq\frac{\mathcal{E}(p)}{\mathcal{R}(p)}\times\frac{1 }{-\log\mathcal{L}(b_{i})} \tag{2}\]  
In Equation (2), the \(\mathcal{L}(b_{i})\) represents the measured packet drop ratio of bearer \(b_{i}\), and \(\mathcal{Q}_{l}(b_{i})\) represents the allowable packet drop ratio of \(b_{i}\) (defined in Section 3). Note that \(\mathcal{L}(b_{i})\) may change over time. Since loss or drop ratios may be small, we use the logarithm to force \(\mathcal{Q}_{l}(b_{i})\) and \(\mathcal{L}(b_{i})\) to be positive values. Next, we explain the rationale of Equation (2). The design of Equation (2) is a dynamic threshold for the packet \(p\). On the left side of Equation (2), the \(\mathcal{Q}_{d}(b_{i})\) and \(\mathcal{Q}_{l}(b_{i})\) are fixed values. The left side of Equation (2) will be smaller if the remaining transmission of \(p\), i.e., \(\mathcal{R}(p)\) becomes smaller, and the packet \(p\) will have more chances to enter GTT. Besides, if the \(\mathcal{Q}_{l}(b_{i})\) is smaller, the loss ratio requirement is more critical, and thus, the packet \(p\) may enter GTT more easily. Moreover, on the right side of Equation (2), if \(\mathcal{R}(p)\) becomes smaller, this equation allows the packet \(p\) to have a higher probability to enter GTT. When the needed transmission time \(\mathcal{E}(p)\) is higher, there may be two possibilities: (i) the size of \(p\) is larger or (ii) the signal quality of destination UE becomes weak. Thus, when \(\mathcal{E}(p)\) is higher, the packet \(p\) can have more chances to enter GTT.