## 3 E2E Latency and Distance Formulation  
The MFH networks require high multiplexing gains to efficiently implement the coordinated multiple point schemes in the C-RANs, which can be improved by increasing the aggregation of RRHs streams over the fronthaul links. However, the simultaneous transmissions of multiple eCPRI streams from the RRHs increased the E2E latencies to an unacceptable level, especially in the Ethernet networks [24; 25; 26]. Currently, the eCPRI-based Ethernet networks are gaining the attention of network operators and telecom vendors due to their low-cost and reconfigurability features, but achieving the required E2E latency is still a challenging issue [27] that requires further exploration. The E2E latency in such networks is the result of indeterministic and deterministic delays. The indeterministic delays such as the encapsulation delay \(Del_{Encp}\), the queuing delay \(Del_{Que}\), and the processing delay \(Del_{Proc}\) vary non-predictably in the EFBNs, while the deterministic delays such as the propagation delay \(Del_{Prop}\) and the transmission delay \(Del_{Tan}\) are pre-determined. The indeterministic delays such as the \(Del_{Encp}\) correspond to the mapping delay of the eCPRI IQ samples within the Ethernet payload at the bridging nodes before transmitting them over the outgoing links. In this study, the \(Del_{Encp}\) for 10-gigabit Ethernet networks is estimated between the 19 \(\upmu\)s to 2 \(\upmu\)s for mapping the eCPRI flows from line rate option 1 to 7 [10], respectively within the Ethernet payload size of 1500 bytes [26]. However, the \(Del_{Encp}\) only increases when the traffic flows first enter the Ethernet networks. Therefore, the \(Del_{Encp}\) values are only considered at the first level of the bridging nodes within which the RRHs are physically connected. The \(Del_{Que}\) is the length of time for which the packets of different streams wait in the buffers of the bridges before transmissions. When the \(f\)-th flow competes the \(g\)-th flow for simultaneous transmission over the \(n\)-th link, these flows are referred to as competitive flows [18]. Hence, the worst-case \(Del_{Que}\) experienced by the \(f\)-th flow over the \(n\)-th link is calculated from Equation (1):  
\[Del_{Que}=\frac{m\lambda}{C} \tag{1}\]  
where \(m\) is the maximum burst size of a flow, and \(C\) is the link capacity, while \(\lambda\) is the number of competitive flows [18]. The \(Del_{Proc}\) is the time that the switches take to decode the header of a packet to output them on the egress ports. The \(Del_{Proc}\) value, including the OpenFlow-based forwarding table lookup delays per bridging node experienced by the eCPRI streams, is estimated as 1.5 \(\upmu\)s for the considered networks [27]. Thus, the indeterministic delays \(Del_{induct}\) in the EFBNs along a route can be calculated from Equation (2), and the deterministic delays \(Del_{det}\) can be calculated from Equation (3). Here, the deterministic delays such as \(Del_{Prop}\) are a measure of the time required for a frame to propagate from one node to the other. The \(Del_{Prop}\) is equal to \(d/s\), where \(d\) is the link distance in km, and \(s\) is the signal propagation speed in copper (i.e., \(2\times 10^{8}\) ms\({}^{-1}\)). The \(Del_{Tan}\) is the time taken by the physical layer at the source to transmit the packets over the link. In this study, the \(Del_{Tan}\) is estimated as 1.2 \(\upmu\)s based on \(L/C\), where \(L\) is the data packet length (i.e., 1500 bytes), and \(C\) is the channel data rate (i.e., 10 Gbps).