# Estimation of the Achievable Performance of Mobile Ad Hoc Networks with Optimal Link State Routing
## 3 Results
### Evaluation Metrics and Performance Analysis in MANETs
#### 3.2.3 End-to-End Delay in Network Transmission  
End-to-end delay (ETED), also known as packet delay (PD) in network transmission, is influenced by various factors such as the number of nodes in the network, network topology, the number of active transmitting nodes, the number of receiving nodes, etc. This section analyzes the impact of these conditions on the delivery time of an IP packet from an end transmitting node to an end receiving node. To calculate the end-to-end delay, the following network scenarios were considered:  
1. Each node in the network generates its own packets and participates in packet transmission. It must transmit to some node a packet within the transmission route from any transmitter terminal node to any receiver terminal node. The maximum delay dependence on the number of nodes in this case is given using the expression \[T=2*\left(\frac{X}{R}\right)*\left(\frac{n}{2}\right)^{2}\] (6)  
\(T\)--time delay for delivering an IP packet;  
\(X\)--packet size including headers;  
\(R\)--speed between nodes;  
\(n\)--number of nodes participating in packet transmission. Delay calculations are performed for different quality of service values, such as 0.1 s, 0.4 s, and 1 s. Table 5 presents the dependencies of PD on the number of nodes for various transmission speeds (channel bandwidths). Figure 5: The dependence of the routing overhead on the number of network nodes. \begin{table}
\begin{tabular}{c c c c c} \hline \multirow{3}{*}{**Packet Delay, s**} & **Number of Nodes for Channels with Bandwidth 20 MHz** & **Number of Nodes for Channels with Bandwidth 20 MHz** & **Number of Channels with Bandwidth 20 MHz** & **Number of Nodes for Channels with Bandwidth 20 MHz** \\ \hline
0.1 & 36 & 47 & 76 & 106 \\ \hline
0.4 & 74 & 90 & 152 & 214 \\ \hline
1 & 112 & 150 & 242 & 338 \\ \end{tabular}
\end{table} 
Table 5: The dependencies of delay on the number of nodes for various transmission speeds (channel bandwidths). According to the data provided in the above tables, the number of relay nodes has a direct proportional effect on the number of nodes in the data transmission route. It is worth noting that the relay nodes should not transmit their own packets until the packet required for relay is delivered to the next two-hop neighbor along the route. 4. Multiple branches with the same number of nodes generate traffic for the gateway node: \[T_{1}=2*\left(\frac{X}{R}\right)*\left(\frac{n}{2}\right)^{2},\] (9) \[T_{2}=2*\left(\frac{X}{R}\right)*\left(\frac{\left(\left(\frac{n}{2}\right)^{2 }-\frac{n}{2}\right)}{2}+\left(\frac{n}{2}-1\right)\right),\] (10) \[T_{3}=2*\left(\frac{X}{R}\right)*\left(\frac{\left(\left(\frac{n}{3}\right)^{ 2}-\frac{n}{3}\right)}{2}+2*\left(\frac{n}{3},-,1\right)\right),\] (11)  
where  
\(T_{1}\)**--ETTD on packet delivery for a single network branch;  
\(T_{2}\)**--ETTD for packet delivery using two branches in the network;  
\(T_{3}\)**--ETTD for packet delivery using three branches in the network. Tables 9 and 10 demonstrate the impact of data transmission path branching on the packet delivery delay for the scenario where all nodes send packets to a single gateway node. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{4}{*}{**Packet Delay, s**} & **Number of Nodes** & **Number of Nodes** & **Number of Nodes for** & **Number of Nodes for** \\  & **Channels with** & **Channels with** & **Channels with** & **Channels with** \\  & **Bandwidth** & **Bandwidth** & **Bandwidth** & **Bandwidth** \\  & **80 MHz** & **80 MHz** & **80 MHz** & **80 MHz** \\  & **100\% of Nodes** & **75\% of Nodes** & **50\% of Nodes** & **25\% of Nodes** \\  & **Are** & **Are** & **Are** & **Are** \\  & **Transmitters** & **Transmitters** & **Transmitters** & **Transmitters** \\ \hline
0.1 & 52 & 62 & 76 & 100 \\ \hline
0.4 & 108 & 124 & 152 & 212 \\ \hline
1 & 170 & 196 & 244 & 340 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: The packet delay depending on the ratio of active and passive nodes.