## 4 Simulation Works and Discussion
### Single Sink with Multi-Radios in a Round Robin Fashion  
In our third scenario we simulate multiple radios, multiple channels with even number of multiple sending nodes; however we define the following equations for the simulation. The equations have the capability to simulate odd or even sending nodes to the sink node. Sending nodes in these equations are referred to as transmitter and the radio interface as receiver. Figure 8: Delivery ratio impact with multichannel multi-radios communication at sink node. Figure 9: Throughput impact with multichannel multi-radios communication at sink node. Even Transmitter to Receiver ratio: (TX: RX, TX = Even Positive Integer and RX \(\geq\) 2, TX \(\geq\) 4). Table 2 equations are containing only logical states (Active (1)/non-active (0)) values. When there are even senders to the sink node, each radio interface shares an even number of sending nodes and the radio interface remain on the assigned channel with all nodes getting an even turn in transmitting its data to the sink in a round robin fashion which is explained later in this section. Uneven Transmitter to Receive ratio: (TX: RX, TX = Uneven Positive Integer and RX \(\geq\) 2, TX \(\geq\) 5). The equations in Table 3 demonstrate when there are uneven numbers of sending nodes to the radio interfaces at the sink node. When there are uneven numbers of senders only one sender can transmit at a given time; a logical state is considered where the active node sending is equal to one and all other senders are set to zero. In the equation we define seven senders and the odd sender is assigned in a sequential order where it receives an equal opportunity to send in respect of which channel it is assigned; however the uneven node has the option to switch channels but not during its period of transmission. \begin{table}
\begin{tabular}{|l|l|l|} \hline
**Senders (TX = 6)** & **Receivers (RX = 3)** & **Equation** \\ \hline A = (TXA) & 1 = (RX1) & RX1 = TXA \(-\) TXD: where TXD = 0 \\ B = (TXB) & 2 = (RX2) & RX2 = TXB \(-\) TXE: where TXE = 0 \\ C = (TXC) & 3 = (RX3) & RX3 = TXC \(-\) TXF: where TXF = 0 \\ D = (TXD) & 1 = (RX1) & RX1 = TXD \(-\) TXA: where TXA = 0 \\ E = (TXE) & 2 = (RX2) & RX2 = TXE \(-\) TXB: where TXB = 0 \\ F = (TXF) & 3 = (RX3) & RX3 = TXF \(-\) TXC: where TXC = 0 \\ \hline \end{tabular}
\end{table} 
Table 2: Equation for even sender to multiple radios at sink node on 3 non-overlapping channels. \begin{table}
\begin{tabular}{|l|l|l|} \hline
**Senders (TX = 7)** & **Receivers (RX = 3)** & **Equation** \\ \hline A = (TXA) & 1 = (RX1) & RX1 = TXA \(-\) TXC - TXG1: where TXC = 0, TXG1 = 0 \\ B = (TXB) & 2 = (RX2) & RX2 = TXB \(-\) TXE - TXG2: where TXE = 0, TXG2 = 0 \\ C = (TXC) & 1 = (RX1) & RX1 = TXC \(-\) TXA - TXG1: where TXA = 0, TXG1 = 0 \\ D = (TXD) & 3 = (RX3) & RX3 = TXD \(-\) TXF - TXG3: where TXF = 0, TXG3 = 0 \\ E = (TXE) & 2 = (RX2) & RX2 = TXE \(-\) TXB - TXG2: where TXB = 0, TXG2 = 0 \\ F = (TXF) & 3 = (RX3) & RX3 = TXF \(-\) TXG3: where TXD = 0, TXG3 = 0 \\ G = (TXG) & *Sequential input to & RX1 = TXG1 \(-\) TXA \(-\) TXC: where TXA = 0, TXC = 0 \\  & receivers & RX2 = TXG2 \(-\) TXB \(-\) TXE: where TXB = 0, TXE = 0 \\  & \{1 + 2 + 3\} & RX3 = TXG3 \(-\) TXD \(-\) TXF: where TXD = 0, TXF = 0 \\  & N.B. TXG1, TXG2, and TXG3 are switchable \\  & communication link from sender G going to each of the receivers. Therefore sender G has the same number of switchable time period to receivers. When G switch to a channel, G waits its turn to transmit then has the option to switch to another channel. \begin{table}
\begin{tabular}{|l|l|l|} \hline
**Senders (TX = 6)** & **Receivers (RX = 3)** & **Equation** \\ \hline A = (TXA) & 1 = (RX1) & RX1 = TXA \(-\) TXD: where TXD = 0 \\ B = (TXB) & 2 = (RX2) & RX2 = TXB \(-\) TXE: where TXE = 0 \\ C = (TXC) & 3 = (RX3) & RX3 = TXC \(-\) TXF: where TXF = 0 \\ D = (TXD) & 1 = (RX1) & RX1 = TXD \(-\) TXA: where TXA = 0 \\ E = (TXE) & 2 = (RX2) & RX2 = TXE \(-\) TXB: where TXB = 0 \\ F = (TXF) & 3 = (RX3) & RX3 = TXF \(-\) TXC: where TXC = 0 \\ \hline \end{tabular}
\end{table}