## 4 Simulation Works and Discussion
### Single Sink with Multi-Radios in a Round Robin Fashion

Table 3: Equation for uneven sender to multiple radios at sink node on 3 non-overlapping channels. The equations contain only logical states (active (1) and inactive (0)) values. When a node is in its active state it is equal to one and when it is in a negative state it is equal to zero. * If a variable is negative then assign a logical 0 to the variable. For example \(-\)TXA = 0. * If a variable is positive assign a logical 1. For example TXA = 1, therefore when RX1 = TXA \(-\) TXC \(-\) TXG1, only TXA can be sending data to the receiving radio. Figure 10 illustrate a radio interface at the sink (receiver, RX1) accepting data from a node (transmitter, TXA = 1) represented by an unbroken link. Other nodes (TXC, TXG1) being zero are represented by broken links to illustrate their negative or inactive state. Uneven Transmitter to Receive ratio: (TX: RX, TX = Uneven Positive Integer and RX \(>=\) 2, TX \(>=\) 5)  
The equations contain only logical states; active (1) and inactive (0) values. Table 4 equations yield the same outcome as Table 3 but have been expressed differently. \begin{table}
\begin{tabular}{|l|l|l|} \hline
**Senders** & **Receivers (RX = 3)** & **Equation** \\ (**TX = 7)** & & \\ \hline A = (TXA) & 1 = (RX1) & RX1 = TXA \(-\) TXC \(-\) TXG1: where TXC = 0, TXG1 = 0 \\ C = (TXC) & 1 = (RX1) & RX1 = TXC \(-\) TXA \(-\) TXG1: where TXA = 0, TXG1 = 0 \\ G = (TXG) & * Sequential time period & RX1 = TXG1 \(-\) TXA \(-\) TXC: where TXA = 0, TXC = 0 \\ B = (TXB) & 2 = (RX2) & RX2 = TXB \(-\) TXE \(-\) TXG2: where TXE = 0, TXG2 = 0 \\ E = (TXE) & 2 = (RX2) & RX2 = TXE \(-\) TXB \(-\) TXG2: where TXB = 0, TXG2 = 0 \\ G = (TXG) & * Sequential time period & RX2 = TXG2 \(-\) TXB \(-\) TXE: where TXB = 0, TXE = 0 \\  & to receivers \(\{1+2+3\}\) & RX3 = TXD \(-\) TXF \(-\) TXG3: where TXF = 0, TXG3 = 0 \\ D = (TXD) & 3 = (RX3) & RX3 = TXF \(-\) TXD \(-\) TXG3: where TXD = 0, TXG3 = 0 \\ F = (TXF) & 3 = (RX3) & RX3 = TXG3 \(-\) TXD \(-\) TXG3: where TXD = 0, TXG3 = 0 \\ G = (TXG) & *Sequential input to & RX3 = TXG3 \(-\) TXD \(-\) TXF: where TXD = 0, TXF = 0 \\ \hline \end{tabular}
\end{table} 
Table 4: Equation for uneven sender to multiple radios at sink node on three non-overlapping channels. Figure 10: Radio receiving from node TXA. * We begin with senders to Receiver in a ratio of 6:3 which represents two transmitters to each receiver (2:1). * By multiplying the output of ODD transmitter by the quantity of receivers we have created an even system where G is the sequential sending nodes that can be on any channel, the radio interface at the sink will sense G and update the number of receivers for data acceptance. However, G is not switchable to another channel when data is being sent to the receiver in a cycle. These equations allow a round robin fashion; each radio operates as a single-Eulerian cycle, which listens to every node on same channel once in a cycle. When the radio is less than the number of sending nodes, we derive the logics so that radio operates in a round robin fashion. The round robin technique does not limit the number of radio interfaces, each interface will operate in the same way which will allow the sink node (s) to receive data from senders in a more effective and efficient manner. Take for example 6 sending nodes as illustrate in Figure 2 and Table 2 with even transmitter to receiver equations, assign to three non-overlapping channels, each radio interface will switch between two nodes per cycle. When the radio interface on channel 1 senses the first sending node, it will receive its data packets and then sense the medium for the next node on the same channel. It will switch to that the sending node receives its data and continues in that fashion throughout the simulation period. Figure 11 illustrates the round robin fashion where the radio interface(s) at the sink can receive from only one sender at any given time.