Four wireless nodes are placed on a straight line (see Figure $1$). Let $D(i, j)$ denote the distance between nodes $i$ and $j$. Each node has a circular communication range of $r = 1.5R$. This means that a packet transmitted by node $i$ is received by a node $j$ if and only if $D(i, j) < r$ and $D(k, j) > r$ for all $k ∈ M, k \neq i$, where $M$ is the set of nodes transmitting data at the same time as $i$. All nodes employ the $\text{RTS-CTS-DATA-ACK}$ protocol with exponential-backoff (on collision) for transferring data that was discussed in class. Assume that $b$ has an infinite amount of back-logged data to transmit to $a$. This means that $b$ always has data to transmit to $a$. Similarly $d$ has an infinite amount of data to transmit to $c$. Nodes $a$ and $c$ have no data to transmit. In such a scenario it is very likely that the throughput from $d$ to $c$ is significantly lower than that from $b$ to $a$. Explain why this is true. Make any reasonable assumptions and state them clearly. (A rough explanation will do.)
