Question
Consider two nodes, A and B, that use the slotted ALOHA protocol to contend for a channel. Suppose node A has more data to transmit than node B, and node A’s retransmission probability p A is greater than node B’s retransmission probability, p B .
a. Provide a formula for node A’s average throughput. What is the total efficiency of the protocol with these two nodes?
b. If p A = 2p B , is node A’s average throughput twice as large as that of node B? Why or why not? If not, how can you choose p A and p B to make that happen?
c. In general, suppose there are N nodes, among which node A has retrans- mission probability 2p and all other nodes have retransmission probability p. Provide expressions to compute the average throughputs of node A and of any other node.
Answer
a)
Formula for node A’s average throughput= pA(1-pB)
The total efficiency of the protocol with these two nodes= pA(1-pB)+pB(1-pA).
b)
A’s throughput = pA(1-pB)
=2pB(1-pB)
=2pB-2(pB)^2.
B’s throughput= pB(1-pA)
=pB(1-2pB)
=pB-2(pB)^2.
It clearly says that A’s throughput is not twice as large as B’s.
In order to make pA(1-pB)=2pB(1-pA), then we need that pA=2–(pA/pB).
c)
Expression to compute the average throughput of node A and of any other node is as follows
A’s throughput = 2p(1-p)N-1, and throughput of any other node = p(1-p)N-2(1-2p).