1) Two nodes x and y are the only nodes in a network that uses slotted ALOHA for
ID: 3701758 • Letter: 1
Question
1) Two nodes x and y are the only nodes in a network that uses slotted ALOHA for medium access. Node’s x retransmission probability is px and it is greater than node’s y retransmission probability, py. a. Express node’s x average throughput as a function of px and py. What is the total efficiency of the protocol in this case? (10pts) b. If px=2py is node’s x average throughput two times larger than that of node y? If yes, why? If not, how can you choose px and py to achieve that? (10pts) Hint: The average throughput of a node in this setting can be modeled through the probability of successfully obtaining a slot. If this probability is for example 0.2, the node is expected to obtain 20% of the slots. If at each successfully slot the throughput that can be obtained is T (this is fixed and depends on the medium), then the average throughput for this node will be 0.2T. Hence, you can use this probability for the throughput (assuming T=1Mbps or in general a fixed quantity).
Explanation / Answer
Answers
1a)
X's average throughput is given by : px * ( 1 - py )
Total efficiency is? px(1-py)+py(1-px)
1b)
X’s throughput is pX(1-pY)=2pY(1-pY)= 2pY- 2(pY)2.
Y’s throughput is pY(1-pX)=pY(1-2pY)= pY- 2(pY)2.
Clearly, X’s throughput is not twice as large as Y’s.
In order to make
pX(1-pY)= 2 pY(1-pX) ,
we need that pX= 2 – (pX / pY)
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