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from computer networks a system approach book please answer the following .. .. (Slotted ALOHA): Suppose...

from computer networks a system approach book

please answer the following ..

..

(Slotted ALOHA): Suppose there are N nodes in a slotted ALOHA network. Every node is trying to transmit a packet at every time slot with probability p, independently of each other. It takes one time slot to transmit a packet.

(a) Express the offered load (the average number of packets per time slot that are arriving to the network) in terms of N and p.

(b) Showthethroughput(theaveragenumberofsuccessfullytransmittedpacketspertimeslot)isequaltoNp(1−p)N−1.

(c) Suppose the nodes can somehow change the probability of transmission p in their favor. Find value of p that maximizes the throughput.

(d) LetusdenotethemaximumthroughputbyT(N),usingthevalueofpfrompart(c).WecallT(N)ascapacity of the network. Calculate the capacity if there are infinite number of nodes, in other words, find limN →∞ T (N ). (I hope the answer looks familiar to you!)

..

please give full answers with a clear explanations.

engineering   Computer-Science   
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