Hello, I\'m trying to solve the following problem 36P from chapter 3 of \"Comput

Question

Hello,

I'm trying to solve the following problem 36P from chapter 3 of "Computer Networking: A Top-Down Approach Featuring the Internet (5th)":

http://www.cramster.com/solution/solution/740551

And I don't think that the solution that Cramster gives is correct. It doesn't answer the question "If lambda_prime_in increases beyond R/2, can lamda_out increase beyond R/3?" In fact, it doesn't mention R/3 in the answer at all!

I will award lifesaver answer to the person who can show a clear and logical proof to the two questions asked in P36. Please show all steps. The solution that cramster gave is incoherent and confusing.

Explanation / Answer

This is from the instructor manual so it is right. If the arrival rate increases beyond R/2 in Figure 3.46(b), then the total arrival rate to the queue exceeds the queue’s capacity, resulting in increasing loss as the arrival rate increases. When the arrival rate equals R/2, 1 out of every three packets that leaves the queue is a retransmission. With increased loss, even a larger fraction of the packets leaving the queue will be retransmissions. Given that the maximum departure rate from the queue for one of the sessions is R/2, and given that a third or more will be transmissions as the arrival rate increases, the throughput of successfully deliver data can not increase beyond ?out. Following similar reasoning, if half of the packets leaving the queue are retransmissions, and the maximum rate of output packets per session is R/2, then the maximum value of ?out is (R/2)/2 or R/4.

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