# hw7sol - CSCI 415 Data Communication Networks Homework 7...

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Unformatted text preview: CSCI 415 Data Communication Networks Homework 7 Solution Saad Mneimneh Visiting Professor Hunter College of CUNY Problem 1: Application of Little’s theorem Two communication nodes 1 and 2 send packets to another node 3. The average lengths for packets generated at 1 and 2 are L 1 and L 2 bytes respectively. The links connecting node 1 and node 2 to node 3 have bandwidths μ 1 and μ 2 bps (bits per second) respectively. Node 3 can processes one packet at a time (no queue) and spends an average of P i seconds on packets from node i . Assume a steady state and a rate of λ 1 and λ 2 packets/sec for nodes 1 and 2, respectively. (a) What is the average number ρ 1 of packets of node 1 that are being processed by node 3 at any given time? ANSWER : The arrival rate of packets from node 1 to node 3 is λ 1 and the average delay per packet in node 3 is P 1 . Therefore, the average number of packets of node 1 that are being processes by node 3 is λ 1 P 1 by Little’s theorem. (b) What is the average number ρ 2 of packets of node 2 that are being processed by node 3 at any given time? ANSWER : Using the same argument above, we get λ 2 P 2 . (c) What should be the relation between ρ 1 and ρ 2 ? ANSWER: Since node 3 can process at most one packet at a time, λ 1 P 1 + λ 2 P 2 ≤ 1. (d) What is the average delay per packet in node 3? ANSWER : By Little’s theorem, it is ρ 1 + ρ 2 λ 1 + λ 2 . (e) What is the average number N 1 of packets of node 1 that are in the system at any given time?...
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## This note was uploaded on 03/27/2010 for the course CSCI 415 taught by Professor Saadmneimneh during the Spring '08 term at CUNY Hunter.

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hw7sol - CSCI 415 Data Communication Networks Homework 7...

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