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EE444HW2.sln.corr

EE444HW2.sln.corr - EE 444 INTRODUCTION TO COMPUTER...

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EE 444 INTRODUCTION TO COMPUTER NETWORKS Spring 2009 HOMEWORK #2 Answers Deadline: March 27 2009 @ 23:59 (No late submission is allowed.) Posted on March 20 2009. Question # 1 Is it possible to apply Little’s Law in a finite buffer M/M/1/m queue? If it is possible, then apply Little’s Law to find the average time a packet spends in an M/M/1/m queue in terms of arrival rate λ , departure rate μ and m? If it is not possible, explain why. Answer # 1 Yes, it is possible to apply Little’s Law in a finite buffer M/M/1/m queue. Yet, the drop rates should be taken into consideration. Let be the probability of packet drop. Net arrival rate to the system is . d P ( ) 1 – P d λ From previous homework, we have 1 1 ( ) 1 i i m p ρ ρ ρ + = and 1 (1 ) (1 ) m d m P ρ ρ ρ + = . 1 1 1 1 [ ] ( ) 1 m m i i m j j E N ip i ρ ρ ρ + = = = = . After some algebraic manipulations, 1 1 [ ] ( 1 ( 1) ) (1 )(1 ) m m m E N m m ρ ρ ρ ρ ρ + + = + + . So, [ ] [ ] (1 ) d E N E T P λ = 1 ( 1 ( 1) [ ] (1 )(1 ) m m m m m E T ) ρ ρ μ ρ ρ + + + = Question # 2 5 stations are sharing a 10 Kbits/s communication channel.

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