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Tcom501midterm03
School: UPenn
Course: Networking – Theory & Fundamentals
TCOM501 Networking: Theory & Fundamentals Midterm Examination Professor Yannis A. Korilis March 5, 2003 Answer all problems. Good Luck! Problem 1 [20 points]: Consider an M/M/1 queue that can accommodate at most K customers in the system (queued or in ser

Spring 2003 Homework 4 Solution
School: UPenn
Course: Networking – Theory & Fundamentals
TCOM 501 Homework 4 Solutions Problem 3.53 (a) If customers are served in the order they arrive then given that a customer departs at time t for queue 1, the arrival time of that customer at queue 1 (and therefore the time spent at queue 1), is independen

Spring 2003 Homework 6 Solution
School: UPenn
Course: Networking – Theory & Fundamentals
TCOM501 Networking: Theory & Fundamentals Professor Yannis A. Korilis Assignment #6 Due April 16, 2003 Problem 1: Consider the embedded Markov chain cfw_L j : j = 1,2,. , that is obtained from the M/G/1 queue observed at departure epochs. As shown in the

Spring 2003midterm Exam 3solution
School: UPenn
Course: Networking – Theory & Fundamentals
TCOM501 Networking: Theory & Fundamentals Midterm Examination Professor Yannis A. Korilis March 5, 2003 Problem 1 [20 points]: Consider an M/M/1 queue that can accommodate at most M customers in the system (queued or in service), and suppose that a custom

Spring 2003 Homework 3 Solution
School: UPenn
Course: Networking – Theory & Fundamentals
TCOM501: Networking: Theory & Fundamentals Prof. Yannis A. Korilis Assignment #3 Solutions Problem 3.23 Let p m = P cfw_the 1st m servers are busy As given by the Erlang B formula. Denote rm = Arrival rate to servers (m+1) and above m = Arrival rate to s

Hw1sol
School: UPenn
Course: Networking – Theory & Fundamentals
TCOM 501 Homework 1 Solutions Problem 3.1 A customer that carries out the order (eat in the restaurant) stays for 5 minutes (25 minutes). Therefore the average customer time in the system is T = 0.5 0.5 + 0.5 25 = 15 minutes Applying Littles Theorem the a

Hw2sol
School: UPenn
Course: Networking – Theory & Fundamentals
TCOM 501 Homework 2 Solutions Problem 3.11(b) Let A, A1 , and A2 as in the hint. Let I be the interarrival interval of A2 and consider the number of arrivals of A1 that lie in I. The probability that this number is n is the probability of n successive arr

Hw3sol
School: UPenn
Course: Networking – Theory & Fundamentals
TCOM501: Networking: Theory & Fundamentals Prof. Yannis A. Korilis Assignment #3 Solutions Problem 3.23 Let p m = P cfw_the 1st m servers are busy As given by the Erlang B formula. Denote rm = Arrival rate to servers (m+1) and above m = Arrival rate to s

Hw4sol
School: UPenn
Course: Networking – Theory & Fundamentals
TCOM 501 Homework 4 Solutions Problem 3.53 (a) If customers are served in the order they arrive then given that a customer departs at time t for queue 1, the arrival time of that customer at queue 1 (and therefore the time spent at queue 1), is independen

HW5Sol
School: UPenn
Course: Networking – Theory & Fundamentals
1 TCOM501: Networking Theory and Fundamentals Professor Yannis A. Korilis Spring 2003 Homework Assignment 5 Problem 3.30: Let p0 denote the probability that the system is empty. This is also the probability that the server is empty. Applying Littles Theor

Hw6sol
School: UPenn
Course: Networking – Theory & Fundamentals
TCOM501 Networking: Theory & Fundamentals Professor Yannis A. Korilis Assignment #6 Due April 16, 2003 Problem 1: Consider the embedded Markov chain cfw_L j : j = 1, 2, . , that is obtained from the M/G/1 queue observed at departure epochs. As shown in th

Tcom501final02sol
School: UPenn
Course: Networking – Theory & Fundamentals
TCOM501 Networking: Theory & Fundamentals Final Examination Professor Yannis A. Korilis April 26, 2002 Problem 1 [30 points]: Consider a ring network with nodes 1,2,K. In this network, a customer that completes service at node i exits the network with pro

Tcom501final02
School: UPenn
Course: Networking – Theory & Fundamentals
TCOM501 Networking: Theory & Fundamentals Final Examination Professor Yannis A. Korilis April 26, 2002 Answer all problems. Good Luck! Problem 1 [30 points]: Consider a ring network with nodes 1,2,K. In this network, a customer that completes service at n

Tcom501midterm02sol
School: UPenn
Course: Networking – Theory & Fundamentals
TCOM501 Networking: Theory & Fundamentals Midterm Examination Professor Yannis A. Korilis March 6, 2002 Answer all problems. Good Luck! Problem 1 [15 points]: 1. State the PASTA theorem. [5 points] 2. Provide an analytical proof of the PASTA theorem. [10

Tcom501midterm02
School: UPenn
Course: Networking – Theory & Fundamentals
TCOM501 Networking: Theory & Fundamentals Midterm Examination Professor Yannis A. Korilis March 6, 2002 Answer all problems. Good Luck! Problem 1 [15 points]: 1. State the PASTA theorem. [5 points] 2. Provide an analytical proof of the PASTA theorem. [10

Tcom501midterm03sol
School: UPenn
Course: Networking – Theory & Fundamentals
TCOM501 Networking: Theory & Fundamentals Midterm Examination Professor Yannis A. Korilis March 5, 2003 Problem 1 [20 points]: Consider an M/M/1 queue that can accommodate at most M customers in the system (queued or in service), and suppose that a custom

Spring 2003 Homework 2 Solution
School: UPenn
Course: Networking – Theory & Fundamentals
TCOM 501 Homework 2 Solutions Problem 3.11(b) Let A, A1 , and A2 as in the hint. Let I be the interarrival interval of A2 and consider the number of arrivals of A1 that lie in I. The probability that this number is n is the probability of n successive arr