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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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