• 4 Pages Spring 2003 Homework 2 Solution
    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

  • 4 Pages tcom501-final02
    Tcom501-final02

    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

  • 8 Pages tcom501-midterm02-sol
    Tcom501-midterm02-sol

    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

  • 2 Pages tcom501-midterm02
    Tcom501-midterm02

    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

  • 10 Pages tcom501-midterm03-sol
    Tcom501-midterm03-sol

    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

  • 4 Pages tcom501-midterm03
    Tcom501-midterm03

    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

  • 41 Pages Lecture4 5
    Lecture4 5

    School: UPenn

    TCOM501: NetworkingTheory&Fundamentals Lectures4&5 February5and12,2003 Prof.YannisA.Korilis 1 4&52 Topics MarkovChains M/M/1Queue PoissonArrivalsSeeTimeAverages M/M/*Queues IntroductiontoSojournTimes 4&53 TheM/M/1Queue Arrivalprocess:Poissonwithrate Servi

  • 33 Pages Lecture6
    Lecture6

    School: UPenn

    TCOM 501: Networking Theory & Fundamentals Lecture 6 February 19, 2003 Prof. Yannis A. Korilis 1 6-2 Topics Time-Reversal of Markov Chains Reversibility Truncating a Reversible Markov Chain Burkes Theorem Queues in Tandem 6-3 Time-Reversed Markov Chains c

  • 2 Pages tcom501-midterm02
    Tcom501-midterm02

    School: UPenn

    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

  • 32 Pages Lecture10
    Lecture10

    School: UPenn

    TCOM 501: Networking Theory & Fundamentals Lectures 9 & 10 M/G/1 Queue Prof. Yannis A. Korilis 1 10-2 Topics M/G/1 Queue Pollaczek-Khinchin (P-K) Formula Embedded Markov Chain Observed at Departure Epochs Pollaczek-Khinchin Transform Equation Queues with

  • 15 Pages tcom501-final02-sol
    Tcom501-final02-sol

    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

  • 10 Pages hw6-sol
    Hw6-sol

    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

  • 4 Pages Spring 2003 Homework 4 Solution
    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

  • 10 Pages Spring 2003 Homework 6 Solution
    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

  • 10 Pages spring 2003-midterm exam 3-solution
    Spring 2003-midterm Exam 3-solution

    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

  • 9 Pages Spring 2003 Homework 3 Solution
    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

  • 7 Pages hw1-sol
    Hw1-sol

    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

  • 4 Pages hw2-sol
    Hw2-sol

    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

  • 9 Pages hw3-sol
    Hw3-sol

    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

  • 4 Pages hw4-sol
    Hw4-sol

    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

  • 80 Pages HW5-Sol
    HW5-Sol

    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

  • 3 Pages hw6
    Hw6

    School: UPenn

    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

  • 7 Pages hw1
    Hw1

    School: UPenn

    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 Little's Theorem the

  • 4 Pages tcom501-final02
    Tcom501-final02

    School: UPenn

    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

  • 8 Pages tcom501-midterm02-sol
    Tcom501-midterm02-sol

    School: UPenn

    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 theore

  • 8 Pages HW5-Sol
    HW5-Sol

    School: UPenn

    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 Litt

  • 39 Pages Lecture11
    Lecture11

    School: UPenn

    TCOM 501: Networking Theory & Fundamentals Lecture 11 April 16, 2003 Prof. Yannis A. Korilis 1 2 Topics Routing in Data Network Graph Representation of a Network Undirected Graphs Spanning Trees and Minimum Weight Spanning Trees Directed Graphs S

  • 20 Pages Lecture11
    Lecture11

    School: UPenn

    TCOM 501: Networking Theory & Fundamentals Lecture 11 April 2003 Prof. Yannis A. Korilis 1 11-2 Topics Shortest-Path Algorithms: Bellman-Ford Dijkstra Floyd-Warshall Distributed Asynchronous Bellman-Ford Algorithm 11-3 Shortest-Path Ro

  • 4 Pages tcom501-final02
    Tcom501-final02

    School: UPenn

    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 serv

  • 39 Pages Lecture11
    Lecture11

    School: UPenn

    TCOM 501: Networking Theory & Fundamentals Lecture 11 April 16, 2003 Prof. Yannis A. Korilis 1 2 Topics Routing in Data Network Graph Representation of a Network Undirected Graphs Spanning Trees and Minimum Weight Spanning Trees Directed Grap

  • 33 Pages Lecture6
    Lecture6

    School: UPenn

    TCOM 501: Networking Theory & Fundamentals Lecture 6 February 19, 2003 Prof. Yannis A. Korilis 1 6-2 Topics Time-Reversal of Markov Chains Reversibility Truncating a Reversible Markov Chain Burkes Theorem Queues in Tandem 6-3 Time-Reversed

  • 4 Pages tcom501-midterm03
    Tcom501-midterm03

    School: UPenn

    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

  • 15 Pages Lecture7
    Lecture7

    School: UPenn

    TCOM 501: Networking Theory & Fundamentals Lecture 7 February 25, 2003 Prof. Yannis A. Korilis 1 7-2 Topics Open Jackson Networks Network Flows State-Dependent Service Rates Networks of Transmission Lines Kleinrocks Assumption 8-3 Networks

  • 5 Pages tcom501-final03
    Tcom501-final03

    School: UPenn

    TCOM501 Networking: Theory & Fundamentals Final Examination Professor Yannis A. Korilis May 8, 2003 Answer all problems. Good Luck! Problem 1 [50 points]: Two types of jobs arrive at a service station according to two independent Poisson processes w

  • 2 Pages tcom501-midterm02
    Tcom501-midterm02

    School: UPenn

    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 theore

  • 8 Pages HW5-Sol
    HW5-Sol

    School: UPenn

    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

  • 24 Pages Lecture8
    Lecture8

    School: UPenn

    TCOM 501: Networking Theory & Fundamentals Lecture 8 March 19, 2003 Prof. Yannis A. Korilis 1 8-2 Topics Closed Jackson Networks Convolution Algorithm Calculating the Throughput in a Closed Network Arrival Theorem for Closed Networks Mean-Value A

  • 36 Pages Lecture3
    Lecture3

    School: UPenn

    TCOM 501: Networking Theory & Fundamentals Lecture 3 January 29, 2003 Prof. Yannis A. Korilis 1 3-2 Topics Markov Chains Discrete-Time Markov Chains Calculating Stationary Distribution Global Balance Equations Detailed Balance Equations Birth-Deat

  • 32 Pages Lecture10
    Lecture10

    School: UPenn

    TCOM 501: Networking Theory & Fundamentals Lectures 9 & 10 M/G/1 Queue Prof. Yannis A. Korilis 1 10-2 Topics M/G/1 Queue Pollaczek-Khinchin (P-K) Formula Embedded Markov Chain Observed at Departure Epochs Pollaczek-Khinchin Transform Equation Que

  • 33 Pages Lecture6
    Lecture6

    School: UPenn

    TCOM 501: Networking Theory & Fundamentals Lecture 6 February 19, 2003 Prof. Yannis A. Korilis 1 6-2 Topics Time-Reversal of Markov Chains Reversibility Truncating a Reversible Markov Chain Burke's Theorem Queues in Tandem 6-3 Time-Reversed Mar

  • 2 Pages hw3
    Hw3

    School: UPenn

    TCOM501: Networking: Theory & Fundamentals Prof. Yannis A. Korilis Assignment #3 Problems from the book: 3.23, 3.24, 3.25, 3.26, 3.50 Problem 1: Consider a single-server queue, with a Poisson arrival rate . The service times are independent identica

  • 7 Pages hw1-sol
    Hw1-sol

    School: UPenn

    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 Little's Theo

  • 15 Pages tcom501-final02-sol
    Tcom501-final02-sol

    School: UPenn

    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 w

  • 15 Pages Lecture7
    Lecture7

    School: UPenn

    TCOM 501: Networking Theory & Fundamentals Lecture 7 February 25, 2003 Prof. Yannis A. Korilis 1 7-2 Topics Open Jackson Networks Network Flows State-Dependent Service Rates Networks of Transmission Lines Kleinrocks Assumption 8-3 Networks of .

  • 36 Pages Lecture3
    Lecture3

    School: UPenn

    TCOM501: NetworkingTheory&Fundamentals Lecture3 January29,2003 Prof.YannisA.Korilis 1 32 Topics MarkovChains DiscreteTimeMarkovChains CalculatingStationaryDistribution GlobalBalanceEquations DetailedBalanceEquations BirthDeathProcess Gen

Back to course listings