ECE6101/CSE6461
Homework 1 Solution
Autumn 2015
Due Date: October 6, 2015
1. Let cfw_N1 (t), t 0 be a Poisson Process with rate . Can Z(t) = N1 (t) + N2 (t) ever be
a Poisson Process, where and are some non-zero constants. In other words, are there
any va
CSE-ECE 6001/6101:
Introduction to Computer
Communication Networks
Ness B. Shroff
Poisson Process
Definitions and Properties
ECE & CSE
Arrival Process or Counting Process
!Denition: An arrival process or counting process is that
stochastic process cfw_N(t
ECE6101/CSE6461
Computer Communication Networks
Switching, Recent Advances, Relevant Problems
Dr. Eylem Ekici
Professor
Department of Electrical and Computer Engineering
The Ohio State University
http:/www.ece.osu.edu/ekici
[email protected]
Autumn 2015
D
ECE6101/CSE6461
Computer Communication Networks
Poisson Process Denitions and Properties
Dr. Eylem Ekici
Professor
Department of Electrical and Computer Engineering
The Ohio State University
http:/www.ece.osu.edu/ekici
[email protected]
Autumn 2015
Dr. Ey
ECE6101/CSE6461
Computer Communication Networks
Networking Architectures
Dr. Eylem Ekici
Professor
Department of Electrical and Computer Engineering
The Ohio State University
http:/www.ece.osu.edu/ekici
[email protected]
Autumn 2015
Dr. Eylem Ekici
ECE610
ECE6101/CSE6461
Computer Communication Networks
Error Management and Control
Dr. Eylem Ekici
Professor
Department of Electrical and Computer Engineering
The Ohio State University
http:/www.ece.osu.edu/ekici
[email protected]
Autumn 2015
Dr. Eylem Ekici
EC
ECE6101/CSE6461
Computer Communication Networks
Congestion Control
Dr. Eylem Ekici
Professor
Department of Electrical and Computer Engineering
The Ohio State University
http:/www.ece.osu.edu/ekici
[email protected]
Autumn 2015
Dr. Eylem Ekici
ECE6101/CSE6
ECE6101/CSE6461
Computer Communication Networks
Elementary Queuing Theory
Dr. Eylem Ekici
Professor
Department of Electrical and Computer Engineering
The Ohio State University
http:/www.ece.osu.edu/ekici
[email protected]
Autumn 2015
Dr. Eylem Ekici
ECE61
ECE6101/CSE6461
Computer Communication Networks
History of Communication Networks
Dr. Eylem Ekici
Professor
Department of Electrical and Computer Engineering
The Ohio State University
http:/www.ece.osu.edu/ekici
[email protected]
Autumn 2015
Dr. Eylem Eki
ECE6101/CSE6461
Homework 2 Assignment
Autumn 2015
Due Date: October 6, 2015
1. Let cfw_N1 (t), t 0 be a Poisson Process with rate . Can Z(t) = N1 (t) + N2 (t) ever be
a Poisson Process, where and are some non-zero constants. In other words, are there
any
ECE6101/CSE6461
Homework 1 Assignment
Autumn 2015
Due Date: September 17, 2015
1. Prove that nite additivity follows from countable additivity.
2. From the axioms of probability, prove the following:
(a) For an event A and its complement Ac , prove that P
ECE6101/CSE6461
Homework 1 Solution
Autumn 2015
Due Date: September 17, 2015
1. Prove that nite additivity follows from countable additivity.
Countable Additivity: Given are a set function and any countable disjoint collection of
sets cfw_Ek . is countab
ECE6101/CSE6461
Midterm Exam Solution
Autumn 2015
1. Consider a queuing system where the customer inter-arrival times are uniformly distributed
between 2 and 6 seconds independent of each other. The service time is xed at X seconds
for all customers.
(a)
ECE6101/CSE6461
Project Assignment
Autumn 2015
Due Date: December 1, 2015
Motivation:
In a data network, Kleinrocks Independence Approximation is a powerful tool to analyze the network.
However, this provides only an approximation owing to the assumption
ECE6101/CSE6461
Computer Communication Networks
Network Design and Queuing Basics
Dr. Eylem Ekici
Professor
Department of Electrical and Computer Engineering
The Ohio State University
http:/www.ece.osu.edu/ekici
[email protected]
Autumn 2015
Dr. Eylem Eki
Class Project
Notes:
The Due Date is Monday Thu. Oct 24, 2012 by 5PM.
You must complete this project ENTIRELY by yourself, i.e., you are not allowed to
discuss it with any one else.
You are allowed to use whatever book or paper that may help you comple
Introduction to Computer
Communication Networks
Ness B. Shroff
Error Management and Control
Communication is Noisy
Communication between nodes is
1.
2.
3.
Inherently asynchronous
Noisy (error filled)
Possibility of packet loss or packet corruption
To prov
Introduction to Computer
Communication Networks
Ness B. Shroff
Routing Basics
Routing Function
n
Layer 3 funtionality in the OSI model.
n
Network Layer Funtionality
ECE & CSE
1
Routing Problem
n
n
Given a set of nodes, associated links and
associated link
[1] (25 points)
10
5
2
4
6
3
2
4
6
1
4
3
4
3
7
3
3
5
2
9
2
6
(a) (20 points) For the above network, nd the shortest path from node 1 to every other
node using Algorithm A (Dijkstras algorithm).
(b) (5 points) For a general graph with the same ratio of nod
Network Layer
Introduction to Computer
Communication Networks
!
Flow Control & Congestion Control
Ness B. Shroff
Congestion Control
ECE & CSE
ECE & CSE
Onset of Congestion
Congestion Collapse
Time Delay
Throughput
Congestion
Onset of
Congestion
Offered Lo
!
Introduction to Computer
Communication Networks
!
Ness B. Shroff
ECE & CSE
[email protected]
The global Internet topology is viewed as a
collection of Autonomous Systems (AS).
An AS is defined as a set of routers or networks
that are technically adminis
TCP/IP Architecture
Machine B
Machine A
Introduction to Computer
Communication Networks
Application
Application
Transport
Internet
Transport
Router/Gateway
Internet
Network Interface
Internet
Network Interface
Network Interface
Ness B. Shroff
TCP/IP Lectu
Homework 1
Due in class by: Tue. Sept. 13, 2016
(1) (4) Solve problems 1.2, 1.5, 1.9, 1.15 from Leon Garcia and Widjijas book (Second Edition).
Probability Review Problems (5) (11)
(5) Prove that finite additivity follows from countable additivity
(6) Fro
Reminder: Queueing Notation
CSE-ECE 6001/6101:
Introduction to Computer
Communication Networks
!
Notation:
Single server
Multiserver queue
Ness B. Shroff
!
Elementary Queueing Theory
Infinite Buffer: A/B/C ! old notation A/B/C/!
number of servers
Inter-ar