Homework 1a: (Due date: Feb. 12, 2004)
Question 1. Prove properties III and IV of a Poisson process (merging and splitting) listed in
the class notes posted on the web site for the lecture on Stochastic processes. For the splitting
case, just prove the ra
Homework 3: (Due date: Feb. , 2004)
Problem: Given a two state Markov chain with the transition probability matrix
P = 1 a a , 0 a, b 1, 1 a b < 1,
b 1b
(1)
n
the n-step transition probability matrix P ( n ) = P is given by
n
n
b + a( 1 a b ) a a( 1 a b )
Homework 4: (Due date: March 4)
Problem 1. Derive an expression for the frequency of entering state 0 (server idle) in an M/M/1
queue. This quantity is useful in estimating the overhead of scheduling. Plot this frequency as a
function of for a fixed .
[So
CS/ECE 715 Spring 2004
Homework 5 (Due date: March 16)
Problem 0 (For fun). M/G/1 Queue with Random-Sized Batch Arrivals. Consider the M/G/1 system with the difference that customers are arriving in batches according to a Poisson process with
rate . Each
CS/ECE 715 Spring 2004
Homework 6 Solution(Due date: April 1)
Problem 1. A communication link provides 1 Mbps for communications between the earth and
the moon. The link sends color images from the moon. Each image consists of 10,000x10,000
pixels, and 16
CS/ECE 715 Spring 2004
Homework 7 Solution
Problem 1. Consider the Markov chain in Fig. 1 of [Reference 1]. Assume m = 2 , q r = 0.5 and
= 0.3 . Solve for steady state probability p 0 , p 1 , and p 2 .
[Solution]
P02
P12
0
1
2
P21
P10
P00
P22
P11
Easy to
CS/ECE 715 Spring 2004
Homework 9 (Due date: April 27)
Problem 1. Consider the network in Figure 1. There are four sessions: ACE, ADE, BCEF, and
BDEF sending Poisson traffic at rates 100, 200, 500, and 600 packets/min, respectively. Packet
lengths are exp
Homework on basic data networking concepts
Multiple Choice Questions (12 points):
More than one item may be correct or ALL items may be wrong. Mark all correct items for each
question. If you think ALL items are wrong, simply do not mark any item. Neatly