Introduction to Computer Networks

Homework #$6$ due on December $29$th

$1.(10$ points$)$ If all the links in the Internet were to provide reliable delivery service, would the TCP reliable delivery service be redundant? Why or why not?

$2.(10$ points$)$ Suppose the information content of a packet is the bit pattern

$1010$

$0111$

$1001$ and an even parity scheme is being used. What would the value of the field containing the parity bits be for the case of a two$-$dimensional parity scheme?

$3.(10$ points$)$ In CRC coding, consider the generator, G$1001,$ and suppose that D has the value $11000111010,$ What are the CRC bits $($value of R$)?$

$4.(20$ points$)$ Suppose four active nodes$-$nodes A$,$ B$,$ C$,$ and D$-$ are competing for access to a channel using slotted ALOHA. Assume each node has an infinite number of packets to send. Each node attempts to transmit in each slot with probability p$.$ The first slot is numbered slot $1,$ the second slot is numbered slot $2,$ and so on$.$

a$)$ What is the probability that node A succeeds for the first time in slot $5?$ b$)$ What is the probability that some node $($either A$,$ B$,$ C$,$ or D$)$ succeeds in slot

b$)$What is the probability that some node $($either A$,$ B$,$ C$,$ or D$)$ succeeds in slot $4?$

c$)$ What is the probability that the first success occurs in slot $37$

d$)$ What is the efficiency of this four$-$node system?

$5.(10$ points$)$ In CSMA$/$CD$,$ after the fifth collision, what is the probability that a node chooses K$-47$ Recall that Ethernet requires a node to wait for $512$ K bit times before sensing the channel again. The result of choosing K$4$ corresponds to a delay of how many seconds on a $10$ Mbps Ethernet?

$6.(10$ points$)$ Why does collision occur in CSMA, if all nodes perform carrier sensing before transmission?