Consider a wireless local area network $($LAN$)$ with an access point and $10$ stations $($Station $1,$

Station $2,$ Station $3,...,$ and Station $10).$ Distributed coordination function $($DCF$),$ which is based

on carrier sense multiple access with collision avoidance $($CSMA$/$CA$),$ is implemented. There is

no hidden station in the network. At time instant $0$ microsecond, the channel becomes idle, and

Station $1,$ Station $2,$ and Station $3($each with one and only one DATA frame to be sent to the

access point$)$ start to contend for channel access, while other stations $($including the access point$)$

do not have data to send. The backoff timers of Station $1,$ Station $2,$ and Station $3$ are $8,20,$ and

$20,$ respectively.

How long is the duration from time instant $0$ microsecond to the time instant when the first

successful transmission starts $($i$.$e$.,$ when the corresponding transmitter sends the first bit of its

RTS$)?$ Here a successful transmission means a successful handshake from RTS to ACK.

How long is the duration from the time instant when the first successful transmission starts to

the time instant when the second successful transmission starts?

How long is the duration from the time instant when the second successful transmission starts

to the time instant when the third successful transmission starts?

Assume DIFS$=50$ microseconds; SIFS$=10$ microseconds; a backoff time slot$=20$ microseconds;

RTS transmission time $=$ CTS transmission time $=$ ACK transmission time $=100$ microseconds; A

DATA frame transmission time $=1200$ microseconds. And a TIMEOUT duration is equal to the

sum of SIFS and CTS transmission time.

We also have the following assumption: if Station $1,2,$ and $3$ need to pick up a new backoff

timer from their contention windows, they always pick up $7,15,$ and $10,$ respectively. $(20$ points$)$