explain how we get the value for RTTs intial $=1\mathrm{.}5?$ in the following answer: $8$ A host sends five packets and receives three acknowledgments. The time is shown

as hour:minute:seconds.

a$.$ Segment $1$ was sent at $0$:$0$:$00.$

b$.$ Segment $2$ was sent at $0$:$0$:$05.$

c$.$ ACK for segments $1$ and $2$ received at $0$:$0$:$07.$

d$.$ Segment $3$ was sent at $0$:$0$:$20.$

e$.$ Segment $4$ was sent at $0$:$0$:$22.$

f$.$ Segment $5$ was sent at $0$:$0$:$27.$

g$.$ ACK for segments $1$ and $2$ received at $0$:$0$:$45.$

h$.$ ACK for segment $3$ received at $0$:$0$:$65.$

Calculate the values of RTTM$,$ RTTS$,$ RTTD$,$ and RTO if the original RTO is $6$ seconds. Did the sender miss the retransmission of any segment? Show which

segments should have been retransmitted and when. Rewrite the events including the

retransmission time. Given:

Segment $1$ was sent at $0$:$0$:$00.$

Segment $2$ was sent at $0$:$0$:$05.$

ACK for segments $1$ and $2$ received at $0$:$0$:$07.$

Segment $3$ was sent at $0$:$0$:$20.$

Segment $4$ was sent at $0$:$0$:$22.$

Segment $5$ was sent at $0$:$0$:$27.$

ACK for segments $1$ and $2$ received at $0$:$0$:$45.$

ACK for segment $3$ received at $0$:$1$:$05(0$:$0$:$65).$

To Find:

RTTM $($Round$-$Trip Time Measurement$)$

RTTS $($Smoothed Round$-$Trip Time$)$

RTTD $($Round$-$Trip Time Deviation$)$

RTO $($Retransmission Timeout$)$

Determine if any segments were missed for retransmission.

Identify which segments should have been retransmitted and when.

Rewrite the events including the retransmission times.

Concept$/$Formula Used:

RTTM for each segment is calculated as the time difference between the sending of the segment and the reception of the ACK.

The initial RTTS and RTTD are given. The formulas for updating RTTS and RTTD are:

$RTT{S}_{\text{n}\text{e}\text{w}}=(1-)*RTT{S}_{\text{o}\text{l}\text{d}}+*RTT{M}^2$

$RTT{D}_{\text{n}\text{e}\text{w}}=(1-)*RTT{D}_{\text{o}\text{l}\text{d}}+*|RTTM-RTT{S}_{\text{o}\text{l}\text{d}}|$

where $=0\mathrm{.}125$ and $=0\mathrm{.}25.$

The RTO is calculated as:

RTO$=RTTS+4*RTTD$

Explanation:

Packet transmission and ACK times, calculate RTTM$,$ RTTS$,$ RTTD$,$ and RTO, determine missed retransmissions, and identify when segments

should have been retransmitted, including rewriting events accordingly. Calculation

RTTM Calculation:

For segments $1$ and $2$: The first ACK is ambiguous as it acknowledges both, but use the second ACK time to calculate the RTTM for

segment $1.$

$RTT{M}_{1,2}=45$ seconds $($from $0$:$0$:$00$ and $0$:$0$:$05$ to $0$:$0$:$45)$

For segment $3$:

$RTT{M}_3=65-20=45$ seconds

Initial RTTS and RTTD: Given initial RTO is $6$ seconds, assuming initial RTTS and RTTD are calculated as:

$RTT{S}_{\text{i}\text{n}\text{i}\text{t}\text{i}\text{a}\text{l}}=1\mathrm{.}5$ seconds

$RTT{D}_{\text{i}\text{n}\text{i}\text{t}\text{i}\text{a}\text{l}}=\frac{\text{R}\text{T}\text{O}-RTTS}{4}=\frac{6-1\mathrm{.}5}{4}=1\mathrm{.}125$ seconds

Update RTTS and RTTD:

Using $=0\mathrm{.}125$ and $=0\mathrm{.}25$ :

For the first ACK $($segments $1$ and $2)$:

$RTT{S}_{\text{n}\text{e}\text{w}}=(1-0\mathrm{.}125)*1\mathrm{.}5+0\mathrm{.}125*45=1\mathrm{.}5*0\mathrm{.}875+5\mathrm{.}625=6\mathrm{.}875$ seconds

$RTT{D}_{\text{n}\text{e}\text{w}}=(1-0\mathrm{.}25)*1\mathrm{.}125+0\mathrm{.}25*|45-1\mathrm{.}5|=0\mathrm{.}75*1\mathrm{.}125+0\mathrm{.}25*43\mathrm{.}5=0\mathrm{.}84375+10\mathrm{.}875=11\mathrm{.}71875$ seconds

For the second ACK $($segment $3)$:

$RTT{S}_{\text{n}\text{e}\text{w}}=(1-0\mathrm{.}125)*6\mathrm{.}875+0\mathrm{.}125*45=6\mathrm{.}875*0\mathrm{.}875+5\mathrm{.}625=12\mathrm{.}78125$ seconds

$RTT{D}_{\text{n}\text{e}\text{w}}=(1-0\mathrm{.}25)*11\mathrm{.}71875+0\mathrm{.}25*|45-6\mathrm{.}875|=0\mathrm{.}75*11\mathrm{.}71875+0\mathrm{.}25*38\mathrm{.}125=8\mathrm{.}7890625+9\mathrm{.}53125=18\mathrm{.}32031.$

Calculate RTO:

RTO$=RTTS+4*RTTD=12\mathrm{.}78125+4*18\mathrm{.}3203125=12\mathrm{.}78125+73\mathrm{.}28125=86\mathrm{.}0625$ seconds

Explanation:

Calculated RTTM$,$ RTTS$,$ RTTD$,$ and RTO using the given formulas. Identified that segments $3,4,$ and $5$ needed retransmissions due to ACK

delays beyond the initial RTO of $6$ seconds. Retransmission Analysis: The sender missed retransmission it no ACK was received within the initial RTO of $6$ seconds.

For Segment $1$: No retransmission needed as ACK was received at $7$ seconds.

For Segment $2$: No retransmission needed as ACK was received at $7$ seconds.

For Segment $3$: ACK received at $65$ seconds, which is much later than the initial RTO. Hence, retransmission should have occurred.

For Segment $4$ and $5$: No ACK received within the initial RTO, implying retransmissions are required.

Retransmission Events:

Segment $3$ should have been retransmitted at $0$:$0$:$26(6$ seconds after the initial $20$ seconds send time$).$

Segment $4$ should have been retransmitted at $0$:$0$:$28(6$ seconds after the initial $22$ seconds send time$).$

Segment $5$ should have been retransmitted at seconds after the initial $27$ seconds send time$).$

Rewritten Events with Retransmission:

Segment $1$ was sent at $0$:$0$:$00.$

Segment $2$ was sent at $0$:$0$:$05.$

ACK for segments $1$ and $2$ received at $0$:$0$:$07.$

Segment $3$ was sent at $0$:$0$:$20.$

Segment $4$ was sent at $0$:$0$:$22.$

Segment $5$ was sent at $0$:$0$:$27.$

Segment $3$ retransmitted at $0$:$0$:$26.$

Segment $4$ retransmitted at $0$:$0$:$28.$

Segment $5$ retransmitted at $0$:$0$:$33.$

ACK for segments $1$ and $2$ r