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Error in Q3-7

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Using longest prefix matching, the IP address 21.44.9.5 will match which entry?

a. 21.0.0.0/8 b. 21.44.9.0/24c. 21.44.9.1/32 d. 21.44.9.2/28 IP address: …….. 0000 0101 .

Prefix: …….. 0000 0010/28

✔

IP address: …….. 0000 0101 . Prefix: …….. 0000 XXXX/28

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CS144An Introduction to Computer Networks

Packet Switching

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Outline

1. End-to-end delay2. Queueing delay3. Simpler queue model4. Rate guarantees5. Delay guarantees (hard!)

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Propagation Delay, tl: The time it takes a single bit to travel over a link at propagation speed c.

l

Example: A bit takes 5ms to travel 1,000km in an optical fiber with propagation speed 2 x 108 m/s.

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Packetization Delay, tp: The time from when the first to the last bit of a packet is transmitted.

p

Example 1: A 64byte packet takes 5.12ms to be transmitted onto a 100Mb/s link.Example 2: A 1kbit packet takes 1.024s to be transmitted onto a 1kb/s link.

r bits/s

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End-to-end delayl1, r1 l2, r2

l3, r3l4, r4

Example: How long will it take a packet of length p to travel from A to B, from when the 1st bit is sent, until the last bit arrives? Assume the switches store-and-forward packets along the path.

A

B

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l1, r1 l2, r2 l3, r3 l4, r4A B

S1 S2 S3

A

B

S1

S2

S3

p/r2

l2/c

p/r3

l3/c

p/r4

l4/ctime

l1/c

p/r1 time

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l1, r1 l2, r2 l3, r3 l4, r4A B

S1 S2 S3

Other packetsData H

Q2(t)

p/r1A

B

S1

S2

S3

p/r2

l1/c

l2/c

p/r3

p/r4

l3/c

l4/c

Q2(t)

time

*Queueing = UK spelling, adopted by Kleinrock at UCLA in 1960s. Queueing and queuing (US spelling) are both widely used.

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Packet delay variation

0 100 200 300 400 500 600 7000%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

Stanford-Princeton4,000 km

Variation ~50ms

Stanford-Tsinghua10,000 km

Variation ~200ms

CDF (%)

RTT (ms)

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Simple model of router queue

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Simple model of a router queue

Properties of A(t), D(t):A(t), D(t) are non-decreasingA(t) >= D(t)

RA(t), l D(t)

Router queue

Q(t)

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Simple model of a queue

A(t)

D(t)

Cumulative number of bytes departed up until time t.

time

Linkrate

Cum

ulati

venu

mbe

r of b

ytes

Cumulative number of bytes arrived up until time t.

R

A(t)

D(t)

Q(t)

Properties of A(t), D(t): A(t), D(t) are non-decreasing

A(t) >= D(t)

R

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D(t)

A(t)

Time

Q(t)

d(t)

Queue occupancy: Q(t) = A(t) - D(t).

Queueing delay, d(t), is the time spent in the queue by a byte that arrived at time t, assuming the queue is served first-come-first-served (FCFS).

Simple model of a queueC

umul

ativ

enu

mbe

r of

byt

es

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Example

Cum

ulati

venu

mbe

r of b

its

Every second, a 100 bit packet arrives to a queue at rate 1000b/s. The maximum

departure rate is 500b/s. What is the average occupancy of the queue?

D(t)

A(t)

time0.1s 0.2s 1.0s

100

Solution: During each repeating 1s cycle, the queue fills at rate 500b/s for 0.1s, then drains at rate 500b/s for 0.1s. Over the first 0.2s, the average queue occupancy is therefore bits.The queue is empty for 0.8s every cycle, and so average queue occupancy:

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Priorities and Rates

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FIFO is a free for all

R

B

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Strict Priorities

R

High

Low

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Weighted Priorities

R

Weight = 2

Weight = 1

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Weighted Priorities

R

Weight = w1

Weight = wn

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What we’d like

R

Weight = w1

Weight = wn

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A practical way to do it

R

Weight = w1

Weight = wn

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Finishing Time

Finishing time: bit-by-bit

Finishing time: pkt-by-pkt

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Summary: Priorities and RatesFIFO queues are a free for all: No priorities and no guaranteed rates.

Strict priorities: High priority traffic “sees” a network with no low priority traffic. Useful if we have limited amounts of high priority traffic.

Weighted Fair Queueing (WFQ) lets us give each flow a guaranteed service rate, by scheduling them in order of their bit-by-bit finishing times.

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Delay Guarantees

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Delay guarantees: Intuition

l1, r1 l2, r2 l3, r3 l4, r4A B

Q2(t)Q1(t) Q3(t)

If we know the upper bound of Q1(t), Q2(t) and Q3(t), then we know the upper bound of the end-to-end delay.

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Delay guarantees: Intuition

R

Rate = R1

Rate = Rn

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So how can we control the delay of packets?

What we already know how to control:1. The rate at which a queue is served (WFQ).2. The size of each queue.

How do we make sure no packets are dropped?

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Zooming in on one queue

R

BA(t) D(t)

time

Cumulativebytes

A(t) D(t)

R

Key idea: In general, we don’t know the arrival process. So let’s

constrain it.

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Constraining traffic

time

Cumulativebits

r

s

t

Number of bits that can arrive in any period of length t

is bounded by:

This is called “( ,s r) regulation”

In our example: s = B and r = R1

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( ,s r)-constrained Arrivals and Minimum Service Rate

time

Cumulativebits

A(t) D(t)

R1

r

s

dmax

Bmax

If flows are leaky-bucket constrained, and routers use WFQ, then end-to-end delay guarantees are possible.

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The leaky bucket regulator

Tokensat rate, r

Token bucket

size, s

Packet buffer

Packets Packets

Send packet if and only if enough tokens

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Putting it all together

A B

Q2(t)Q1(t)

Leaky BucketRegulator

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An exampleIn the network below, an application wants a rate of 10Mb/s and

an end to end delay of less than 5ms for 1000byte packets.

A B10km, 1Gb/s 100km, 100Mb/s 10km, 1Gb/s

Once we decided to bound the delay to no more than 2.15ms in each router, we concluded that we need to make sure: (a) we don't store more than 2960 bytes in each router, which we accomplish by setting the token bucket at the source equal to 2960 bytes, and (b) the router buffer can hold at least 2960 bytes so we don't drop data (we can make the router buffer bigger if we'd like to; we just won't use it).

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In practice

While it is technically possible to do so, very few networks actually control end to end delay.

Why?- It is complicated to make work, requiring coordination.- In most networks, a combination of over-provisioning

and priorities work well enough.

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SummaryIf we know the size of a queue and the rate at which it is served, then we can bound the delay through it.

We can pick the size of the queue, and WFQ lets us pick the rate at which it is served.

Therefore, we just need a way to prevent packets being dropped along the way. For this, we use a leaky bucket regulator.

We can therefore bound the end to end delay.