EECS 122:
Introduction to Computer Networks
Packet Scheduling and QoS
Computer Science Division
Department of Electrical Engineering and Computer Sciences
University of California, Berkeley
Berkeley, CA 94720-1776
Katz, Stoica F04
Today’s Lecture: 15
2
17, 18, 19
6
10,11
Transport
14, 15,
16
7, 8, 9
21, 22, 23
25
Application
Network (IP)
Link
Physical
Katz, Stoica F04
2
Packet Scheduling

Decide when and what packet to send on output link
- Usually implemented at output interface of a router
flow 1
1
2
Classifier
flow 2
Scheduler
flow n
Buffer
management
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3
Goals of Packet Scheduling



Provide per flow/aggregate QoS guarantees in terms of
delay and bandwidth
Provide per flow/aggregate protection
Flow/Aggregate identified by a subset of following fields in
the packet header
-

source/destination IP address (32 bits)
source/destination port number (16 bits)
protocol type (8 bits)
type of service (8 bits)
Examples:
-
All packets from machine A to machine B
All packets from Berkeley
All packets between Berkeley and MIT
All TCP packets from EECS-Berkeley
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4
Outline



QoS guarantees
Link sharing
Service curve (short)
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5
Recap: Token Bucket and Arrival Curve

Parameters
- r – average rate, i.e., rate at which tokens fill the bucket
- b – bucket depth
- R – maximum link capacity or peak rate (optional parameter)


A bit is transmitted only when there is an available token
Arrival curve – maximum number of bits transmitted within an
interval of time of size t
r bps
Arrival curve
bits
slope r
b*R/(R-r)
b bits
slope R
<= R bps
time
regulator
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6
How Is the Token Bucket Used?

Can be enforced by
- End-hosts (e.g., cable modems)
- Routers (e.g., ingress routers in a Diffserv domain)

Can be used to characterize the traffic sent by an
end-host
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7
Source Traffic Characterization


Arrival curve – maximum amount of bits transmitted
during an interval of time Δt
Use token bucket to bound the arrival curve
bps
bits
Arrival curve
Δt
time
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8
Source Traffic Characterization: Example
Arrival curve – maximum amount of bits transmitted
during an interval of time Δt
Use token bucket to bound the arrival curve


bits
(R=2,b=1,r=1)
Arrival curve
2
5
4
bps
3
2
2
1
1
0
1
2
3
4
5
time
1
3
4
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Δt
9
QoS Guarantees: Per-hop Reservation

End-host: specify
- the arrival rate characterized by token-bucket with parameters (b,r,R)
- the maximum maximum admissible delay D

Router: allocate bandwidth ra and buffer space Ba such that
- no packet is dropped
- no packet experiences a delay larger than D
slope ra
bits
slope r
Arrival curve
b*R/(R-r)
D
Ba
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Packet Scheduling


Make sure that at any time the flow receives at
least the allocated rate ra
The canonical example of such scheduler:
Weighted Fair Queueing (WFQ)
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11
Recap: Fair Queueing

Implements max-min fairness: each flow receives min(ri,
f) , where
- ri – flow arrival rate
- f – link fair rate (see next slide)

Weighted Fair Queueing (WFQ) – associate a weight
with each flow
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Fair Rate Computation: Example 1

If link congested, compute f such that
 min( r , f )  C
i
i
8
6
2
10
4
4
2
f = 4:
min(8, 4) = 4
min(6, 4) = 4
min(2, 4) = 2
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Fair Rate Computation: Example 2


Associate a weight wi with each flow i
If link congested, compute f such that
 min( r , f  w )  C
i
i
i
(w1 = 3) 8
(w2 = 1) 6
(w3 = 1) 2
10
4
4
2
f = 2:
min(8, 2*3) = 6
min(6, 2*1) = 2
min(2, 2*1) = 2
Flow i is guaranteed to be allocated a rate >= wi*C/(Σk wk)
If Σk wk <= C, flow i is guaranteed to be allocated a rate >= wi
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Fluid Flow System


Flows can be served one bit at a time
WFQ can be implemented using bit-by-bit weighted
round robin
- During each round from each flow that has data to send, send a
number of bits equal to the flow’s weight
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Fluid Flow System: Example 1
Packet
Size (bits)
Packet inter-arrival
time (ms)
Rate
(Kbps)
Flow 1
1000
10
100
Flow 2
500
10
50
Flow 1 (w1 = 1) 100 Kbps
Flow 2 (w2 = 1)
Flow 1
(arrival traffic)
1
2
5
time
Flow 2
(arrival traffic)
Service
in fluid flow
system
4
3
1
2
3
4
5
6
time
1
0
3
2
10
1
20
4
2
30
3
40
5
4
50
5
60
6
70
80
time (ms)
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Fluid Flow System: Example 2

link
Red flow has packets
backlogged between time 0
and 10
- Backlogged flow  flow’s
queue not empty


flows
weights
Other flows have packets
continuously backlogged
All packets have the same size
0
2
4
6
8
5
1
10
1
1
1
15
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1
Implementation In Packet System


Packet (Real) system: packet transmission
cannot be preempted. Why?
Solution: serve packets in the order in which they
would have finished being transmitted in the fluid
flow system
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Packet System: Example 1
Service
in fluid flow
system

1
3
2
1
4
2
3
5
4
5
6
time (ms)
Select the first packet that finishes in the fluid flow system
Packet
system
1
2
1
3
2 3
4
4 5
5
6
time
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Packet System: Example 2
Service
in fluid flow
system
0

2
4
6
8
10
Select the first packet that finishes in the fluid flow system
Packet
system
0
2
4
6
8
10
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Implementation Challenge



Need to compute the finish time of a packet in the
fluid flow system…
… but the finish time may change as new
packets arrive!
Need to update the finish times of all packets
that are in service in the fluid flow system when a
new packet arrives
- But this is very expensive; a high speed router may
need to handle hundred of thousands of flows!
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Example

Four flows, each with weight 1
Flow 1
time
Flow 2
time
Flow 3
time
Flow 4
time
ε
Finish times computed at time 0
time
0
1
2
3
Finish times re-computed at time ε
time
0
1
2
3
4
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Solution: Virtual Time

Key Observation: while the finish times of packets may
change when a new packet arrives, the order in which
packets finish doesn’t!
- Only the order is important for scheduling

Solution: instead of the packet finish time maintain the
number of rounds needed to send the remaining bits of
the packet (virtual finishing time)
- Virtual finishing time doesn’t change when the packet arrives

System virtual time – index of the round in the bit-by-bit
round robin scheme
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System Virtual Time: V(t)


Measure service, instead of time
V(t) slope – normalized rate at which every backlogged flow receives
service in the fluid flow system
- C – link capacity
- N(t) – total weight of backlogged flows in fluid flow system at time t
V(t)
V (t )
C

t
N (t )
time
Service
in fluid flow
system
1
2
1
2
3
3
4
4
5
6
5
time
Katz, Stoica F04 24
System Virtual Time (V(t)): Example 1

V(t) increases inversely proportionally to the sum
of the weights of the backlogged flows
Flow 1 (w1 = 1)
time
Flow 2 (w2 = 1)
time
1
2
V(t)
3
1
4
2
3
5
4
5
6
C/2
C
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System Virtual Time: Example
w1 = 4
w2 = 1
w3 = 1
w4 = 1
w5 = 1
V(t)
C/4
C/8
C/4
0
4
8
12
16
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Fair Queueing Implementation

Define
- Fi k- virtual finishing time of packet k of flow i
k
- ai - arrival time of packet k of flow i
k
- Li - length of packet k of flow i
- wi – weight of flow i

The finishing time of packet k+1 of flow i is
Fi k 1  max( V (aik 1 ), Fi k )  Lki 1/ wi
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Properties of WFQ

Guarantee that any packet is transmitted within
packet_lengt/link_capacity of its transmission time
in the fluid flow system
- Can be used to provide guaranteed services

Achieve max-min fair allocation
- Can be used to protect well-behaved flows against
malicious flows
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Outline



QoS guarantees
Link sharing
Service curve (short)
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Hierarchical Link Sharing
Link
155 Mbps
55 Mbps
100 Mbps
Provider 1
50 Mbps
Provider 2
50 Mbps
Berkeley
20 Mbps
EECS
seminar
video
Stanford.
10 Mbps
Math
seminar
audio
Campus


Resource contention/sharing
at different levels
Resource management
policies should be set at
different levels, by different
entities
-
Resource owner
Service providers
Organizations
Applications
WEB
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Hierarchical WFQ (H-WFQ) Example


Red session has
packets backlogged
at time 5
Other sessions have
packets continuously
backlogged
10
5
1
4
1
1
1
1
1
First red packet arrives at 5 …and it is served at 7.5
Service
in fluid flow
system
0
10
20
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Packet Approximation of H-WFQ

Fluid Flow H-WFQ
Packetized H-WFQ
10
6
WFQ
2
WFQ
WFQ
4
WFQ
1
- Select packet finishing first in
H-WFQ assuming there are no
future arrivals
- Problem:
• Finish order in system
dependent on future
arrivals
• Virtual time implementation
won’t work
10
WFQ
6
1
3
WFQ
WFQ
4
WFQ
WFQ
2
WFQ
WFQ
3
WFQ
Idea 1

Idea 2
- Use a hierarchy of WFQ to
approximate H-WFQ
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Problems with Idea 1

10
The order of the 4th blue
packet finish time and of
the first green packet finish
time changes as a result of
a red packet arrival
Make decision here
5
1
4
1
1
1
1
1
Green packet finish first
Blue packet
finish first
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Problem with Idea 2
10

A packet on the
second level can
miss its deadline
(finish time)
5
1
4
1
1
1
1
1
First level packet schedule
Second level packet schedule
First red packet arrives at 5
…but it is served at 11 !
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Solution


Hierarchical-WFQ with a better implementation of
WFQ, called Worst-Case Weighted Fair
Queueing (WF2Q)
Main idea of WF2Q
- Consider for scheduling only eligible packets
- Eligible packet at time t: a packet that has started being
serviced in the fluid flow system at time t
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Example
Fluid-Flow System
WFQ (smallest finish time first)
WF2Q (smallest eligible finish time first)
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Hierarchical-WF2Q Example
10

In WF2Q, all packets
meet their deadlines
modulo time to
transmit a packet (at
the line speed) at
each level
5
1
4
1
1
1
1
1
First level packet schedule
Second level packet schedule
First red packet arrives at 5
..and it is served at 7
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Outline



QoS guarantees
Link sharing
Service curve (short)
Katz, Stoica F04 38
Bandwidth-Delay Coupling

Assume
- An arrival curve specified by token bucket (R, r, b)
- A reservation request (rmin, D), where rmin – minimum bandwidth, D – maximum delay

WFQ can be inefficient: to satisfy delay D, the allocated rate ra may need to be
much higher than r !
slope ra
bits
b*R/(R-r)
slope r
Arrival curve
D
Katz, Stoica F04 39
Example


End-host: request a worst-case delay D=10ms
for a flow characterized by token bucket
(R=1Mbps, b=10Kb, r=100Kbps)
Router: allocate rate ra, where
ra = b*R / (D*(R-r) + b) = 0.52Mbps

Thus, the router needs to allocate to the flow
more than 5 times its average rate r !
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Solution: Service Curve

Generalize the service allocated to a flow
- Assume a flow that is idle at time s and it is backlogged
during the interval (s, t)
- Service curve: the minimum service received by the flow
during the interval (s, t)
bits
Arrival Curve
D
B
S (t) = service curve
t
WFQ implements a linear service curve
Katz, Stoica F04 41
Linear Service Curves: Example
bits
Service
curves
bits
FTP
Video
t
t
Arrival
process
bits
bits
Arrival
traffic
t
t
bits
bits
Service
t
Video packets have to wait after ftp packets
t
t
Katz, Stoica F04 42
Non-Linear Service Curves:
Example
bits
Service
curves
bits
FTP
Video
t
t
Arrival
process
bits
bits
Arrival
traffic
t
t
bits
bits
Service
t
t
Video packets transmitted
as soon as they arrive
t
Katz, Stoica F04 43
What You Need to Know

Basic concepts
-

Arrival & service curve
Token-bucket specification
System virtual time / finish virtual time
WFQ properties
Link sharing requirements and challenges
Bandwidth-delay coupling problem
Mechanisms:
- WFQ implementation in the fluid flow & packet system

You don’t need to know
- Details of WF2Q
- How service curve works
Katz, Stoica F04 44