Scheduling:
Buffer
Management
Lecture 4
# 1
The setting
Lecture 4
# 2
Buffer Scheduling
 Who to send next?
 What happens when buffer is full?
 Who to discard?
Lecture 4
# 3
Requirements of scheduling
 An ideal scheduling discipline
 is easy to implement
 is fair and protective
 provides performance bounds

Each scheduling discipline makes a
different trade-off among these
requirements
Lecture 4
# 4
Ease of implementation
 Scheduling discipline has to make a decision
once every few microseconds!
 Should be implementable in a few instructions
or hardware
for hardware: critical constraint is VLSI space
 Complexity of enqueue + dequeue processes

 Work per packet should scale less than
linearly with number of active connections
Lecture 4
# 5
Fairness
 Intuitively
 each
connection should get no more than
its demand
 the excess, if any, is equally shared
 But it also provides protection
 traffic hogs cannot overrun others
 automatically isolates heavy users
Lecture 4
# 6
Max-min Fairness:
Single Buffer
 Allocate
bandwidth equally among all users
 If anyone doesn’t need its share, redistribute
 maximize the minimum bandwidth provided to any
flow not receiving its request
 Ex: Compute the max-min fair allocation for a set
of four sources with demands 2, 2.6, 4, 5 when
the resource has a capacity of 10.
• s1= 2;
• s2= 2.6;
• s3 = s4= 2.7

More complicated in a network.
Lecture 4
# 7
FCFS / FIFO Queuing
 Simplest Algorithm, widely used.
 Scheduling is done using first-in first-out
(FIFO) discipline
 All flows are fed into the same queue
Lecture 4
# 8
FIFO Queuing (cont’d)
 First-In First-Out (FIFO) queuing
First Arrival, First Transmission
 Completely dependent on arrival time
 No notion of priority or allocated buffers
 No space in queue, packet discarded

 Flows
can interfere with each other; No
isolation; malicious monopolization;

Various hacks for priority, random drops,...
Lecture 4
# 9
Priority Queuing
 A priority index is assigned to each packet upon arrival
 Packets transmitted in ascending order of priority index.


Priority 0 through n-1
Priority 0 is always serviced first
 Priority i is serviced only if 0 through i-1 are empty
 Highest priority has the



lowest delay,
highest throughput,
lowest loss
 Lower priority classes may be starved by higher priority
 Preemptive and non-preemptive versions.
Lecture 4 # 10
Priority Queuing
Packet discard
when full
High-priority
packets
Transmission link
Low-priority
packets
Packet discard
when full
When
high-priority
queue empty
Lecture 4
# 11
Round Robin: Architecture
 Round Robin: scan class queues serving one from
each class that has a non-empty queue
Flow 1
Transmission link
Flow 2
Round robin
Flow 3
Hardware requirement:
Jump to next non-empty queue
Lecture 4 # 12
Round Robin Scheduling
 Round Robin: scan class queues serving one from
each class that has a non-empty queue
Lecture 4 # 13
Round Robin (cont’d)
 Characteristics:
Classify incoming traffic into flows (sourcedestination pairs)
 Round-robin among flows

 Problems:
 Ignores packet length (GPS, Fair queuing)
 Inflexible allocation of weights (WRR,WFQ)
 Benefits:
 protection against heavy users (why?)
Lecture 4 # 14
Weighted Round-Robin
 Weighted round-robin
 Different weight wi (per flow)
 Flow j can sends wj packets in a period.
 Period of length  wj
 Disadvantage
 Variable packet size.
 Fair only over time scales longer than a period time.
• If a connection has a small weight, or the number of
connections is large, this may lead to long periods of
unfairness.
Lecture 4 # 15
DRR algorithm
 Choose a quantum of bits to serve from each
connection in order.
 For each HoL (Head of Line) packet,



if its size is ≤ (quantum + credit) send and save excess,
otherwise save entire quantum.
If no packet to send, reset counter (to remain fair)
 Each connection has a deficit counter (to store
credits) with initial value zero.
 Easier implementation than other fair policies

WFQ
Lecture 4 # 16
Deficit Round-Robin
 DRR can handle variable packet size
Quantum size : 1000 byte
2000
1000
1500
500 300
1200
Second
Round
First
Round
 1st Round
 A’s count : 1000
0
 B’s count : 200 (served twice)
A
 C’s count : 1000
 2nd Round
B
 A’s count : 500 (served)
 B’s count : 0
C
 C’s count : 800 (served)
Head of
Queue
Lecture 4 # 17
DRR: performance
 Handles variable length packets fairly
 Backlogged sources share bandwidth equally
 Preferably, packet size < Quantum
 Simple to implement

Similar to round robin
Lecture 4 # 18
Generalized
Processor
Sharing
Lecture 4 # 19
Generalized Process Sharing (GPS)
 The methodology:

Assume we can send infinitesimal packets
• single bit

Perform round robin.
• At the bit level
 Idealized policy to split bandwidth
 GPS is not implementable
 Used mainly to evaluate and compare real
approaches.
 Has weights that give relative frequencies.
Lecture 4 # 20
GPS: Example 1
40
30
A
20
B
C
10
0
30
Packets of size 10, 20 & 30
arrive at time 0
50
60
Lecture 4 # 21
GPS: Example 2
25
20
A
15
B
10
C
5
0
5
15
30
Packets: time 0 size 15
time 5 size 20
time 15 size 10
40
45
Lecture 4 # 22
GPS: Example 3
GPS examlpe 3
25
queue size
20
15
A
10
B
C
5
0
5
15
Packets: time 0
time 5
time 15
time 18
30
time
size
size
size
size
45
15
20
10
15
60
Lecture 4 # 23
GPS : Adding weights
 Flow j has weight wj
 The output rate of flow j, Rj(t) obeys:
d
R (t )  R j (t ) 
dt
'
j

wj
kACTIVE ( t )
wk
 For the un-weighted case (wj=1):
d
1
R (t )  R j (t ) 
dt
| ACTIVE (t ) |
'
j
Lecture 4 # 24
Fairness using GPS
 Non-backlogged connections, receive what
they ask for.
 Backlogged connections share the remaining
bandwidth in proportion to the assigned
weights.
 Every backlogged connection i, receives a
service rate of :
R (t ) 
'
i
wi
 jACTIVE ( t ) w j
Active(t): the set of
backlogged flows at time t
Lecture 4 # 25
GPS: Measuring unfairness
 No packet discipline can be as fair as GPS
while a packet is being served, we are unfair to others
Degree of unfairness can be bounded
Define: workA (i,a,b) = # bits transmitted for flow i in time
[a,b] by policy A.
Absolute fairness bound for policy S
 Max (workGPS(i,a,b) - workS(i, a,b))
Relative fairness bound for policy S
 Max (workS(i,a,b) - workS(j,a,b))
assuming both i and j are backlogged in [a,b]





Lecture 4 # 26
GPS: Measuring unfairness
 Assume fixed packet size and round robin
 Relative bound: 1
 Absolute bound: 1-1/n
 n is the number of flows
 Challenge: handle variable size packets.
Lecture 4 # 27
Weighted Fair
Queueing
Lecture 4 # 28
GPS to WFQ
 We can’t implement GPS
 So, lets see how to emulate it
 We want to be as fair as possible
 But also have an efficient implementation
Lecture 4 # 29
Lecture 4 # 30
GPS vs WFQ (equal length)
Queue 1
@ t=0
GPS:both packets
served at rate 1/2
1
Queue 2
@ t=0
Both packets complete
service at t=2
t
0
1
Packet from
queue 2 waiting
2
Packet-by-packet system (WFQ):
queue 1 served first at rate 1;
then queue 2 served at rate 1.
1
Packet from
queue 1 being
served
Packet from queue 2
being served
t
0
1
2
Lecture 4 # 31
GPS vs WFQ (different length)
2
Queue 1
@ t=0
GPS: both packets served
at rate 1/2
1
Queue 2
@ t=0
Packet from queue
2 served at rate 1
0
2
t
3
Packet from
queue 2 waiting
queue 2 served at rate 1
1
Packet from
queue 1 being
served at rate 1
0
1
2
t
3
Lecture 4 # 32
GPS vs WFQ
Queue 1
@ t=0
GPS: packet from queue 1
served at rate 1/4;
Queue 2
@ t=0
1
Packet from queue 1
served at rate 1
Weight:
Packet from queue 2
Queue 1=1
served at rate 3/4
Queue 2 =3
t
0
1
Packet from
queue 1 waiting
2
WFQ: queue 2 served first at rate 1;
then queue 1 served at rate 1.
1
Packet from queue 1
being served
Packet from
queue 2 being
served
t
0
1
2
Lecture 4 # 33
Completion times
 Emulating a policy:
Assign each packet p a value time(p).
 Send packets in order of time(p).

 FIFO:
 Arrival of a packet p from flow j:
last = last + size(p);
time(p)=last;
 perfect emulation...
Lecture 4 # 34
Round Robin Emulation
 Round Robin (equal size packets)
Arrival of packet p from flow j:
 last(j) = last(j)+ 1;
 time(p)=last(j);

 Idle queue not handle properly!!!
 Sending packet q: round = time(q)
 Arrival: last(j) = max{round,last(j)}+ 1
 time(p)=last(j);
 What kind of low level scheduling?
Lecture 4 # 35
Round Robin Emulation
 Round Robin (equal size packets)
Sending packet q:
 round = time(q); flow_num = flow(q);
 Arrival:
 last(j) = max{round,last(j)}
 IF (j < flow_num) & (last(j)=round)
THEN last(j)=last(j)+1
 time(p)=last(j);

 What kind of low level scheduling?
Lecture 4 # 36
GPS emulation (WFQ)
 Arrival of p from flow j:
last(j)= max{last(j), round} + size(p);
 using weights:
last(j)= max{last(j), round} + size(p)/wj;

 How should we compute the round?
 We like to simulate GPS:
 round(t+x) = round(t) + x/B(t)
 B(t) = active flows
 A flow j is active while round(t) < last(j)
Lecture 4 # 37
WFQ: Example (equal size)
Time 0: packets arrive to flow 1 & 2.
last(1)= 1; last(2)= 1; Active = 2
round (0) =0; send 1
Time 1: A packet arrives to flow 3
round(1) = 1/2; Active = 3
last(3) = 3/2; send 2
Time 2: A packet arrives to flow 4.
round(2) = 5/6; Active = 4
last(4) = 11/6; send 3
Time
Time
Time
Time
2+2/3:
3 :
3+2/3:
4 :
round
round
round
round
=
=
=
=
1; Active = 2
7/6 ; send 4;
3/2; Active = 1
11/6 ; Active=0
Lecture 4 # 38
WFQ: Example (GPS view)
1
½
0
1
0
1/2
2
3
5/6
7/6
4
11/6
t
round
Note that if in a time interval round progresses by amount x
Then every non-empty buffer is emptied by amount x during the interval
Lecture 4 # 39
Worst Case Fair
Weighted Fair
2
Queuing (WF Q)
Lecture 4 # 40
Worst Case Fair Weighted Fair Queuing
(WF2Q)
 WF2Q fixes an unfairness problem in WFQ.
 WFQ: among packets waiting in the system, pick
one that will finish service first under GPS
 WF2Q: among packets waiting in the system,
that have started service under GPS, select one
that will finish service first GPS
 WF2Q provides service closer to GPS
 difference in packet service time bounded by
max. packet size.
Lecture 4 # 41
Lecture 4 # 42
Lecture 4 # 43
Lecture 4 # 44
Lecture 4 # 45
Multiple Buffers
Lecture 4 # 46
Buffers
Fabric
Buffer locations
 Input ports
 Output ports
 Inside fabric
 Shared Memory
 Combination of all
Lecture 4 # 47
fabric
Outputs
Inputs
Input Queuing
Lecture 4 # 48
Input Buffer : properties
•
•
•
•
•
Input speed of queue – no more than input line
Need arbiter (running N times faster than input)
FIFO queue
Head of Line (HoL) blocking .
Utilization:
• Random destination
• 1- 1/e = 59% utilization
• due to HoL blocking
Lecture 4 # 49
Head of Line Blocking
Lecture 4 # 50
Lecture 4 # 51
Lecture 4 # 52
Overcoming HoL blocking:
look-ahead
 The fabric looks ahead into the input
buffer for packets that may be
transferred if they were not blocked by
the head of line.
 Improvement depends on the depth of the
look ahead.
 This corresponds to virtual output queues
where each input port has buffer for each
output port.
Lecture 4 # 53
Input Queuing
Virtual output queues
Lecture 4 # 54
Overcoming HoL blocking:
output expansion
 Each output port is expanded to L output
ports
 The fabric can transfer up to L packets to
the same output instead of one cell.
Karol and Morgan,
IEEE transaction on communication, 1987: 1347-1356
Lecture 4 # 55
Input Queuing
Output Expansion
L
fabric
Lecture 4 # 56
Output Queuing
The “ideal”
2
1
1
2
1
2 1
2
11
2
2
1
Lecture 4 # 57
Output Buffer : properties
 No HoL problem
 Output queue needs to run faster than input lines
 Need to provide for N packets arriving to same
queue
 solution: limit the number of input lines that can be
destined to the output.
Lecture 4 # 58
MEMORY
FABRIC
FABRIC
Shared Memory
a common pool of buffers divided into
linked lists indexed by output port number
Lecture 4 # 59
Shared Memory: properties
•
•
•
•
Packets stored in memory as they arrive
Resource sharing
Easy to implement priorities
Memory is accessed at speed equal to sum of
the input or output speeds
• How to divide the space between the sessions
Lecture 4 # 60