Lecture 4: scheduling: buffer managment

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SchedulingBuffer Management
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The setting
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Buffer Scheduling

• Who to send next?
• What happens when buffer is full?
• Who to discard?

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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

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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

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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

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Max-min Fairness Single Buffer

• Allocate bandwidth equally among all users
• If anyone doesnt need its share, redistribute
• maximize the minimum bandwidth provided to any
  flow not receiving its request
• To increase the smallest need to take from
  larger.
• Consider fluid example.
• 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.

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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

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FIFO Queuing (contd)

• 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,...

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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.

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Priority Queuing
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Round Robin Architecture

• Round Robin scan class queues serving one from
  each class that has a non-empty queue

Hardware requirement Jump to next non-empty
queue
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Round Robin Scheduling

• Round Robin scan class queues serving one from
  each class that has a non-empty queue

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Round Robin (contd)

• Characteristics
• Classify incoming traffic into flows
  (source-destination pairs)
• Round-robin among flows
• Problems
• Ignores packet length (GPS, Fair queuing)
• Inflexible allocation of weights (WRR,WFQ)
• Benefits
• protection against heavy users (why?)

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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.

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DRR (Deficit RR) algorithm

• Choose a quantum of bits to serve from each
  connection in order.
• For each HoL (Head of Line) packet,
• credit credit quantum
• if the packet size is credit send and save
  excess,
• otherwise save entire credit.
• If no packet to send, reset counter (to remain
  fair)
• If some packet sent counter min excess,
  quantum
• Each connection has a deficit counter (to store
  credits) with initial value zero.
• Easier implementation than other fair policies
• WFQ

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Deficit Round-Robin

• DRR can handle variable packet size

Quantum size 1000 byte

• 1st Round
• As count 1000
• Bs count 200 (served twice)
• Cs count 1000
• 2nd Round
• As count 500 (served)
• Bs count 0
• Cs count 800 (served)

2000
1000
0
1500
A
300
B
500
1200
C
Head of Queue
Second Round
First Round
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DRR performance

• Handles variable length packets fairly
• Backlogged sources share bandwidth equally
• Preferably, packet size lt Quantum
• Simple to implement
• Similar to round robin

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Generalized Processor Sharing
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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.

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GPS Example 1
60
50
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Packets of size 10, 20 30 arrive at time 0
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GPS Example 2
40
45
15
5
30
Packets time 0 size 15 time 5 size 20 time 15
size 10
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GPS Example 3
15
5
30
60
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Packets time 0 size 15 time 5 size 20 time 15
size 10 time 18 size 15
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GPS Adding weights

• Flow j has weight wj
• The output rate of flow j, Rj(t) obeys
• For the un-weighted case (wj1)

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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

Active(t) the set of backlogged flows at time t

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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

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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.

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Weighted Fair Queueing
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GPS to WFQ

• We cant implement GPS
• So, lets see how to emulate it
• We want to be as fair as possible
• But also have an efficient implementation

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GPS vs WFQ (equal length)
GPSboth packets served at rate 1/2
Packet-by-packet system (WFQ) queue 1 served
first at rate 1 then queue 2 served at rate 1.
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GPS vs WFQ (different length)
Queue 1 _at_ t0
Queue 2 _at_ t0
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GPS vs WFQ
Weight Queue 11 Queue 2 3
WFQ queue 2 served first at rate 1 then queue 1
served at rate 1.
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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...

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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) maxround,last(j) 1
• time(p)last(j)
• What kind of low level scheduling?

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Round Robin Emulation

• Round Robin (equal size packets)
• Sending packet q
• round time(q) flow_num flow(q)
• Arrival
• last(j) maxround,last(j) 1
• IF (j gt flow_num) (last(j)round)
• THEN last(j)last(j)-1
• time(p)last(j)
• What kind of low level scheduling?

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GPS emulation (WFQ)

• Arrival of p from flow j
• last(j) maxlast(j), round size(p)
• using weights
• last(j) maxlast(j), round size(p)/wj
• How should we compute the round?
• We like to simulate GPS
• x is the period of time in which active did not
  change
• round(tx) round(t) x/B(t)
• B(t) active flows (unweighted case)
• B(t) sum of weights of active flows (weighted
  case)
• A flow j is active while round(t) lt last(j)

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WFQ Example (GPS view)
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
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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 22/3 round 1 Active 2 Time 3
round 7/6 send 4 Time 32/3 round 3/2
Active 1 Time 4 round 11/6 Active0
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WFQ Example (GPS view)
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
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Worst Case Fair Weighted Fair Queuing (WF2Q)
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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.

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Multiple Buffers
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Buffers
Fabric
Buffer locations

• Input ports
• Output ports
• Inside fabric
• Shared Memory
• Combination of all

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Input Queuing
fabric
Outputs
Inputs
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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

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Head of Line Blocking
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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.

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Input QueuingVirtual output queues
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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
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Input Queuing Output Expansion
L
fabric
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Output QueuingThe ideal
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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.

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Shared Memory
MEMORY
FABRIC
FABRIC
a common pool of buffers divided into linked
lists indexed by output port number
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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