Packet Scheduling

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Packet Scheduling

• IT610
• Prof. A. Sahoo
• KReSIT

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Packet Scheduling

• Responsible for enforcing resource allocation to
  individual flows
• Decides which packet should get resources
• Intuitively works like a dispatcher it keeps
  track of how many packets each flow has sent and
  compares that with the amount of resources the
  flow has reserved.
• Arriving packets from a flow are sent only when
  the flow has not used up the reserved resources

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Basic Requirement

• Isolation and sharing
• Allow sharing of common resources in a controlled
  way
• In circuit switched network full isolation, no
  sharing
• Under-utilization of resources
• In datagram based internet (FCFS) resources are
  shared on a per-packet basis
• No isolation

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Basic Requirement (Contd)?

• Delay Bounds
• Scheduler should provide some delay bound
• Either deterministic (guaranteed service) or
  statistical
• Deterministic bounds give the best isolation
• Statistical delay bound allow more efficient
  sharing, less isolation
• Bandwidth allocation
• When there is a contention for resources, bw must
  be allocated fairly to all competing flows.

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Types of scheduler

• Work Conserving
• Scheduler is idle only when there are no packets
  waiting for transmission
• Example FCFS
• Non-work-conserving
• Transmits packet when it is eligible for
  transmission
• If no packets are eligible, scheduler will be
  idle even when there are packets in the queue.
• Example Rate controlled scheduler

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Max-Min Fairness

• An allocation is fair if it satisfies max-min
  fairness
• each connection gets no more than what it wants
• the excess, if any, is equally shared

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Max-Min Fairness

• N flows share a link of rate C.
• Flow f wishes to send at rate W(f), and is
  allocated rate R(f).
• Pick the flow, f, with the smallest W(f).
• If W(f) lt C/N, then set R(f) W(f).
• If W(f) gt C/N, then set R(f) C/N.
• Set N N 1. C C R(f).
• If N gt 0 goto 1.

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Max-Min Fairness example
W(f1) 0.1
1
W(f2) 0.5
C
R1
W(f3) 10
W(f4) 5

• Round 1 Set R(f1) 0.1
• Round 2 Set R(f2) 0.9/3 0.3
• Round 3 Set R(f4) 0.6/2 0.3
• Round 4 Set R(f3) 0.3/1 0.3

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Simple Priority scheduling

• Number of priority levels
• Packet is served from a given priority level only
  if no packets exist at higher levels (multilevel
  priority with exhaustive service)?
• Higher priority will always have precedence over
  lower priority
• May lead to starvation of lower priority packets

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Deadline based scheduler

• Deadline based scheduler schedules packets based
  on the earliest deadline (EDF) principle.
• Flow with lowest deadline gets scheduled first
• Delay and bw requirements are decoupled flow
  requiring small bandwidth can get small delay.
• Admission control is more complex has to do
  schedulability test and also make sure that total
  bw capacity is not exceeded

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Rate based scheduler

• Two components regulator and a scheduler.
• Regulator determines eligibility time for the
  packet.
• The result is that the traffic is shaped by the
  regulator before it arrives at the scheduler.
• Examples token bucket regulator
• Scheduler can do FCFS or fair queueing.

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Token bucket
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Round robin scheduling

• Scan class queues serving one from each class
  that has a non-empty queue
• Assumption Fixed packet length
• Pros and cons
• Provides Max-min fairness and Protection within
  contending flows
• More complex than FIFO per flow queue/state

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Weighted round robin

• Round robin
• Unfair if packets are of different length or
  weights are not equal
• Weighted round robin
• Serve more than one packet per visit
• Number of packets are proportional to weights

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Weighted round robin

• Normalize the weights so that they become integer

WA1.4 WB0.2 WC0.8
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Weighted RR variable length packet

• If different connection have different packet
  size, then divide the weight of each connection
  with connections mean packet size before
  normalizing
• weights 0.5, 0.75, 1.0,
• mean packet sizes 50, 500, 1500
• normalize weights 0.5/50, 0.75/500, 1.0/1500
  0.01, 0.0015, 0.000666,
• normalize again 60, 9, 4

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Generalized Processor Sharing

• For best effort service main requirement is
  fairness, protection.
• GPS can provide fairness and protection.
• Visit each non-empty queue in turn
• Serve infinitesimal from each
• GPS is not implementable we can serve only
  packets

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GPS

• Generalized Processor Sharing (GPS) is an ideal
  fair-queuing algorithm based on the fluid model.
• If there are N flows served by a server with
  service rate R and the ith flow is assigned a
  weight Fi and let S(i, t, t) be the amount of
  data served for flow i, which is continuously
  backlogged during an interval (t, t) then

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GPS (cont.)?

• In interval (t, t) the flow i receives a min fair
  share proportional to its weight
• Where V is the set of flows that are backlogged.

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GPS (cont.)?

• If traffic source is constrained by a token
  bucket with burst size b and token rate r
• GPS can guarantee a delay bound of b/r.

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Weighted Fair Queuing (WFQ)?

• WFQ is approximation of GPS does not assume
  infinitesimal packet size
• Scheduler needs to find the finish time of a
  packet if packet was processed in fluid model
  (this is known as the finish number).
• Then packets are scheduled in the increasing
  order of their finish number.

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WFQ (cont.)?

• In effect, WFQ simulates GPS on the side and uses
  the result to determine service order.
• WFQ supports bandwidth allocation and delay
  bounds
• Have been widely used in routers to support QoS.

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WFQ details

• Uses notions of round number and finish number
• Suppose, in each round, the server served one bit
  from each active connection
• Round number is the number of rounds already
  completed
• can be fractional
• also called virtual time

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Weighted Fair Queueing (WFQ)?

• Deals better with variable size packets and
  weights
• Also known as packet-by-packet GPS (PGPS)?
• Find finish time of a packet, had we been doing
  GPS (this is the finish number) serve packets in
  order of their finish number

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WFQ (cont.)?

• Computation of finish number complex for a
  general case.
• For a simple case where all flows are backlogged
  all the time, the finish number of packet k from
  flow i is equal to the finish number of the
  previous packet from the same flow plus the time
  for transmitting the current packet (in GPS)

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WFQ (Cont.)?

• But in a more general case flows may move back
  and forth between backlogged and non-backlogged
  so there will be idle time between packets. The
  finish number in this case
• R(t) round number at the arrival of packet k
  virtual time of the system at time t

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WFQ (Cont.)?

• Due to packetization effect, the worst-case delay
  for WFQ is more than GPS and the worst case delay
  when a flow goes through K WFQ schedulers is
• Lmax is the max packet size in the system, ri is
  the reserved rate of flow i, Rm is the service
  rate of hop m. Li is the max packet size of flow i

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WFQ (Cont.)?

• First term GPS delay for leaky bucket traffic
• Second term Worst case delay of a packet of
  flow i which has a guaranteed rate ri
• Third term packet may have to wait after the
  current packet to be served (packet may be
  blocked by a max size packet)?

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WFQ Example
t0 Packets of sizes 1,2,2 arrive at connections
A, B, C. t4 Packet of size 2 arrives at
connection A
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Example (contd.)?

• At time 0, slope of 1/3,
• Finish number of A 1, Finish number of B, C 2
  
• At time 3, connection A become inactive, slope
  becomes 1/2
• At time 4,
• second packet at A gets finish number 2 1.5
  3.5, Slope decreases to 1/3

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Example (contd.)?

• At time 5.5,
• round number becomes 2 and connection B and C
  become inactive, Slope becomes 1
• At time 7,
• round number becomes 3.5 and A becomes inactive.

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WFQ Evaluation

• Protection
• The rate provided to each flow is not affected by
  the sending rate of other flows.
• This firewalling property is desirable by public
  networks.
• Requires per connection scheduler state
• Computing round numbers with iterated deletion is
  costly
• Bound on end to end delay for a regulated (e.g.,
  token bucket) source.

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Iterated Deletion Problem in WFQ

• The main problem in computing packets finish
  number is determining the current round number
  (virtual time) of the simulated GPS server
• Due to iterated deletion problem
• Rate of increase of round number changes as flows
  becomes active or inactive
• Example
• Rate is 1/3 (three connections active)?
• One would think the round number will be 1 at
  time t3
• But a flow may become inactive at t2. Thus the
  round number at t3 would be 1/3 2 1/2 1
  1.167
• Another connection may have finish number less
  than 1.167, then the above calculation would have
  to be redone.
• Hence a WFQ server has to check if round number
  should be recalculated on every packet arrival
  and departure
• It has to do a fairly complex computation every
  few microseconds!!

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Variants of WFQ

• There are less expensive variants of WFQ
• Self Clocked Fair Queueing (SCFQ)?
• Start Time Fair queueing
• Worst Case fair WFQ (WF2Q)?
• WRR

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SCFQ

• Avoid the costly computation of round number
• The finish number of a packet is given by
• Where CF finish number of the packet currently
  being served
• The worst case latency in this case could be
• All the (N-1) connections may have a tie (finish
  number) with the currently served packet.

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Start Time Fair Queuing

• SCFQ has simpler finish number calculation, but
  at the cost of increased worst case delay
• STFQ has finish number and start number
• Start number of a packet arriving into inactive
  connection is the current round number
• Otherwise it is the finish number of the previous
  packet
• Round number is set to start number of the
  current packet
• Packets scheduled in the increasing order of
  start number

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WF2Q

• WFQ can result in bursty service for a flow (many
  packets of a flow is served before other flows
  are served)?
• In WF2Q, instead of choosing the packet with
  smallest finish number among all packets, the
  scheduler chooses smallest finish number among
  all packet that would have started service in the
  GPS system.

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WF2Q Example

• Every packet is of length 1
• 1 flow with weight 0.5 (flow A)?
• 10 flows each with weight 0.05
• 10 packets from flow A arrives at t0
• 1 packet each from the other 10 flows arrive
  at t0

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WF2Q Example
10
1
2
Flow A
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WFQ
40
WF2Q Example
20
2
4
Flow A
GPS
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WF2Q Example
1
3
2
Flow A
WF2Q