Soft Real Time: Proportional Share and Fairness

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Soft Real TimeProportional Share and Fairness

• Fred Kuhns
• (fredk_at_cse.wustl.edu, http//www.arl.wustl.edu/fr
  edk)
• Applied Research Laboratory
• Department of Computer Science and Engineering
• Washington University in St. Louis

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Providing GPS Like service

• emulates sporadic task (ps, es)
• Scheduling aperiodic tasks in deadline driven
  systems
• Emulate Generalized Processor Sharing (GPS)
  Algorithm
• provides server an infinitesimally small time
  slice of length proportional to server size.
• Timing isolation

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Terminology and background

• Density of a sporadic job Ji
• ei maximum execution time ri release time
  di deadline, density ei/(di-ri) active in
  feasible interval (ri, di
• Sporadic Task Si comprised of a string of jobs
  Jij with execution times eij, interrelease times
  of pij and instantaneous utilization of eij/pij
  when dij pij.
• Instantaneous utilization of a sporadic task
• ui maxj(eij/pij)
• independent, preemptable sporadic jobs are
  schedulable by EDF if total density lt 1
• if total instantaneous utilization lt 1 and
  deadline equals period then schedulable by EDF.
• if total of periodic tasks utilization and
  sporadic tasks instantaneous utilization lt 1
  then schedulable

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Constant Utilization Servers

• Server emulates a sporadic task.
• Defined by size us instantaneous
  utilization,
• d is always defined
• emulates sporadic task with constant us
• Scheduled with periodic tasks on EDF basis

• Consumption rules
• C1 consume when executing
• Replenishment rules
• R1 initially es 0, d 0
• R2 aperiodic job e arrives to empty queue at
  time t, if tltd, do nothing, else set d t
  e/us, ans set es e
• R3 At deadline d of serverif backlogged, set d
  d e/us, es eelse do nothing

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Total Bandwidth Servers

• Uses background time to improve responsiveness
  over that of a constant utilization server

• Consumption rules
• C1 Consume only when executing.
• Replenishment rules
• R1 Initially, es 0, d 0
• R2 aperiodic job e arrives to empty queue at
  time t, set d max(d, t) e/us and es e.
• R3 when done with current job, remove from queue
  and if backlogged, set d d e/us and es
  eelse if idle then do nothing.

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Fairness and Starvation

• fair within an interval I if the fraction of time
  received by each backlogged server is
  proportional to the its size.
• Total bandwidth server is not fair
• Consider a system which only consists of n such
  servers.
• let wi(t1,t2) equal the processor time used by
  server i (i.e. allocated processor time) in
  interval I (t1, t2) for t2 gt t1.
• Normalized service wi(t1,t2)/ui fair if the
  normalized service of all servers differ by no
  more than a fairness threshold FRgt0.

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Weighted Fair Queuing Servers

• Goal is to provide fair access to processor while
  permitting jobs to use an idle processor
• Total bandwidth server is not fair
• Same worst case response time as total bandwidth
  server
• Non-preemptive version used for network packet
  scheduling
• Jobs are assigned a finish number that represents
  the round in which its deadline occurs (think of
  this as virtual time).

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Weighted fair queuing preemptive

• FN system finish number, Ub backlogged
  utilization
• Scheduling
• A server is eligible when it has budget and an
  assigned finish number
• Priority assigned to eligible servers based on
  finish number Server with smallest finish time
  has highest priority

• Consumption
• Consume only when running
• Initialization
• I1 Idle system, set FN0, Ub0, t-1 0 ei,fni
  0 for all i.
• I2 first job arrives to an Idle system for some
  server FQk set t-1 t, Ub uk, budget ek e
  and fnk e/uk
• Updating current finish number and replenishment
• R1 job arrives at an idle server FQi, then 1
  increment system FN FN (t-t-1)/Ub 2 set t-1
  t and increment Ub ui 3 update FQi ei
  e fni FN e/ui and place in ready queue
• R2 FQi completes a job, remove it from the
  queue if still backlogged ei e fni
  e/ui else (idle) FN (t - t-1)/Ub, set t-1
  t decrement Ub - ui