Scheduling for Performance

1
Scheduling for Performance

• UMass-Boston
• Ethan Bolker
• April 21, 1999

2
Acknowledgements

• Joint work with Jeff Buzen (BMC Software)
• BMC Software
• Dan Keefe
• Yefim Somin
• Chen Xiaogang (oliver_at_cs.umb.edu)

3
Outline

• Impossibly much to cover
• Performance metrics for workloads
• Beyond priorities
• Modeling. Degradation as a performance metric
• Conservation laws and the permutahedron
• Specifying response times (IBM goal mode)
• Specifying CPU shares (Sun Fair Share)
• Priority distributions
• Work in progress

4
Workload Performance Metrics

• Transaction (open) workload jobs arrive at
  random from an external source
• web or database server, eris with many
  interactive users
• inputs job arrival rate (throughput), service
  time
• performance metric response time
• Batch (closed) workload jobs always waiting
  (latent demand)
• weather prediction, data mining
• input job service time
• performance metrics response time, throughput

5
Beyond priorities

• User wants performance assurance
• response time (open wkls), throughput (closed
  wkls)
• Single workload performance depends on resources
  available (CPU, IO, network)
• Multiple workloads prioritize resource access
• Nice isnt nice - hard to predict performance
  from priorities
• Better set performance goals, system tunes
  itself
• Examples IBM Goal Mode, Sun Fair Share, Eclipse,
  SMART, ...

6
Tuning by Tinkering
Workload Performance (Response Time)
Administrator
Priority Assignments
7
Scheduling for Performance
Administrator
Performance Goals
rarely change
measure frequently
Workload Performance (Response Time)
Priority Assignments
8
Modeling

• System is dynamic, state changes frequently
• Model is a static snapshot, deals in averages and
  probabilities
• Can ask what if? inexpensively
• Modelers measure of performance degradation
  (elapsed time)/(service time)
• deg ? 1, deg 1 when no contention
• (deg lt 1 if parallel computation possible)
• deg n for n closed workloads (no priorities)

9
Modeling One Open Workload

• arrival rate ? (job/sec) (Poisson)
• service time s (sec/job) (exponential distn)
• utilization u ?s, 0 ? u lt 1
• Theorem deg 1/(1-u)
• Often a useful guide even when hypotheses fail
• depends only on u many small jobs few large
  jobs
• faster system ? smaller s ? smaller u ? smaller
  deg
• want u small when waiting is costly (telephones)
• want u near 1 when system is costly
  (supercomputers)

10
Multiple (open) workloads

• Priority state order workloads by priority (ties
  OK)
• two workloads, 3 states 12, 21, 12
• three workloads, 13 states 123 (3! 6 ordered
  states), 123 (3 of these), 123
  (3 of these), 123
• n wkls, f(n) states (simplex lock combos), n!
  ordered
• At each time instant, system runs in some state
  s, V(s) vector of workload
  degradations
• Measure or model V(s) (operational analysis)
• p(s) prob( state s ) fraction of time in
  state s
• V ?s p(s)V(s) (time average, convex
  combination)

11
Two workloads (general case)
wkl 2 degradation
V(12) (wkl 1 high prio)
?
achievable region
?
V(12) (no priorities)
?
0.5 V(12) 0.5V(21)
note u1 lt u2
?
V(21)
wkl 1 degradation
12
Two workloads (conservation)
wkl 2 degradation
V(12)
?
d1 d2
V(12) (no priorities, degradation)
?
?
0.5 V(12) 0.5V(21)
achievable region
u1 d1 u2 d2 --------------- constant avg
degradation u1 u2
?
V(21)
wkl 1 degradation
13
Conservation

• Theorem For any priority assignments
  (1/util)?wkls wutil(w)deg(w) constant avg deg
• Provable from some hypotheses, observable
  (false for printer queues)
• For any set A of workloads
• imagine giving those workloads top priority
• discover (measure or model) avg degradation
  deg(A)
• (1/util(A))?w ?A util(w)deg(w) ? deg(A)
• These linear inequalities determine the convex
  achievable region

14
Two workloads (conservation)
u1 d1 u2 d2 --------------- constant avg
degradation u1 u2
V(12)
?
achievable region
d2
V(12))
?
d1 ? 1/(1- u1 )
d2 ? 1/(1- u2 )
?
V(21)
d1
15
Three workloads
d3
u1 d1 u2 d2 u3 d3 -----------------------
avg degradation u1 u2 u3
V(123)
?
?
V(213)
d2
d1
16
Three workload permutahedron
d2
d1 d2
132
312
132
312
123
123
3
321
123
231
12
123
231
d2 d3
213
213
d1
17
Four workload permutahedron
4! 24 vertices (ordered states) 24 - 2 14
facets (proper subsets) (conservation
constraints) 74 faces (states)
Simplicial geometry and transportation
polytopes, Trans. Amer. Math. Soc. 217 (1976) 138.
18
Scheduling for Performance

• Administrator specifies goals - e.g. degradations
• Software determines priorities, trying to meet
  goals
• Model maps goals to achievable degradations

workload performance goals
achievable region
19
IBM OS390 Goal Mode
Administrator specifies workload degradation goals
wkl 2 degradation
too generous
?
achievable region
?
too ambitious
?
wkl 1 degradation
20
Modeling Goal Mode

• Find right point in permutahedron for given V
• Linear programming solution (Coffman Mitrani)
• Algorithm modeling problem more closely
• for each subset A of workloads
• scale(A) factor to force conservation true
  for A
• for each workload w
• scale(w) min scale(A) scale(A) lt 1
  w ?A
• V(w) scale
• // inequalities now OK, scale back to phedron if
  necessary
• O(2n), fast enough, conjecture ?(2n)
• Refinements for workload importance

21
SUN SRM (Solaris Resource Manager)

• Administrator specifies workload CPU shares
• Share f (0 lt f lt 1) means wkl guaranteed fraction
  f of CPU when its on run queue, can get more if
  no competition
• Share utilization only for closed workloads
• Model f1 1, f2 f3 0
  means wkl 1 has preemptive highest priority
• Two wkls V f1 V(12) f2 V(21)

22
Map Shares to Degradations

• Three (n) workloads
• f1
  f2 f3
• weight(123) ------------------------------
• (f1 f2 f3) (f2 f3)
  (f3)
• V ?ordered states s weight(s) V(s)
• Theorem weights sum to 1
• interesting identity generalizing adding
  fractions
• prove by induction, or by coupon collecting
• O(n!), ?(n!), fast enough for n lt 9 (12)

23
Three workload example
24
Map Shares to Degradations

• Normalize f1 f2 f3 1 (barycentric
  coordinates)

f1 1
achievable region
f1 0
25
Experimental results for 3 workloads
26
Mapping a triangle to a hexagon
f1 1
f2 0
132
312
132
312
123
f1 0
f2 1
3
321
123
231
12
123
wkl 1 high priority
231
213
213
wkl 1 low priority
27
(No Transcript)
28
Map Goals to Shares

• For open workloads, specifying shares is as as
  unintuitive as specifying priorities
• Specify degradation goals
• Map to achievable region
• Reverse map from achievable region to shares
• do
• guess shares // bisection argument
• compute degradations
• until error is acceptably small
• 10 O(n!) is good to 1

29
Map degradations to priorities

• Real system works with priorities
• pdist(w,p) prob( wkl w at prio p) time
  fraction

pdist space (dim n(n-1)
achievable region (dim n-1)
30
Pdists to degradations and back
d2
6 pieces, each combinatorially a square
d1 d2
123
123
123
123
d2 d3
d1
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Pdists to degradations and back
1 0 0 0 .5 .5 0 .5 .5
.33 .33 .33 .33 .33 .33 .33 .33 .33
123
123
1 0 0 0 1 0 0 0 1
.5 .5 0 .5 .5 0 0 0 1
123
123
32
Work in progress

• Model mixed open and closed workloads
• Prove algorithms correct
• Solaris benchmark studies (under way)
• OS390 validation - does data exist?
• Write the paper ...
• Build a product for IBM/Sun/BMC customers