maryam elahi bmelahi@ucalgary.ca fairness in speed scaling design joint work with: carey williamson...
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M a r y a m E l a h ib m e l a h i @ u c a l g a r y. c a
Fairness in Speed Scaling Design
J o i n t w o r k w i t h : C a re y W i l l i a m s o n a n d P h i l i p p Wo e l f e l
2
SCHEDULING
• Sharing resources• Maximize efficiency• Minimize cost
Datacenters
LocksDatabase
s
RoutersInternet
And more…
Requests
(Jobs)Queue
Arrival Rate (λ)
Shared Resource (server)
CPUs
Fixed Service Rates
3
THE DECISION
• Scheduler:• Which job to serve?• Preemptive• Non-preemptive
• Goal(s):• 1: Minimize response
time
Simple Model
?
M/M/1
4
SCHEDULERS
• FCFS: First-Come-First-Served
• PS: Processor Sharing
• SRPT: Shortest-Remaining-Processing-Time• ...
System Load0 0.25 0.5 0.75
Mean
Resp
on
se T
ime
PS
SRPT
FCFS
SRPT is proved optimal, but in practice often PS is used.
5
OTHER GOALS?
• Goal(s):• 1: Minimize response
time
Other QoS:
• 2: Fairness
• 3: Robustness• …
• Optimizes response time
• Is it fair to large jobs?
• What is fair?
SRPT
6
JUSTIFICATION
• Aristotle's notion of fairness• Treat like cases alike• Treated different cases differently, in proportion to their
differences
Response times should be proportional to job sizes
E[T(x)]/x should be constant
Normalized response time or slowdown
T(x): Response
Time of a job with size x
Policy P is fair if: [Wierman et al. 2003]
7
x
E[T
(x)]
/ x
FAIRNESS OF SCHEDULERS
• PS: Always Fair
• FCFS: Always Unfair
• SRPT: Sometimes Fair
• ...
• Fair and Optimal?
FCFS
SRPTPS
x
E[T
(x)]
/ x
SRPT
PS
Lig
ht
load
Hig
h e
nou
gh
load
8
FAIR AND OPTIMAL?
• FSP: Fair Sojourn Protocol [Friedman, et al. 2003]
• Implement SRPT on the PS remaining times
• Slowdown: never worse than PS
• Mean response time: close to that of SRPT
E[T
(x)]
/ x
SRPTPS
FSP
x
• Compute the completion time under virtual PS
• Order the jobs based on their virtual completion times
• Execute the job with the earliest PS completion time
9
THE DECISIONS
• Scheduler:• Which job to serve?
• What speed to use?• Dynamic speed scaling• Gated-static (shut-down)
• Goal(s):• 1: Minimize response time (T)
• 2: Minimize energy usage (E)
?
Adjustable Service Rates
Speed
Pow
er
P(s) = sα
10
THE TRADEOFF
• Combined Goal: Linear combination of the goals:
• Other objectives considered:• Minimize energy for jobs with
deadlines• Minimize response time
subject to energy budget• response-time x energy response-timeenergy 𝑇E
How much reduction in response time justifies using one extra joule
β: cost of energy
11
DYNAMIC SPEED SCALING
Which job to serve?
• Speed Scaling Policy
What speed?
• Job scheduling
SRPT
?
P(s) = sα
n: jobs in the system
+
[Bansal et al. 2009]: 3-competitive for arbitrary power function
12
FAIRNESS AND SPEED SCALING
FCFS
SRPT
PS
FSP
Biased towards big jobs
Biased towards small jobs
Treats all the same
?
[Andrew et al. 2010]: Jobs that run when the queue is big, run faster
13
FAIRNESS AND SPEED SCALING
• Is Slowdown of PS still the right criterion for fairness?
[Andrew et al. 2010]:
- For PS with speed scaling, stays constant.
- Dynamic Speed Scaling magnifies unfairness under SRPT and non-preemptive policies like FCFS.
14
SIMULATION STUDY
• Discrete event simulator written in C++• Scheduling policies: FCFS, PS, SRPT, FSP• Speed Scaling:
• Workload:• Poisson Arrival: rate λ• Exponentially distributed job sizes: rate μ
19
CONCLUSIONS
• FSP with speed scaling shows better fairness behavior in comparison to speed scaled SRPT
• The definition of fairness for scheduling with speed scaling requires further investigations
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