Response Time-Optimized Distributed Cloud Resource Allocation - - PowerPoint PPT Presentation

▶
response time optimized distributed cloud resource
SMART_READER_LITE
LIVE PREVIEW

Response Time-Optimized Distributed Cloud Resource Allocation - - PowerPoint PPT Presentation

Aug 08, 2023 43 likes •329 views

Response Time-Optimized Distributed Cloud Resource Allocation Matthias Keller Holger Karl Computer Networks Group Universitt Paderborn Minimizing response times Latency-critical service Interactive, emergency service request t

slide-1
SLIDE 1

Computer Networks Group Universität Paderborn

Response Time-Optimized Distributed Cloud Resource Allocation

Matthias Keller Holger Karl

slide-2
SLIDE 2

Response Time-Optimized Distributed Cloud Resource Allocation

Minimizing response times

21

request t Response Time answer

DCC 2014

  • Latency-critical service
  • Interactive, emergency service
slide-3
SLIDE 3

Response Time-Optimized Distributed Cloud Resource Allocation

Minimizing response times

22

request t

DCC 2014

  • Latency-critical service
  • Interactive, emergency service

Time to compute the answer answer Response Time

slide-4
SLIDE 4

Response Time-Optimized Distributed Cloud Resource Allocation

Minimizing response times

23

request t

DCC 2014

answer Response Time Queuing System:

Time in Queue Processing Time Time in System (TIS)

+

slide-5
SLIDE 5

Response Time-Optimized Distributed Cloud Resource Allocation

Minimizing response times

24

request t

DCC 2014

  • Latency-critical service
  • Interactive, emergency service
  • Decision: Spend time on RTT or TIS

answer Response Time Queuing System:

Time in Queue Processing Time Time in System (TIS)

+

slide-6
SLIDE 6

Response Time-Optimized Distributed Cloud Resource Allocation

Minimizing response times

25

request

DCC 2014

  • Latency-critical service
  • Interactive, emergency service
  • Decision: Spend time on RTT or TIS

answer Response Time

Time in System (TIS)

slide-7
SLIDE 7

10 20 30 40 50 arrival rate 2 4 6 8 10 12 14 average response time

RTT solution

Response Time-Optimized Distributed Cloud Resource Allocation

Example: RTT + TIS

26 DCC 2014

  • Demand assignment
  • Facility Location Solution with RTT only

Better

slide-8
SLIDE 8

Response Time-Optimized Distributed Cloud Resource Allocation

Example: RTT + TIS

27 DCC 2014

  • Demand assignment
  • Facility Location Solution with RTT only

10 20 30 40 50 arrival rate 2 4 6 8 10 12 14 average response time

RTT solution RTT solution with TIS

Better

slide-9
SLIDE 9

Response Time-Optimized Distributed Cloud Resource Allocation

Example: RTT + TIS

28 DCC 2014

  • Demand assignment
  • Facility Location Solution with RTT only

10 20 30 40 50 arrival rate 2 4 6 8 10 12 14 average response time

RTT solution RTT solution with TIS

Better Surprise at runtime

slide-10
SLIDE 10

Response Time-Optimized Distributed Cloud Resource Allocation

Example: RTT + TIS

29 DCC 2014

  • Demand assignment
  • Facility Location Solution with RTT only
  • With RTT + TIS

10 20 30 40 50 arrival rate 2 4 6 8 10 12 14 average response time

RTT solution RTT solution with TIS RTT+TIS solution

Better

slide-11
SLIDE 11

Goal

30 DCC 2014 Response Time-Optimized Distributed Cloud Resource Allocation

Given

  • Network
  • Data centres

Objective

  • Minimize response time

Means

  • Allocation of n VMs at data

centres

slide-12
SLIDE 12

Goal

31 DCC 2014 Response Time-Optimized Distributed Cloud Resource Allocation

Number of VMs Response Time Optimal Solutions

Given

  • Network
  • Data centres

Objective

  • Minimize response time

Means

  • Allocation of n VMs at data

centres

Characterise:

  • How does response time

depend on number n of VMs?

slide-13
SLIDE 13

Two Approaches

Accurate Solution

  • Mixed Integer Convex Problem
  • Convex TIS function for each

data centre

32 DCC 2014 Response Time-Optimized Distributed Cloud Resource Allocation

0.00 0.30 0.60 0.90 utilization 2 4 6 8 10 time in system

  • Tough to solve – slow?
slide-14
SLIDE 14

Two Approaches

Accurate Solution

  • Mixed Integer Convex Problem
  • Convex TIS function for each

data centre

Approximate Solution

  • Reformulation: Mixed Integer

Linear Problem

  • Linearization of TIS function

33 DCC 2014 Response Time-Optimized Distributed Cloud Resource Allocation

0.00 0.30 0.60 0.90 utilization 2 4 6 8 10 time in system 0.00 0.30 0.60 0.90 utilization 2 4 6 8 10 time in system

  • riginal

uniform

  • Accuracy? Speed?
  • Tough to solve – slow?
slide-15
SLIDE 15

Improve accuracy of linearization

  • Objective:
  • Minimize the maximum difference
  • Control knobs
  • Number of basepoints
  • End point at asymptote
  • Basepoint positions

34 DCC 2014 Response Time-Optimized Distributed Cloud Resource Allocation

utilization 2 4 6 8 10 time in system

  • riginal

uniform

0.00 0.30 0.60 0.90 0.0 0.5 1.0 1.5 2.0 2.5 difference to org.

Better

slide-16
SLIDE 16

Improve accuracy of linearization

  • Objective:
  • Minimize the maximum difference
  • Control knobs
  • Number of basepoints
  • End point at asymptote
  • Basepoint positions
  • Evaluation in Paper

35 DCC 2014 Response Time-Optimized Distributed Cloud Resource Allocation

utilization 2 4 6 8 10 time in system

  • riginal

uniform imamoto

0.00 0.30 0.60 0.90 0.0 0.5 1.0 1.5 2.0 2.5 difference to org.

Better

slide-17
SLIDE 17

Evaluation of both approaches Convex Problem

  • Reference Solution
  • Tough to solve – slow?

Linear Problem

  • Approximate Solution
  • Accuracy? Speed?

36 DCC 2014 Response Time-Optimized Distributed Cloud Resource Allocation

Linearization

slide-18
SLIDE 18

Evaluation of both approaches Convex Problem

  • Reference Solution
  • Tough to solve – slow?

Linear Problem

  • Approximate Solution
  • Accuracy? Speed?

37 DCC 2014 Response Time-Optimized Distributed Cloud Resource Allocation

Linearization Configurations

  • 6 topologies, 12 – 54 nodes
  • à 50 random demand realizations
  • 10 data centre fix
slide-19
SLIDE 19

Evaluation of both approaches Convex Problem

  • Reference Solution
  • Tough to solve – slow?

Linear Problem

  • Approximate Solution
  • Accuracy? Speed?

38 DCC 2014 Response Time-Optimized Distributed Cloud Resource Allocation

Linearization Configurations

  • 6 topologies, 12 – 54 nodes
  • à 50 random demand realizations
  • 10 data centre fix

VM limit: 5 – 10

slide-20
SLIDE 20

Results – Approximation Ratio

39 DCC 2014 Response Time-Optimized Distributed Cloud Resource Allocation dfn-bwin di-yuan norway atlanta zib54 ta2 topology 1.00 1.02 1.04 1.06 1.08 1.10 1.12 1.14 1.16 approximation ratio

Better

  • approx. ratio = Resp.timeLinear

Resp.timeConvex

small large

slide-21
SLIDE 21

Results – Approximation Ratio

40 DCC 2014 Response Time-Optimized Distributed Cloud Resource Allocation dfn-bwin di-yuan norway atlanta zib54 ta2 topology 1.00 1.02 1.04 1.06 1.08 1.10 1.12 1.14 1.16 approximation ratio

Better

  • approx. ratio = Resp.timeLinear

Resp.timeConvex

small large

slide-22
SLIDE 22

Results – Runtime Ratio

41 DCC 2014 Response Time-Optimized Distributed Cloud Resource Allocation dfn-bwin di-yuan norway atlanta zib54 ta2 topology 10-4 10-3 10-2 10-1 100 runtime ratio

Better

small large

runtime ratio = RuntimeLinear RuntimeConvex

slide-23
SLIDE 23

Results – Runtime Ratio

42 DCC 2014 Response Time-Optimized Distributed Cloud Resource Allocation dfn-bwin di-yuan norway atlanta zib54 ta2 topology 10-4 10-3 10-2 10-1 100 runtime ratio

Better

small large

runtime ratio = RuntimeLinear RuntimeConvex

RuntimeLinear RuntimeConvex 2s 0:28h 7s 1:03h 5s 1:15h

slide-24
SLIDE 24

Results – Runtime Ratio

43 DCC 2014 Response Time-Optimized Distributed Cloud Resource Allocation dfn-bwin di-yuan norway atlanta zib54 ta2 topology 10-4 10-3 10-2 10-1 100 runtime ratio

Better

small large

runtime ratio = RuntimeLinear RuntimeConvex

RuntimeLinear RuntimeConvex 2s 0:28h 7s 1:03h 5s 1:15h

slide-25
SLIDE 25

Results – Optimal Solutions

  • More Resources:
  • Shorter time in queuing system
  • VMs at closer data centres

44 DCC 2014 Response Time-Optimized Distributed Cloud Resource Allocation

di-yuan norway dfn-bwin 5 6 7 8 9 10 5 6 7 8 9 10 5 6 7 8 9 10 Resource Limit (#VM) 50 100 150 200 250 300 350 Response Time (ms)

RTT TIS

slide-26
SLIDE 26

Results – Optimal Solutions

  • More Resources:
  • Shorter time in queuing system
  • VMs at closer data centres

45 DCC 2014 Response Time-Optimized Distributed Cloud Resource Allocation

di-yuan norway dfn-bwin 5 6 7 8 9 10 5 6 7 8 9 10 5 6 7 8 9 10 Resource Limit (#VM) 50 100 150 200 250 300 350 Response Time (ms)

RTT TIS

slide-27
SLIDE 27

In the paper…

  • Convex/Linear Problem Formulation
  • Facility Location Problem & queuing model
  • P-median facility location + convex cost function
  • P-median facility location + piecewise linear cost function
  • Piecewise Linear Function: Minimize maximal difference
  • Convexity Proof
  • Evaluation
  • Pareto optimal solutions
  • Compare linear/convex problem
  • Approx. Ratio
  • Runtime

46 DCC 2014 Response Time-Optimized Distributed Cloud Resource Allocation

slide-28
SLIDE 28

In conclusion…

… adjust your latency-sensitive service:

  • Faster!
  • Adapt to demand fluctuations swiftly
  • Accurate!
  • With queuing delay – no surprises at runtime

47 DCC 2014 Response Time-Optimized Distributed Cloud Resource Allocation