Download Document

Queueing analysis for multi-core
performance improvement: Two case
studies
Deng, J.D. and Purvis, M.K.
Dept. of Information Science., Univ. of Otago, Dunedin
Telecommunication Networks and Applications Conference,
2007. ATNAC 2007. Australasian
1
Outline
Introduction
 Evaluation model

◦ Tandem queueing model for two case studies

Two case studies
◦ Snort
◦ POISE

Conclusion
2
Outline
Introduction
 Evaluation model
 Two case studies
 Conclusions

3
Introduction

Analysis of Multi-core performance
◦ Tandem system model for applications
◦ Queueing analysis
◦ Problem
 Given a tandem queueing model, and find the
optimal number of cores, so that the total service
time is minimal

Case studies
◦ Snort and POISE
◦ Evaluation results is consistent with queueing
analysis
4
Outline
Introduction
 Evaluation model
 Two case studies
 Conclusions

5
Evaluation model

Tandem queueing model
◦ Pipeline
◦ Applications
 Being able to parallelized into independent
procedures
 Each procedure can be served by one or more
cores
6
Evaluation model

Terms definition
◦
◦
◦
◦

λ : arrival/departure rate
μi : service time
ci : number of cores
n : total number of procedures
Burke’s Theorem
◦ When tandem in a steady state
 Arrival rate = departure rate for each procedure
7
Evaluation model

Problem definition
◦ Given the arrival rate (λ), processing times μi
and a total number of cores available, find the
optimal choice of ci, so that the total time in
system is minimal.
8
Evaluation model

To solve the problem
◦ Using D/D/c model for each procedure
◦ Arrival rate/departure rate/number of
services
◦ D is for deterministic (D = λ)
9
Evaluation model

D/D/c model
◦ No queueing delay
◦ Consider only processing overhead
◦ Total processing time T
◦ Total number of cores

, C for maximum number of cores
10
Evaluation model

To find minimum T
◦ Lagrange multiplier
 By letting
→

=>
11
Evaluation model

Lagrange multiplier
◦ In mathematical optimization, the method of
Lagrange multipliers (named after Joseph
Louis Lagrange) provides a strategy for finding
the maxima and minima of a function subject
to constraints




Maximize f (x, y )
subject to g(x, y) = c
Λ (x, y, λ) = f (x, y ) + λ (g (x, y) – c )
maximum : partial derivatives of Λ are zero
12
Evaluation model

Lemma
◦ Assign the numbers of servers to the
subsystems in proportion to the square roots
of their processing time, respectively

This lemma can also work well in more
generic systems with M/D/c subsystems
13
Outline
Introduction
 Evaluation model
 Two case studies
 Conclusions

14
Two case studies - Snort

Snort
◦ A free and open source Network Intrusion
Prevention System (NIPS) and Network
Intrusion Detection System (NIDS)
15
Two case studies - Snort

Snort flow
16
Two case studies - Snort

Measurement
◦ Packets injection
 100,000 to 1 million
◦ Queueing discipline: FIFO
◦ Using three types of traffic
 Attack free, light attacks, heavy attacks
17
Two case studies - Snort

Scenario 1
◦ Without pipelining
◦ Packet distribution: round-robin
◦ Packet rate
 Light: 0.1 packets/μs
 Medium: 0.2 packets/μs
 Heavy: 0.4 packets/μs
18
Two case studies - Snort

Evaluation of scenario 1
◦ Performance curve
19
Two case studies - Snort

Scenario 2
◦ With pipelining
◦ Queueing model
 M/D/c for core group 1
 M/D/1 for core group 2
◦ 2~8 number of Cores
◦ Packet rate
 Light: 0.1 packets/μs
 Medium: 0.2 packets/μs
 Heavy: 0.4 packets/μs
2.31 μs
0.12 μs
0.16 μs
20
Two case studies - Snort

Evaluation of scenario 2
◦ Performance curve
21
Two case studies - Snort

Conclusions
◦ Scheme 2 copes much better with heavy
packet traffic
◦ Relevant queueing delay is significantly
reduced to minimum with 3-4 cores
◦ The 4-core results shown in Fig. 6 are
consistent with Lemma 1
 3 cores for group1 and 1 core for group 2
22
Two case studies - POISE

POISE
◦ An image retrieval and organization
application
23
Two case studies - POISE

Measurement
◦ 200 images
◦ 3.2GHz Pentium 4 single-core with 1GB RAM
24
Two case studies - POISE

Scenario
0.097s

0.007s
0.036 s
Assignment of number of cores
◦ 4-core as an example
◦
round to 3
◦ Group 1 : group 2 = 3:1
25
Two case studies - POISE

Evaluation in 8-core
◦ Markovian image arrival rate
 20 images per second

5+3 has a minimal
total processing time
26
Outline
Introduction
 Evaluation model
 Two case studies
 Conclusions

27
Conclusions
A simplified tandem queueing model is
analyzed for two case studies
 Using queueing analysis to gain
quantitative assessment
 The ideal proportion of core number
distribution is worked out

28