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Approximate Mean Value Analysis of a Approximate Mean Value Analysis of a Database Grid ApplicationDatabase Grid Application

Dale R. ThompsonDale R. Thompson

Computer Science and Computer EngineeringComputer Science and Computer Engineering

University of ArkansasUniversity of Arkansas

March 1, 2004March 1, 2004 22

ContentsContents

IntroductionIntroduction Queueing Network Queueing Network

SystemSystem MVA algorithmsMVA algorithms Comparison of AMVAComparison of AMVA Proposed SystemProposed System Current Queueing Current Queueing

ModelModel CPU and Network CPU and Network

DemandDemand Maximum Throughput Maximum Throughput

and Block Sizeand Block Size

Uniform DistributionUniform Distribution Nonuniform Nonuniform

DistributionDistribution Uniform : number of Uniform : number of

ClientsClients Proposed change to Proposed change to

applicationapplication Segregation of batch Segregation of batch

and interactive classesand interactive classes ConclusionConclusion Future WorkFuture Work

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IntroductionIntroduction

A database grid application is modeled using an approximate mean A database grid application is modeled using an approximate mean value analysis algorithm. value analysis algorithm.

The system is represented by a queueing network. The system is represented by a queueing network. The analysis of a queueing network is important for predicting the The analysis of a queueing network is important for predicting the

performance of a system.performance of a system. Several algorithms will be explained and compared.Several algorithms will be explained and compared. Database grid application is introduced and the performance objectives Database grid application is introduced and the performance objectives

are defined and analyzed by using an approximate MVA algorithm called are defined and analyzed by using an approximate MVA algorithm called the Bard-Schweitzer algorithm or the proportional estimate (PE) the Bard-Schweitzer algorithm or the proportional estimate (PE) algorithm.algorithm.

Several models will be modeled. For example, uniform, non-uniform, etc.Several models will be modeled. For example, uniform, non-uniform, etc. A system in which the batch and interactive requests are segregated is A system in which the batch and interactive requests are segregated is

modeled. modeled. Conclusions of analysis.Conclusions of analysis.

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Queueing Network SystemQueueing Network System

server

client

queue

[Single class queueing server]

server

client2

queue

[Multiple class queueing server]

client3

client1

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MVA algorithmsMVA algorithms

0)(, NQ cd

Mean Value Analysis Mean Value Analysis calculates throughput (calculates throughput (XXcc), ), response time (response time (RRcc), and ), and queue length (queue length (QQd,cd,c)of each )of each class.class.

It can be classified with the It can be classified with the number of client – open or number of client – open or closed.closed.

It also can be classified with It also can be classified with how to get the values how to get the values Exactly or Approximately.Exactly or Approximately.

Single class or multiple Single class or multiple classes?classes?

when class c is a batch processing,Zc=0

K

dcdc

cc

NRZ

NNX

1, )(

)(

)](1[)( ,,, NQDNR cdcdcd

When Queueing Server,

When Delay Server,

0)(, NQ cd

0)(, NQ cd

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Classification of MVA Classification of MVA algorithmsalgorithms

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Comparison of AMVA Comparison of AMVA algorithmsalgorithms

AlgorithmsRank of

AccuracySpace Complexity Time Complexity

Exact MVA 1O(KC∏O(KC∏CC

c=1c=1(N(Ncc+1+1))

O(KC∏O(KC∏CCc=1c=1(N(Ncc+1+1

))

Linearizer 2 O(KCO(KC22)/iteration)/iteration O(KCO(KC33)/iteration)/iteration

PE 3 O(KC)/iterationO(KC)/iteration O(KC)/iterationO(KC)/iteration

LCP 4 O(KC)/iterationO(KC)/iteration O(KC)/iterationO(KC)/iteration

AlgorithmsRank of Accuracy

Space Complexity Time ComplexityNo con. Congestion

Exact MVA 1 1O(KC∏O(KC∏CC

c=1c=1(N(Ncc++1)1)

O(KC∏O(KC∏CCc=1c=1(N(Ncc+1+1

))

FL 2 4 O(KC)/iterationO(KC)/iteration O(KC)/iterationO(KC)/iteration

QL 3 2 O(KC)/iterationO(KC)/iteration O(KC)/iterationO(KC)/iteration

PE 4 3 O(KC)/iterationO(KC)/iteration O(KC)/iterationO(KC)/iteration

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Proposed SystemProposed System

High-level Overview of System

Database Link Application Example

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Cont.Cont.

A high-level view of the grid The Flow of Records

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Current Queueing ModelCurrent Queueing Model

Queueing Model

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CPU and Network DemandCPU and Network Demand

Record size - 500bytes, Ethernet - 26bytes, Record size - 500bytes, Ethernet - 26bytes, IP - 20bytes, TCP - 20bytes. Total actual IP - 20bytes, TCP - 20bytes. Total actual record size - 566bytesrecord size - 566bytes

Service demand1 : computers in the clients, Service demand1 : computers in the clients, the director grid, and database grid.the director grid, and database grid.

Service demand2 : network cards in the Service demand2 : network cards in the clients, the director grid, and database grid.clients, the director grid, and database grid.

recordssbits

bytebitsrecordbytes /10528.4/101

1)/8()/566( 6

9

recordssbits

bytebitsrecordbytes /10528.4/10100

1)/8()/566( 5

6

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Maximum Throughput and Block Maximum Throughput and Block sizesize

Maximum attainable throughput : 79.5Mega Maximum attainable throughput : 79.5Mega record/hrrecord/hr

The block size : The block size : Batch class : 1150 recordsBatch class : 1150 records Interactive class : 1 recordInteractive class : 1 record. .

hrMreccordhrsrecords

/5.7910//3600/10528.4

1 65

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Uniforms DistributionsUniforms Distributions

Each record was equally likely to go to any of the computers in the Each record was equally likely to go to any of the computers in the database grid,database grid,

Block size : varyingBlock size : varying

Uniform

0.00

0.05

0.10

0.15

0.20

50 500 950 1400 1850Block Size (records)

Dela

y Ti

me

(s/re

cord

)

10 Dir

15 Dir

20 Dir

Uniform

0102030405060708090

50 500 950 1400 1850Block Size (records)

Thro

ugpu

t (M

reco

rds/

hr)

20 Dir

15 Dir

10 Dir

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Non-uniform DistributionNon-uniform Distribution

Non-uniform distribution of demands was created by Non-uniform distribution of demands was created by assuming that assuming that 20 clients : 10,15,20 director computers : 70 database 20 clients : 10,15,20 director computers : 70 database

computerscomputers 80% of the requests from clients (16 clients) => 20% of the 80% of the requests from clients (16 clients) => 20% of the

database grid (14 Computers). database grid (14 Computers). The remaining 20% of the requests (4 clients)=> the The remaining 20% of the requests (4 clients)=> the

remaining 80% of the database grid (56 Computers)remaining 80% of the database grid (56 Computers)Throughput Throughput

(Mrecords/hr)(Mrecords/hr) 10 directors10 directors 15 directors15 directors 20 directors20 directors

UniformUniform 4040 5959 7979

Non-uniformNon-uniform 4040 5959 7171

Delay time Delay time (s/records)(s/records) 10 directors10 directors 15 directors15 directors 20 directors20 directors

UniformUniform 0.10430.1043 0.07830.0783 0.05230.0523

Non-uniformNon-uniform 0.10430.1043 0.07830.0783 0.05810.0581

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Uniform : Number of ClientsUniform : Number of Clients

Uniform : 1150 recordsUniform : 1150 records Varying number of Clients : 20, 40, 60Varying number of Clients : 20, 40, 60

Throughput Throughput (Mrecords/hr)(Mrecords/hr) 20 clients20 clients 40 clients40 clients 60 clients60 clients

10 directors10 directors 4040 2020 1313

15 directors15 directors 5959 3030 2020

20 directors20 directors 7979 4040 2626

Delay time Delay time (s/record)(s/record) 20 clients20 clients 40 clients40 clients 60 clients60 clients

10 directors10 directors 0.10430.1043 0.20840.2084 0.31260.3126

15 directors15 directors 0.07830.0783 0.14330.1433 0.20840.2084

20 directors20 directors 0.05230.0523 0.10430.1043 0.15640.1564

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Proposed Change to Proposed Change to applicationapplication

It assume that there are two times update (new geo. and old geo.)It assume that there are two times update (new geo. and old geo.) This proposed change was modeled by having 5% of the clients (1 This proposed change was modeled by having 5% of the clients (1

client out of 20) require demand from two different database grid client out of 20) require demand from two different database grid computers. computers.

Block size : 1150 recordsBlock size : 1150 recordsThroughput Throughput

(Mrecords/hr)(Mrecords/hr) 10 directors10 directors 15 directors15 directors20 20 directodirecto

rsrs

Original ApplicationOriginal Application 4040 5959 7979

Proposed ApplicationProposed Application 3939 5757 7777

% decrease% decrease 2.502.50 3.323.32 2.492.49

Delay time (s/record)Delay time (s/record) 10 directors10 directors 15 directors15 directors20 20 directodirecto

rsrs

Original ApplicationOriginal Application 0.10430.1043 0.07830.0783 0.05230.0523

Proposed ApplicationProposed Application 0.10950.1095 0.08090.0809 0.05490.0549

% increase% increase 4.984.98 3.323.32 4.974.97

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Segregation of batch and Segregation of batch and interactive classesinteractive classes

This model is for This model is for the real systemthe real system.. 20 clients : 16 director computers : 70 database computers.20 clients : 16 director computers : 70 database computers.

There are 12 clients batch and 8 clients interactive record. There are 12 clients batch and 8 clients interactive record. Batch 12 clients => 12 directorsBatch 12 clients => 12 directors Interactive 8 clients => 4 directors.Interactive 8 clients => 4 directors.

Throughput (Mrecords/hr)Throughput (Mrecords/hr)

InteractiveInteractive 3.43.4

BatchBatch 47.547.5

TotalTotal 50.950.9

Avg. Delay (s/record)Avg. Delay (s/record)

InteractiveInteractive 0.00020.0002

BatchBatch 0.03140.0314

TotalTotal 0.03160.0316

This reduces the mean delay This reduces the mean delay per record to better serve the per record to better serve the interactive clientsinteractive clients

The database link application The database link application could use the 0.0002 s/record could use the 0.0002 s/record parameter as a design parameter as a design parameterparameter

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Conclusions of WorkConclusions of Work

First, the number of directors should be approximately equal First, the number of directors should be approximately equal to the number of clients to obtain the maximum throughput of to the number of clients to obtain the maximum throughput of the system.the system.

Second, the bottleneck device in this system is the network.Second, the bottleneck device in this system is the network. The proposed application change that caused 5% of the The proposed application change that caused 5% of the

records to require service from two database grid computers records to require service from two database grid computers did not significantly decrease the performance of the system. did not significantly decrease the performance of the system.

Segregating the batch and interactive classes at the director Segregating the batch and interactive classes at the director level causes the response time of the interactive classes to level causes the response time of the interactive classes to decrease. The decreased response time comes at the price of decrease. The decreased response time comes at the price of lowering the overall throughput of the system. As discussed, lowering the overall throughput of the system. As discussed, the model can be used to determine the trade offs of the model can be used to determine the trade offs of decreased response time versus increased throughput.decreased response time versus increased throughput.

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Future WorkFuture Work

Traffic analysis of submitted recordsTraffic analysis of submitted records Simulation of alternate configurationsSimulation of alternate configurations Scheduling of grid computersScheduling of grid computers Modeling/Simulation of different Modeling/Simulation of different

applicationsapplications Grid-enable applications that run in Grid-enable applications that run in

different locations different locations andand organizations organizations Others?Others?