1. Approximate Mean Value Analysis of a Database Grid Application
Dale R. Thompson
Computer Science and Computer Engineering
University of Arkansas
March 1, 2004

2. Contents Introduction Queueing Network System MVA algorithms
Comparison of AMVA
Proposed System
Current Queueing Model
CPU and Network Demand
Maximum Throughput and Block Size
Uniform Distribution
Nonuniform Distribution
Uniform : number of Clients
Proposed change to application
Segregation of batch and interactive classes
Conclusion
Future Work
March 1, 2004

3. Introduction
A database grid application is modeled using an approximate mean value analysis algorithm.
The system is represented by a queueing network.
The analysis of a queueing network is important for predicting the performance of a system.
Several algorithms will be explained and compared.
Database grid application is introduced and the performance objectives are defined and analyzed by using an approximate MVA algorithm called the Bard-Schweitzer algorithm or the proportional estimate (PE) algorithm.
Several models will be modeled. For example, uniform, non-uniform, etc.
A system in which the batch and interactive requests are segregated is modeled.
Conclusions of analysis.
March 1, 2004

4. Queueing Network System
server
client
queue
[Single class queueing server]
client2
[Multiple class queueing server]
client3
client1
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5. when class c is a batch processing,
MVA algorithms
when class c is a batch processing,
Zc=0
Mean Value Analysis calculates throughput (Xc), response time (Rc), and queue length (Qd,c)of each class.
It can be classified with the number of client – open or closed.
It also can be classified with how to get the values Exactly or Approximately.
Single class or multiple classes?
When Queueing Server,
When Delay Server,
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6. Classification of MVA algorithms
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7. Comparison of AMVA algorithms
Rank of Accuracy
Space Complexity
Time Complexity
Exact MVA 1
O(KC∏Cc=1(Nc+1)
Linearizer 2
O(KC2)/iteration
O(KC3)/iteration PE 3
O(KC)/iteration
LCP 4
Algorithms
Rank of Accuracy
Space Complexity
Time Complexity
No con.
Congestion
Exact MVA 1
O(KC∏Cc=1(Nc+1) FL 2 4
O(KC)/iteration QL 3 PE
1. Average errors in throughput and response time for three algorithm is less than 1%~2%.
2. QL is a little bit better than PE algorithm when congestion. So, they are not much different.
3. We decided use PE algorithm for analyzing our system.
March 1, 2004

8. Proposed System Database Link Application Example
Director grid services the particular client and receives the block of records and splits the records according to a key.
Database grid is logically partitioned to serve different keys.
March 1, 2004
Database Link Application Example
High-level Overview of System

9. A high-level view of the grid
Cont.
A high-level view of the grid
The Flow of Records
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10. Current Queueing Model
March 1, 2004
Queueing Model

11. CPU and Network Demand
Record size - 500bytes, Ethernet - 26bytes, IP - 20bytes, TCP - 20bytes. Total actual record size - 566bytes
Service demand1 : computers in the clients, the director grid, and database grid.
Service demand2 : network cards in the clients, the director grid, and database grid.
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12. Maximum Throughput and Block size
Maximum attainable throughput : 79.5Mega record/hr
The block size :
Batch class : 1150 records
Interactive class : 1 record.
March 1, 2004

13. Uniforms Distributions
Each record was equally likely to go to any of the computers in the database grid,
Block size : varying
Throughput : 20 directors(79.2 MR/hr), 15 directors(59.4 MR/hr), 10 directors(39.7 MR/hr)
Delay time : 20 directors( S/R), 15 directors( S/R), 10 directors( S/R)
March 1, 2004

14. Non-uniform Distribution
Non-uniform distribution of demands was created by assuming that
20 clients : 10,15,20 director computers : 70 database computers
80% of the requests from clients (16 clients) => 20% of the database grid (14 Computers).
The remaining 20% of the requests (4 clients)=> the remaining 80% of the database grid (56 Computers)
Throughput (Mrecords/hr)
10 directors
15 directors
20 directors
Uniform 40 59 79
Non-uniform 71
Delay time (s/records)
0.1043
0.0783
0.0523
0.0581
1. If all clients distribute their requests uniformly across the database grid, the overall efficiency of the system improves.
2. To demonstrate this affect on the performance, a uniform distribution of demands was compared with a non-uniform distribution of demands both using a block size of 1150
March 1, 2004

15. Uniform : Number of Clients
Uniform : 1150 records
Varying number of Clients : 20, 40, 60
Throughput (Mrecords/hr)
20 clients
40 clients
60 clients
10 directors 40 20 13
15 directors 59 30
20 directors 79 26
Delay time (s/record)
0.1043
0.2084
0.3126
0.0783
0.1433
0.0523
0.1564
March 1, 2004

16. Proposed Change to application
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 client out of 20) require demand from two different database grid computers.
Block size : 1150 records
Throughput (Mrecords/hr)
10 directors
15 directors
20 directors
Original Application 40 59 79
Proposed Application 39 57 77
% decrease
2.50
3.32
2.49
Delay time (s/record)
0.1043
0.0783
0.0523
0.1095
0.0809
0.0549
% increase
4.98
4.97
March 1, 2004

17. Segregation of batch and interactive classes
This model is for the real system.
20 clients : 16 director computers : 70 database computers.
There are 12 clients batch and 8 clients interactive record.
Batch 12 clients => 12 directors
Interactive 8 clients => 4 directors.
Throughput (Mrecords/hr)
Interactive
3.4
Batch
47.5
Total
50.9
Avg. Delay (s/record)
0.0002
0.0314
0.0316
This reduces the mean delay per record to better serve the interactive clients
The database link application could use the s/record parameter as a design parameter
March 1, 2004

18. Conclusions of Work
First, the number of directors should be approximately equal to the number of clients to obtain the maximum throughput of the system.
Second, the bottleneck device in this system is the network.
The proposed application change that caused 5% of the records to require service from two database grid computers did not significantly decrease the performance of the system.
Segregating the batch and interactive classes at the director level causes the response time of the interactive classes to decrease. The decreased response time comes at the price of lowering the overall throughput of the system. As discussed, the model can be used to determine the trade offs of decreased response time versus increased throughput.
March 1, 2004

19. Future Work Traffic analysis of submitted records
Simulation of alternate configurations
Scheduling of grid computers
Modeling/Simulation of different applications
Grid-enable applications that run in different locations and organizations
Others?
March 1, 2004