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

University of Arkansas Introduction The analysis of a queueing network is important for predicting the performance of a system. A database grid application was modeled using a queueing network. The queueing network was analyzed by using an approximate mean value analysis algorithm called the Bard-Schweitzer algorithm or the proportional estimate (PE) algorithm. Several different types of record flows were modeled. For example, uniform, non-uniform, etc. A system in which the batch and interactive requests are segregated was modeled. March 1, 2004 University of Arkansas

Queueing Network System server client queue [Single class queueing server] client2 [Multiple class queueing server] client3 client1 March 1, 2004 University of Arkansas

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, March 1, 2004 University of Arkansas

Classification of MVA algorithms March 1, 2004 University of Arkansas

Comparison of MVA 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 University of Arkansas

Database Grid Application 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. Database Link Application Example High-level Overview of System March 1, 2004 University of Arkansas

Database Grid Application Cont. A high-level view of the grid The Flow of Records March 1, 2004 University of Arkansas

Current Queueing Model March 1, 2004 University of Arkansas

University of Arkansas 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. March 1, 2004 University of Arkansas

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 University of Arkansas

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(0.0523 S/R), 15 directors(0.0783 S/R), 10 directors(0.0523 S/R) March 1, 2004 University of Arkansas

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 University of Arkansas

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 University of Arkansas

Proposed Change to application It was assumed that there were two updates per request 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 University of Arkansas

Segregation of batch and interactive classes This model is for the actual 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 0.0002 s/record parameter as a design parameter March 1, 2004 University of Arkansas

University of Arkansas Conclusions The number of directors should be approximately equal to the number of clients to obtain the maximum throughput of the system. 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 University of Arkansas

University of Arkansas 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 University of Arkansas

University of Arkansas Contact Information and Copy of this Presentation Dale R. Thompson 311 Engineering Hall Fayetteville, Arkansas, USA 72701 Phone: +1 (479) 575-5090 E-mail: drt@uark.edu WWW: http://csce.uark.edu/~drt March 1, 2004 University of Arkansas