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Mean Value Analysis

Evaluates performance of chaining and aggregator patterns for some use cases(Pass Through, CPU bound, DB and DB with caching)

MVA is a recursive algorithm to find the expected waiting times, queue lengths of a closed queueing network. In our implementation, we use K servers with M/M/1 queues and altogether N requests(concurrency) in the system.

MVA assumes exponentially distributed inter-interval and exponentially distributed service times (aka markovian assumptions).

How to use the code

Modeling the System Thoughput and Latency

General MVA is implemented in mva_multipleSystems.py script. You can run the code by,

tip: set number of scenarios to 1 as in data_single_scenario for a single closed system.

python mva_multipleSystems.py < data/data_single_scenario

Compare several scenarios of closed systems using MVA is implemented in mva_multipleSystems.py script. You can run the code by,

python mva_multipleSystems.py < data/<relavent data file>

data file has the following structure

  • first line is the systems which you want to compare (S). If you are not comparing multiple systems just pass 1.
  • seccond line is the maximum concurrency in the system (N)
  • next S blocks of lines depicts the characteristics related to each S scenarios (each different closed system).
    • first line has the service rates of the ith closed system(ith scenario) where (1 < i <= K). Let's say we have K servers in the system.
    • second line of the ith block represents the additional overheads in the server (set to 0's for no additional overhead)
    • next K lines in the ith block are the routing probabilities. mth column in jth row (1 < j <= K) in these these K lines shows the routing probability of kth server to mth server

Example 1

Screenshot from 2022-04-21 22-58-27

  • Input for the above example would be,

1
100
s1, s2, s3
0, 0, 0
0, 1, 0
0.5, 0, 0.5
0, 1, 0

  • Explanation - first line is 1 because we're not comparing multiple systems but only have one system. Second line we have the maximum concurrent users (=100). Next are the service rates of each servers. Overheads are set to zero for each server. routing probabilities are given as shown in the only diagram.

For Windows

To run the code in windows, you just need to run the mva_multipleSystems.py and enter the required input data in the terminal according to the above structure. You can run like this even with Ubuntu and MacOS.