Erlang B Model

Description

This is a program for simulating an arbitrary network of M/M/c/c systems. The simulation result is shown as the blocking probability of the whole network.

Simulation

Two random nodes initiate connection at a rate that is distributed exponentially with parameter lambda (specified by command line option -l or --lambda) with each connection having duration that is also distributed exponentially (with parameter -d or --duration). The two nodes are selected randomly with a uniform distribution. After a certain number of completed connections (-t or --total), the blocking probability of the network is calculated. The initial 10% of the connections are ignored in order to observe the steady state behavior.

Wavelength conversion capability can be enabled (with -c or --converter) to allow using an empty wavelength when a connection is initiated. It is assumed that there are enough converters (i.e. however many wavelengths there are) in each node to accommodate converting any wavelength request. This simplifies the search algorithm.

Building

Boost Graph Library is used for this project. Boost unit testing framework is also used for unit testing.

cd ./build
cmake ..
make -j5

For unit tests, run ctest in the build directory.

Usage

The program is invoked with:

PROGRAM_NAME <input file> <num wavelengths>

Running the program with option -h or --help shows the available command line options. The number of wavelengths is the number of servers available for one node. The more wavelengths there are, the lower the blocking probability gets.

The following figure shows a sample network with 10 nodes and 20 edges.

The input file for this network is written as:

20
0 5
1 5
2 4
2 6
3 2
3 7
4 3
4 8
5 3
5 7
5 9
6 5
7 1
7 2
7 4
8 0
8 6
8 9
9 2
9 3

The first number is the number of edges. The misc/make_connections.rb script is a utility script to generate random vertices and edges.

Another input file included is shown in the following figure:

In this network, connections are always between the same two nodes. Thus, the Erlang B formula can be used to verify the results of the simulation.

The following figure shows a network with ten nodes connected in a bus topology.

No theoretical value can be calculated, but this is included just in case.

Thanks

cxxopts for command line option parsing.

License

MIT License

Author

Naoki Mizuno