fast-engset

Release notes

🧰 Maintenance

• Add long description for PyPI.

fast-engset

Release notes

💥 API-breaking changes and new features

This version is backwards incompatible with the previous release. A high level overview of the API-breaking changes and new features is given below, but I recommend you to refer to the README for details.

• Change routines to return a Result(n_iters, status, value) tuple detailing the number of iterations to convergence, a status code, and the value computed
• Add support for choosing the numerical algorithm to use in a routine via the alg argument
• Add new routines to compute the number of sources (fe.n_sources) and the offered traffic (fe.total_traffic) were added
• Rename existing routines to compute the blocking probability (fe.blocking_prob) and the number of servers (fe.n_servers)

🚀 Speed improvements

• Use JIT compilation to get ~10x speedup

📖 Documentation

• New README with in-depth tutorial

🧰 Maintenance

• Add tox to orchestrate linting and testing in both Python 2.7 and 3
• Add 1000s of randomly generated tests

fast-engset

fast-engset

Python code to compute the blocking probability P in the Engset model:

                         m
         binom{N - 1}{m}M                            E/N
P = --------------------------    where    M = ---------------.
     __ m                    X                  1 - E/N(1 - P)
    \        binom{N - 1}{X}M
    /__ X = 0

N denotes the number of sources, m the number of servers, and E the offered traffic from all sources.

E is the total offered traffic given by E = N * alpha, where alpha is the offered traffic per-source.

Installation

pip install fast_engset

Example

from fast_engset import fe

m     = 5          # Number of servers
N     = 10         # Number of sources
alpha = 0.2        # Offered traffic from a SINGLE source
E     = N * alpha  # Total offered traffic from ALL sources

# Blocking probability
P = fe.compute(m, N, E)

fast-engset

fast-engset

Warning: This is a legacy release (for MATLAB/GNU Octave users) that is now unmaintained. Please consider using the Python version (see https://github.com/parsiad/fast-engset/releases for the latest releases), which is actively maintained.

MATLAB/GNU Octave code to compute the blocking probability P in the Engset model:

                         m                              
         binom{N - 1}{m}A                            E        
P = --------------------------    where    A = -------------.
     __ m                    X                  N - E(1 - P)   
    \        binom{N - 1}{X}A                           
    /__ X = 0                                           

N denotes the number of sources, m the number of servers, and E the offered traffic from all sources.

E is usually given by E = lambda mu, where lambda is the arrival rate of all sources and mu is the mean service time for a given request.

Warning: Certain texts use instead the normalized offered traffic, which is instead defined as E = lambda mu / N.

m = 5  % Number of servers
N = 10 % Number of sources
E = 2  % Total offered traffic from all sources

% Blocking probability
P = fast_engset(m, N, E)