About BuTools
BuTools is a collection of useful tools for Markovian performance evaluation.
Main features:
- 11 packages to support traffic modeling and queue analysis, including packages for
- Phase-Type (PH) distributions:
- density function, distribution function, moment calculations,
- moment matching tools,
- representation transformation tools,
- tools to obtain canonical representations,
- tools to obtain the minimal representation,
- tools to generate random samples and random PH distributions,
- continuous and discrete PH distributions, matrix-exponential and matrix-geometric distributions are all supported.
- Markovian arrival processes (MAPs):
- marginal distribution and marginal moment calculations,
- joint moments and autocorrelation function calculations,
- joint moment and autocorrelation matching tools,
- representation transformation tools,
- tools to obtain canonical representations,
- tools to obtain the minimal representation,
- tools to generate random samples and random MAPs,
- continuous and discrete MAPs, rational arrival processes (RAPs), and their marked variants are all supported.
- Analysis and fitting of empirical measurement traces:
- calculation of empirical moments, density and distribution functions from traces,
- calculation of joint moments and autocorrelations from traces,
- EM-based fitting algorithms for PH distributions and MAPs,
- Various distance functions to evaluate the accuracy of the fitting.
- Matrix-analytic methods:
- tools to obtain the fundamental matrices and stationary distributions of QBDs, M/G/1 and G/M/1 type queues,
- tools to obtain the fundamental matrices and stationary distributions of canonical and general Marovian fluid models.
- State-of-the art solution of queueing models:
- QBD queues and MAP/MAP/1 queues
- Multi-type MMAP[K]/PH[K]/1-FCFS queues
- Multi-type MMAP[K]/PH[K]/1-Preemptive Resume priority queues
- Multi-type MMAP[K]/PH[K]/1-Non-preemptive priority queues
- Fluid queues with dependent and independent input and output processes
- The distribution and moments of the number of customers in the system and of the sojourn time can be obtained for all these queues
- Matrix-exponential/Phase-type representations of the performance measures can be obtained where possible
- Three mathematical frameworks are supported: Matlab, Mathematica and Python/NumPy
- Extensive documentation, examples and demos are available