Tools for the Analysis of Queues (:mod:`butools.queues`)
========================================================

.. module:: butools.queues

To load this package, either start the :func:`BuToolsInit()` 
script, or execute

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    :widths: 50 50

    * - :code:`addpath('butools/queues')` 
      - in Matlab,
    * - :code:`<<BuTools`Queues`` 
      - in Mathematica,
    * - :code:`from butools.queues import *` 
      - in Python/Numpy.

Type of queues supported by BuTools
-----------------------------------
The BuTools queues package supports the efficient analysis of 
queueing models that are driven by some Markovian structures.

The supported queues can be classified to two groups:

* Discrete queues, where the jobs waiting in the queue are discrete.
  In most of the supported queueing models the inter-arrival and the service times are either given by 
  Markovian arrival processes or PH distributions. 
  BuTools has a relatively large set of tools to obtain, transform and analyze MAPs and PH distributions.
  Several performance measures of these queues are also PH distributed, which is the main motivation to 
  restrict the focus of BuTools on these queues.
* In continuous queues the jobs are intinifesimally small, they are considered to be fluid drops.
  The rate at which fluid drops arrive and are being served are modulated by Markov chains. Again, 
  several performance measures are PH distributed, thus these queues have their well deserved places in 
  BuTools as well.

Performance measures
--------------------
Currently, the functions in the queues package calculate two performance measures:

* Number of customers in the system. By our definition, the jobs in the server and in the waiting room
  are all included.
* Sojourn time distribution. The sojourn time of the jobs, including the waiting time in the waiting room
  and the service time. This quantity is also called "system time" or "response time".

Functions for discrete queues
-----------------------------

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    * - :py:func:`QBDQueue <butools.queues.QBDQueue>`
      - Returns various performance measures of a continuous time QBD queue.
    * - :py:func:`MAPMAP1 <butools.queues.MAPMAP1>`
      - Returns various performance measures of a continuous time MAP/MAP/1 queue.
    * - :py:func:`MMAPPH1FCFS <butools.queues.MMAPPH1FCFS>`
      - Returns various performance measures of a continuous time multi-class MMAP[K]/PH[K]/1 first-come-first-served queue.
    * - :py:func:`MMAPPH1PRPR <butools.queues.MMAPPH1PRPR>`
      - Returns various performance measures of a continuous time multi-class MMAP[K]/PH[K]/1 preemptive resume priority queue.
    * - :py:func:`MMAPPH1NPPR <butools.queues.MMAPPH1NPPR>`
      - Returns various performance measures of a continuous time multi-class MMAP[K]/PH[K]/1 non-preemptive priority queue.

Functions for continuous queues
-------------------------------

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    :widths: 25 150

    * - :py:func:`FluidQueue <butools.queues.FluidQueue>`
      - Returns various performance measures of a fluid queue.
    * - :py:func:`FluFluQueue <butools.queues.FluFluQueue>`
      - Returns various performance measures of a fluid queue, where the input and output processes are independent.

.. toctree::
    :hidden:

    QBDQueue
    MAPMAP1
    MMAPPH1FCFS
    MMAPPH1PRPR
    MMAPPH1NPPR
    FluidQueue
    FluidQueue
    FluFluQueue
    FluFluQueue