List of Queueing Theory Software
This page gives a list of queueing theory software. The list
was compiled by Dr. Myron Hlynka of the University of Windsor, who
welcomes any additions to the list. His e-mail address is
The URL of this page is http://www2.uwindsor.ca/~hlynka/qsoft.html
Last updated: February 15, 2021.
(Feb., 2021)QSA Applications. from University of Debrcen (Hungary)
It has been developed to help queueing related education, but it is very
useful for research purposes, too.
Besides the usual mean value it calculates the variance of the main
performance measures, and where it is possible determines the distribution
function of the waiting and response times, as well.
In addition, it visualizes these metrics and one of the most important
features of this tool that it runs on most devices, including smartphones
which helps the work of a teacher. It is integrated into the lecture note
- (2018)KPC-Toolbox. "KPC-Toolbox is a library of MATLAB functions for
fitting an empirical dataset into a Markov model such as a phase-type
distribution (PH) or a Markovian arrival process (MAP)."
- (added March 10, 2017)
The R package queuecomputer
queuecomputer is a computationally efficient method for simulating queues
with arbitrary arrival and service times. There is a submitted paper on
describing the algorithm used in
the package. Examples can be found within the arXiv paper and the
A web app based on the package is available at
Kind regards, Anthony Ebert
- Octave-Forge - Extra packages for GNU Octave (added June 10,
- Java Modelling Tools(added June 10, 2014)
- Solutions to Queueing Systems (added June 10, 2014)
- Queueing Theory Calculator. (confirmed February 28, 2014).
- Call Center calculator and several others. (confirmed Feb. 28,
Communications Engineering: Queueing Simulation demo (added Feb. 1, 2014)
A few comments:
Queueing Simulation demo (added Feb. 1, 2014)
Queueing Simulation demo (added Feb. 1, 2014)
- (added June, 2013)
DATAPLOT. This is not a queueing package but it includes some useful
distributions used in queueing (like Borel Tanner).
- Erlang Library for Excel (added November,
"This Excel add-in works in all versions of Excel and
provides efficient implementations of many queueing
functions related to the Erlang C and Erlang B
queueing models. The functions are made available as
worksheet functions in Excel. See my website
AbstractMicro.com, or do a google search for “Erlang
Library for Excel”"
- (added March 16, 2012)
We have designed a tool which enables the
simulation of extended queuing network models
transparently on local or distributed environments, in
particular on IEEE HLA (the most prominent standard
distributed simulation). Thank you, Daniele Gianni
The tool webpage and the code are available through
- (added March 15, 2012) SimEvents with MATLAB and Simulink can be used for
exploring queuing theory. Thanks, Teresa Hubscher-Younger
- (added Nov. 30, 2011)
Please find below a link that leads to an online
Queueing Theory Software tool.
We provide a fast solution for the Ph/M/c/N-like and
queues based on a simple and stable recurrence that
accepted for publication by Journal of Applied
In the future, we intend to extend this webstite to
other queues such
as M/Ph/1-like queue and Ph/Ph/1-like queue and
Best regards, Thomas BEGIN and Alexandre BRANDWAJN
- (added July 24, 2011, message from Xavier Lagrange)
"We developped in my university software related to
queuing systems: VISTAD. It is not software to find solutions to some
queuing problems but a tool for teaching : VISTAD is a simulator with a
user-friendly interface. You can compare the results given by
classical formulae (Erlang B, Erlang C) with simulation results.
You can find it (Java applet) at:
- (added February 24, 2011)
Basic Markovian queueing models (in R),
from Pedro Canadilla.
- (added February 24, 2011)
- (added February 15. 2011)
qnetworks. Queueing Networks analysis package for GNU Octave.
Find a manual at
- (added February 14, 2011)
"Expokit is a software package that provides matrix exponential routines
for small dense or very large sparse matrices, real or complex. "
- (added February 1, 2011)
CADP ("Construction and Analysis of Distributed Processes")
is a popular toolbox for
the design of communication protocols and distributed systems.
- (added December 14, 2010)
From B. Van Houdt:
The QMAM tool consists of a set of MATLAB functions (i.e., .m files)
to compute the queue length,
waiting time and delay distribution of various queueing systems of
infinite size. It includes amongst others implementations
of the following queueing models both in discrete and continuous time:
PH/PH/1, MAP/MAP/1, MAP/M/c, MAP/D/c, RAP/RAP/1,
MMAP[K]/PH[K]/1, MMAP[K]/SM[K]/1, SM[K]/PH[K]/1. State-of-the-art
solution techniques are used to solve these models effciently.
The QMAM functions rely on the SMCSolver MATLAB tool (also available
on this webpage) for solving QBD-, M/G/1- and GI/M/1-type Markov
Software Tools based on Matrix Analytic Methods:
- SMCSolver: A MATLAB Toolbox for solving Quasi-Birth-and-Death (QBD) type Markov chains
- SMCSolver: A MATLAB Toolbox for solving M/G/1, GI/M/1 and Non-Skip-Free type Markov chains
- A MATLAB Tool for computing the transient distribution of a QBD Markov chain (with marked time epochs).
- Q-MAM: A MATLAB Toolbox for solving Infinite Queues using Matrix Analytic Methods
- (updated Nov. 02, 2010) JAVA MODELLING
TOOLS (JMT) Version 8.0 is a suite of applications developed by Politecnico di Milano and released under GPL license.
The current stable version of the suite encompasses six Java applications:
- JSIMgraph - Queueing network models simulator with graphical user interface
- ;JSIMwiz - Queueing network models simulator with wizard-based user interface
- JMVA - Mean Value Analysis of queueing network models
- JABA - Asymptotic Analysis of queueing network models
- JWAT - Workload Analysis from log and usage data
- JMCH - Markov chain simulator (didactic tool)
- Some R programs for queueing and call centers by Christian Dombacher. (added May 23,
Related documentation appears at
Check out the entire site at
- SimulME software. (added December 25, 2009)
"SimulME is a Java ME (J2ME) application with Queuing calculator,
Stopwatch, Monte Carlo simulation, Random Number Generator (GNA),
Probability distributions, Kolmogorov-Smirnov and Chi-square tests. It
works with MIDP 2.0 and CLDC 1.1 profiles." (Carlos Bernardo)
Jan 23, 2009.
Queuing Theory Mathcad E-book by Stephen A. Thomas
For information, go to
- QNet Approximator (added October 3, 2009)
This software computes lower bounds on the optimal average cost for a
broad class of queueing networks by solving an approximate linear program
(ALP). It is fully documented and can use either the CPLEX or GLPK
open-source solver. The accuracy of the bound and size of the LP can be
controlled by selecting the form of the differential cost approximation,
as a function of the queue lengths:
certain exponential functions,
indicator functions for certain states, and
The control problem minimizes a linear holding cost for multiclass
networks or more general stochastic processing networks. Some capability
is also provided to compute upper bounds and policies from ALP solutions.
QNet Approximator is available at
Most of the methods are described in the paper
M.H. Veatch. Approximate dynamic programming for networks: Fluid models
and constraint reduction . 2009.
For more information, contact Mike Veatch email@example.com
This software was developed with support from NSF Grant CMMI-0620787.
- DELSI 2.0 (info added Apr. 23, 2008)
Dr. H: I have a pleasure to introduce to you Discrete-event simulation
system Delsi 2.0. The system is implemented as a set of components for
.NET 2.0 Framework and designed for simulation of queuing systems with
The trial version of Delsi 2.0 has no expiration time and can be used
in educational process.
More information is available at
If you have any questions or opinions, please, contact me.
Herman Holushko, Holushko Software, Richmond Hill, ON, Canada
- Andrew Ross' links to queueing software.
- (added July 25, 2007)
LQNS "solves layered queueing
networks, which includes as a subset conventional mixed model
queueing networks." Greg
Franks. For more
- (added July 7, 2007)
Clinic Planning Model Generator
would like to nominate our queueing software, called the Clinic Planning
Model Generator, designed specifically for public health emergency
preparedness planners, for your list of Queueing Theory Software. The URL
for the software is"
Jeffrey W. Herrmann
- (added Sept. 25, 2006)
"our software extensively deals with simulation
and queues, and we provide free academic versions for students and
educators" (Tim Schmitt, Director of Marketing)
- (added Sept. 10, 2006)
MOSEL 2. "MOSEL-2 is a textual model description language for the
performance and reliability modeling of computer, communication, and
manufacturing systems. "
- (added Sept. 10, 2006)
1. SHARPE (Symbolic Hierarchical Automated Reliability and
2. SPNP (Stochastic Petri Net Package).
- (added October 5, 2005. Thanks to Haitham Abu Ghazaleh for his
information.) WinPEPSY-QNS (Performance Evaluation and
System for Queueing NetworkS) It claims to be able to accurately calculate
various performance measures of queueing networks. It can be downloaded
through the appropriate link on the following website
- (information updated Jan 1, 2010)
Release of VisSim version 7.0, simulation environment.
interfaces to Maple, Mathcad and Matlab.
A fully working trial is available.
- Richard Steyn Health Service Models (updated December 1, 2010)
Christenson's Tool Page (updated January 1, 2011)
PhoneCalc Queueing Models (inserted June 10, 2005)
by Mike Tanner. Copyright MITAN Ltd
- QTSPLUS (updated February 20, 2010)
Spreadsheet Workbooks to Solve Queueing Models
The QtsPlus software is distributed by John Wiley & Sons, Inc in
connection with the book "Fundamentals of Queueing Theory," Fourth
Edition, by Donald Gross, John Shortle, James Thompson and Carl Harris.
The software is available freely from the Wiley public ftp server at
- (entered Feb. 12, 2005) Henk Tijms' software package MCQueue can be
found at his web
and freely downloaded. This package contains two modules. The first
module deals with steady-state and transient analysis for discrete-time
and continuous-time Markov chains. The second module calculates
performances measures including queue-length probabilities and
waiting-time probabilities for a wide variety of queueing models ( M/G/1
queue, M/M/c queue, M/D/c queue, G/M/c queue, transient M/M/1 queue among
- (entered April, 2005)
Ger Koole Call Center calculators. Erlang C.
- (entered April, 2005)
An Erlang B Calculator for Call Centers.
- (entered June 8, 2004) Discrete Simulation software list 1.
- (updated June 1, 2010) SIMPY. Discrete Event
- (entered May 7, 2004) "We have developed Java applets for queueing
formulas" Janos Strzik.
PQTJ ( Practical Queueing Theory in Java )
- (updated January 1, 2011)
Queueing ToolPak 4.0: (by A. Ingolfsson, U of Alberta)
- A library of functions for MS Excel to calculate performance measures
M/M/s and M/M/s/s+C queueing systems and approximate performance measures
for G/G/s systems. The spreadsheet functions make it easy to perform
sensitivity analysis or incorporate queueing measures in economic models.
- Available for free from
- (updated March 5, 2011)
PDQ (Pretty Damn Quick) written in the C language and open-sourced under
PDQ is also intended to accompany the book "The Practical Performance
Analyst" by Neil Gunther
- (entered April 8, 2003)
Open Directory Project (dmoz) SIMULATION. Editor Stanislaw Raczynski.
A large list of links to a variety of different simulation packages.
- (entered March 4, 2003)
Q1.0. A program for analysing queues.
"Q was written by Marko Boon and Michel Vollebregt for the Faculty of
Mathematics and Computer Science of the Eindhoven University of Technology.
It was written for education purposes."
(updated January 1, 2010)
Software from the web site for the
text book "Discrete-Event System Simulation" (fifth ed.) by Banks, Carson,
Nelson, and Nicol. Click on Source Code.
- (entered Nov 5, 2002)
QLib library. "The library implements a number of functions for solving
several queueing problems encountered in the performace analysis of modern
broadband communications networks. "
- (entered Sept. 23, 2002)
MAM Solver. (Matrix Analytic Methods
- (entered April 19, 2002)
Queuing Model Simulator (QMS). by Stanislaw Raczynski
P.O.Box 22-783. 14000 Mexico D.F.Mexico.
- (updated December 15, 2010)
PRISM: Probabilistic Symbolic Model Checker (Version 4.0)
The tool can be downloaded free for academic purposes either in binary
or source code form.
- (entered on Nov. 11, 2001)
Demo-version of SIRIUS+. From Alexander Dudin. Available at his web
``It is the software created for calculation of characteristics of
different queues having the BMAP (batch Markovian Arrival Process)
as input. The software was created by my students and PhD
students during the past 5 years and mainly realizes our own theoretical
results in this direction."
- (entered Oct. 16, 2001)
Queueing Add-on for Excel to accompany Operations Research Models and
Methods by Paul A. Jensen & Jonathan F. Bard.
- (entered Oct. 6, 2001)
OMNeT++ and Queues. (The queueing tutorial is by Nicky van Foreest.)
- (entered Oct. 1, 2001)
MARCA (Markov Chain Analyzer) by William Stewart.
- (entered Sept. 21, 2001)
SAS(Statistical Analysis System) has an Operations Research module
which includes a queueing simulation tool called QSIM.
- (entered Sept 7, 2001)
Graphical spreadsheet queueing simulation.
This page contains the files discussed in the article Graphical Spreadsheet Queueing Simulation, by Armann Ingolfsson and Tom Grossman, published in volume 2, number 2 of
INFORMS Transactions on Education.
- (entered April, 2001) JPQ - Java Powered Queueing.
Version 1.0 (Beta).
Developed by Muhammad El-Taha and Bacel Maddah
With the right plugin people will enjoy online computation.
No need to download.
No limit on number of servers in multiserver and loss models.
compared to 170 servers in Excel based software. (No overflow
Easy to use and self explanatory notation.
- (information updated December 10, 2002)
Telpack Version 2
is now available for unrestricted general use free of
charge. This new extended version is much more powerful than Version,
and it works on Windows and Intel-Linux platforms.
(Information from Nihat C. Oguz, University of Missouri - Kansas City
School of Interdisciplinary Computing and Engineering)
Telpack (Teletraffic Analysis Package) Version 2 solves a rich set of
stochastic models and queueing problems frequently encountered in
teletraffic analysis. These fall into two categories: 1) Discrete-state
problems: G/M/1-and M/G/1-type structured Markov chains, QBD processes,
combined G/M/1-M/G/1 structure, and discrete G/G/1 queue; 2)
Continuous-state problems: MAP/G/1, PH/PH/1, MMPP/G/1, and GI/G/1 queues,
and fluid-flow and Brownian motion models. Using Telpack, you can obtain
stationary queue-length distributions for discrete-state problems, and
stationary waiting time (unfinished work) distributions for
continuous-state problems. These solutions take matrix-geometric and
matrix-exponential forms, respectively. You can also obtain the moments and
tail behavior characterizations of these distributions. For discrete-state
problems, it also computes and outputs detailed queue-length probability
vectors, and aggregate and overflow probabilities as desired.
KEYWORDS: teletraffic analysis, stochastic models, queueing models, Markov chains,
structured Markov chains, G/M/1, M/G/1, QBD, quasi-birth-and-death, G/G/1,
MAP/G/1, PH/PH/1, MMPP/G/1, GI/G/1, fluid flow, brownian motion, queue
length, waiting time, unfinished work, matrix geometric, matrix
exponential, tail distribution
- QNAT Queueing Network Analysis Tool
Date: Nov. 12, 1999.
Please note that the software requires Mathematica 5
Here is a quick list of the types of queueing networks that can be
solved using QNAT -
Our distribution includes documentation on the analytical techniques
that have been used. This has been provided through a Microsoft Word
file that is a part of this distribution. The documentation provides a
summary of the actual algorithm used by each solution technique in
QNAT and examples of networks solved using this technique in QNAT.
These examples may be found in the samples distributed with QNAT.
- Networks of Multi-server Infinite Capacity Queues with Multiple
- Networks of Multi-server Infinite Capacity Queues with a
Single Job Class
- Networks of Multi-Server Finite Capacity Queues with a Single
Job Class (some or all nodes may be of finite/infinite capacity)
Home Page: of QNAT:
Prof. Sanjay K. BOSE, Dept. of Electrical Eng., Indian Institute
of Technology, Kanpur - 208 016, INDIA
- (entered June 28, 2000). The Queueing Theory Cookbook of Samuel Baker
gives spreadsheet formulas for some queueing measures.
- ExtendSim 8.0.1 released November 18, 2010.
- Information checked 2006.
"ERLANG: Traffic and Queuing Software"
Software for Queues, traffic blockage, Voice and
Packetized Data Networks
Keywords Erlang, Delay, Blocking, Queues, Traffic
A utility of use in the Voice, or Packetized Data Network industries, to
help model traffic blockage (loss), and/or delays.
Generally it calculates one of the following (given the others):
in the following cases:
Traffic per trunk (server)
Infinite Sources Blocked traffic lost (Erlang B)
Blocked traffic held (Poisson)
Blocked traffic delayed (Erlang C)
Finite Sources Blocked traffic lost (Engset)
Blocked traffic held (Binomial)
Blocked traffic delayed (Delay)
- Message received Apr. 16, 1998, from
Ananth Krishnamoorthy, Research Assistant, Center for CIM,
Oklahoma State University.
"We at the Center for
Computer Integerated Manufacturing at Oklahoma
State University have a queueing network solver RAQS that was developed
as part of an NSF funded research.
This software is free and can be downloaded from our homepage
- Brian Fox. 1996.
Quick Q. For Windows 3.x and Windows 95. Shareware version available
- Mike Tanner. 1995. Practical Queueing Analysis (Book and disk)
PhonCalc - call centre "calculator" , by Mike Tanner.
CCRSim - call centre simulator, by Mike Tanner.
Mike now runs a company called MITAN. Some Erlang spreadsheet
material is available at
- Chaudhry, M.L. 1994.
QPACK Software Package. ISBN 1-895032-00-8. queuing models software packages.
A&A Publications, 395 Carrie Crescent, Kingston, Ontario K7M 5X7.
QROOT Software Package. ISBN 0-895021-X root-finding software package.
A&A Publications, 395 Carrie Crescent, Kingston, Ontario K7M 5X7.
Contact the author for access.
- Harris, Carl and Gross, Donald. 1993. Queueing Analyses with
TK Solver, 260 pp. Universal Technical Systems. (with diskette).
Myron Hlynka's Queueing Theory Page.