**On-Line Simulators**

M/M/1 Solver & Simulator solves and simulates
the M/M/1 queuing system. Use it to learn about Queuing Systems, to get the
derivation of the M/M/1 mathematical model and to compare simulated and computed results.

**Simulators of general single queue systems**

Simulator #1 enables
simulation of single queue systems with single arrivals and single service.
For arrival intervals and service duration
the user either selects a theoretical distribution or enters an empirical distribution
in table form.
Then the user selects the number of channels and possibly the maximum queue length and the total number
of customers if these are limited. Queue organization can be either FIFO or LIFO.
All usual simulation results are provided. There is the possibility to save
results in a separate browser window for further use.

Simulator #2 enables
simulation of single queue systems with bulk (batch) arrivals and bulk (batch) service.
Batch sizes can be constant or random. Channel(s) either wait for complete batches to
start service or alternatively smaller batches can be served.
For arrival intervals and service duration
the user either selects a theoretical distribution or enters an empirical distribution
in table form.
Then the user selects the number of channels and the maximum queue length in case
of limited system capacity. The population is unlimited.
Queue organization can be either FIFO or LIFO.
All usual simulation results are provided. There is the possibility to save
results in a separate browser window for further use.

Simulator of Open Queueing Networks.
With this simulator you can simulate open queueing networks with practically any size and topology.
Queueing networks are made of generators of customers and service stations.
After arrival the first station is chosen randomly. After a completed service
the customer either leaves the network or proceeds to a randomly chosen next
station. All routing distributions are entered by the user. Help with a tutorial is available, read it
before you start experimenting.

Simulator of Closed Queueing Networks.
With this simulator you can simulate closed queueing networks with practically any size and topology.
Queueing networks are made of service stations with given initial numbers of customers.
After a completed service the next station is chosen randomly. The routing
distributions are entered by the user. Help is available, read it
before you start experimenting.

**The simulators are free, you can download all files and run them locally.
Please e-mail me first something about yourself
and about your use of the simulators. Then I shall send you the downloading details.**

The on-line testers check the uniform distribution of
generated singles, pairs and triples. The interval [0,1] in each dimension is
first divided into a certain number *n* of equal subintervals that
generates *n*, *n ^{2}*, and

Tester #1 tests the native JavaScript generator Math.random() in 10 intervals in each dimension.

Tester #2 tests the native JavaScript generator Math.random() in any number of intervals.

Tester #3 tests the native JSSim generator in 10 intervals in each dimension.

Tester #4 tests the native JSSim generator in any number of intervals.

The following two testers allow entering the generator constants. Use them to modify the default JSSim generator and/or to study properties of Linear Congruential Generators.

Tester #5 tests any Linear Congruential Generator in 10 intervals in each dimension.

Tester #6 tests any Linear Congruential Generator in any number of intervals.

Hint: enter the constants (*m* = 2^{31} = 2147483648,
* a* = 2^{16}+3 = 65539, *c* = 0) of the infamous RANDU
generator and perform the test of triples for 10 and 20 intervals in each
dimension.

All routines used to create these simulation models are now available as a
JavaScript based simulation tool called JSSim
(__J__ava__S__cript __Sim__ulation).

Look at its on-line manual from where you can also try some example simulation models.

Download JSSim to start working on your own simulation models.

Back to TopIn case of any problems do not hesitate to contact me:

Jaroslav Sklenar

Associate Professor

Department of Statistics and Operations Research

University of Malta

Msida Malta

e-mail: jaroslav.sklenar@um.edu.mt

Web: http://staff.um.edu.mt/jskl1/

This article is translated to French language by Anna Chekovsky.

This article is translated to German language by Lisa Kok.