On-Line Simulators

[ On-Line Simulators | Testing Random Generators | JSSim | The Author ]

On-Line Solvers & 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.

Simulators of Queueing Networks

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.

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Testing Random Generators

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, n2, and n3 bins. The programs then find the actual frequencies of all bins and compare them with the theoretical frequency. Results contain the maximum and the minimum frequencies, the chi-square test value and the table of frequencies with simple semi-graphics bar chart, that should be as flat as possible. Read help & intro to learn more. These testers are available to test JavaScript and JSSim random generators:

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 = 231 = 2147483648, a = 216+3 = 65539, c = 0) of the infamous RANDU generator and perform the test of triples for 10 and 20 intervals in each dimension.

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JSSim

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

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.

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The Author

In 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/

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This article is translated to French language by Anna Chekovsky.

This article is translated to German language by Lisa Kok.


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