Package ikr.simlib.distributions

In order to reproduce the stochastic processes in the system (e.g., arrival processes, service processes) using events it is necessary to generate random variables for time stamps according to a pre-defined distribution function, possibly taking the system state into consideration.

See: Description

Class Summary

Class	Description
Distribution	Distribution is the common base class for all distributions.
DistributionVector	This class contains an array-like structure which holds two vectors of same length.
ProbabilityVector	A discrete probability vector.

Exception Summary

Exception	Description
DistributionException

Package ikr.simlib.distributions Description

In order to reproduce the stochastic processes in the system (e.g., arrival processes, service processes) using events it is necessary to generate random variables for time stamps according to a pre-defined distribution function, possibly taking the system state into consideration. The simulation library offers a number of distributions.

Generating Random Numbers

The generation of random variables from a distribution function is based on the generation of pseudo-random number sequences with a large period following a uniform distribution between 0 and 1.

Some classes have been derived from RandomNumberGenerator that serve as random number generators. In most cases they override the index operator operator() and return a random number between 0 and 1:
StdRandomNumberGenerator is a relatively simple but generally sufficient generator [1]. A global instance SYSTEM_RNG of this type is generated that is used as the default random number generator for the system.

Random variables needed for the simulation are generated based on these random numbers and a specific distribution function (e.g., for random service times or arrival intervals). The distribution function must be inverted (Fig. 1), which in some cases can be done exactly, in other cases only approximately [2]. The task of inversion is executed by the distribution classes.


Creating a random number according to a certain distribution

Structure and Interface of Distribution Classes

All distribution classes are derived from the class Distribution, which has the following characteristics:
a final reference rng to the its random number generator, which will by default be initialized with a reference to the system default random number generator (see ikr.simlib.random)

Basically, discrete and continuous distributions are treated differently. They are represented by the classes DiscreteDistribution and ContinuousDistribution , which have been derived from Distribution.


[1] S. K. PARK, K. W. MILLER: "Random number generators: good ones are hard to find." Communications of the ACM, pp. 1192-1201, Oct. 1988.
[2] A. M. LAW, W. D. KELTON: Simulation Modeling & Analysis, 2nd edition, McGraw- Hill, 1991