POISSON_SIMULATION
Simulation of a Poisson Process

POISSON_SIMULATION is a FORTRAN90 program which simulates a Poisson process in which events occur uniformly at random, with an average waiting time of Lambda, creating output for graphics by gnuplot.

Note that the Poisson distribution therefore also describes the distribution of distances from one point to the next, assuming the points are distributed uniformly at random along a line, with average density Lambda per unit length.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

POISSON_SIMULATION is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

BROWNIAN_MOTION_SIMULATION, a FORTRAN90 program which simulates Brownian motion in an M-dimensional region.

DUEL_SIMULATION, a FORTRAN90 program which simulates N repetitions of a duel between two players, each of whom has a known firing accuracy.

FAIR_DICE_SIMULATION, a FORTRAN90 program which simulates N tosses of 2 dice, making a histogram of the results.

GNUPLOT, FORTRAN90 programs which illustrate the use of the gnuplot graphics program.

HIGH_CARD_SIMULATION, a FORTRAN90 program which simulates a situation in which you see the cards in a deck one by one, and must select the one you think is the highest and stop; the program uses GNUPLOT for graphics.

ISING_2D_SIMULATION, a FORTRAN90 program which carries out a Monte Carlo simulation of an Ising model, a 2D array of positive and negative charges, each of which is likely to "flip" to be in agreement with neighbors.

ISING_3D_SIMULATION, a FORTRAN90 program which carries out a Monte Carlo simulation of an Ising model, a 3D array of positive and negative charges, each of which is likely to "flip" to be in agreement with neighbors.

REACTOR_SIMULATION, a FORTRAN90 program which a simple Monte Carlo simulation of the shielding effect of a slab of a certain thickness in front of a neutron source. This program was provided as an example with the book "Numerical Methods and Software."

THREE_BODY_SIMULATION, a FORTRAN90 program which simulates the behavior of three planets, constrained to lie in a plane, and moving under the influence of gravity, by Walter Gander and Jiri Hrebicek.

TWO_BODY_SIMULATION, a FORTRAN90 program which simulates the behavior of two bodies, constrained to lie in a plane, moving under the influence of gravity, with one body much more massive than the other, creating graphics files for processing by gnuplot.

Source Code:

• poisson_simulation.f90, the source code.

Examples and Tests:

• poisson_simulation_test.f90, a sample calling program.
• poisson_simulation_test.txt, the output file.

The calling program creates data and command files which can be used by GNUPLOT to create images.

• poisson_events_data.txt, data for Poisson events plot.
• poisson_events_commands.txt, commands for Poisson events plot.
• poisson_events.png, the Poisson events plot.
• poisson_timeline_data.txt, data for Poisson timeline plot.
• poisson_timeline_commands.txt, commands for Poisson timeline plot.
• poisson_timeline.png, the Poisson timeline plot.
• poisson_times_data.txt, data for Poisson events plot.
• poisson_times_commands.txt, commands for Poisson events plot.
• poisson_times.png, the Poisson events plot.

List of Routines:

• POISSON_FIXED_EVENTS waits for a given number of Poisson events.
• POISSON_FIXED_TIME counts the Poisson events in a fied time.
• R8_UNIFORM returns a scaled pseudorandom R8.
• R8VEC_CUM computes the cumulutive sums of an R8VEC.
• R8VEC_UNIFORM_01 returns a unit pseudorandom R8VEC.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

You can go up one level to the FORTRAN90 source codes.