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Method for Generating a Sequence of Poisson Process Arrival Times

IP.com Disclosure Number: IPCOM000108090D
Original Publication Date: 1992-Apr-01
Included in the Prior Art Database: 2005-Mar-22
Document File: 2 page(s) / 76K

IBM

Related People

Daykin, DR: AUTHOR

Abstract

A fast, simple method is disclosed for generating a sequence of numbers whose differences closely approximate a Poisson distribution. Such a sequence can be used as a schedule of arrival times for real-time performance exercising tools or for simulation models. Access to the next scheduled event can be done very quickly because the schedule list is created in advance of the real-time measurement or the simulation run.

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Method for Generating a Sequence of Poisson Process Arrival Times

A fast, simple method is disclosed for generating a
sequence of numbers whose differences closely approximate a Poisson
distribution.  Such a sequence can be used as a schedule of arrival
times for real-time performance exercising tools or for simulation
models.  Access to the next scheduled event can be done very quickly
because the schedule list is created in advance of the real-time
measurement or the simulation run.

This invention depends on the observation that if a series of N
uniformly distributed random numbers are placed in an interval (A,B),
then the successive differences between these numbers are independent
of each other and approach, with large N, an average value of
(B-A)/N.  When considered in increasing order, such a series can be
viewed as a segment of a Poisson process with an average interarrival
time of (B-A)/N.

The invention is to generate a series of pseudo-random numbers
by one of the well-known techniques such as a congruential random
number generator.  These numbers are placed in a list.  The list must
be sorted in ascending order, either at the time of number placement
or after the list is complete.  Scaling of the numbers to give the
desired average differences can be done by an appropriate combination
of:
1.   Choosing the interval within which the pseudo-random
numbers are generated.
2.   Choosing the number, N, of pseudo-random numbers to place
in the list.
3.   Multiplying the values in the list by an appropriate
factor.

A typical embodiment of the invention consists of carrying out
the following steps:
1.   Choose a number, N, of pseudo-random numbe...