I. M. Sobol – The Monte Carlo Method

Section 05 – Simulation of a Mass Servicing System

Consider one of the simplest systems of mass servicing. This system consists of n lines (or channels, or servicing stations) each of which can “serve on the customers”. The system receives requests arriving at random moments of time. Each request arrives at the N1 line. If the arrival time of the k-th request ( let us call it Tk ) finds this line free, the line starts servicing the request; this takes tb minutes (tb is the holding time of the line). If N1 line is busy at the moment Tb the request is immediately transferred to the N2 line. And so on … Finally, if all n lines are busy at the moment Tk , the system rejects the request. The problem is, what will be the (average) number of requests serviced by the system during the period T and how many rejections will be given?


Section 06 – Reliability Simulation

Suppose we want to estimate the mean duration of failure-proof operation of the apparatus provided all characteristics of the failure-proof operation of each of the elements are known. If we assume that the duration of failure-proof operation of each element t(k) is fixed, then the calculation of time t of failure-proof operation of the whole unit presents no problems. For example, failure of anyone of the elements of the unit drawn in Fig-18 entails the failure of the whole unit, i.e.


Section 07 – Computation of Neutron Transmission Through a Plate

The probabilistic laws of interaction of an individual elementary particle (neutron, photon, meson, etc.) with matter are known. Usually it is needed to find the macroscopic characteristics of processes in which the number of participating particles is enormous, such as densities, fluxes and so on.

 


Section 08 – Calculation of the Definite Integral

One of widely used methods that we know about the calculation of the definite integral is the method of infinitesimal rectangles. We know that we get a more and more precise answer as the width of the rectangles decreases. In this page, we will look at the Monte Carlo Method of calculation of definite integrals. The Algorithm is outlined below.