DYNAMIC MODEL OF MARKOVIAN HUMAN-MACHINE-ENVIRONMENT SYSTEM THAT IS EFFECTED BY
Kharkov National University Of
The closed “Man-machine-environment” system is considered. It has
either classic flow of events, or a flow of unstable of natural disasters with
different densities, that are approximated by piecewise constant functions. The
process of liquidation of the accident in all the models is held in several
stages, with different intensities. The phases can be made repeatedly in the
case of "multi-catastrophes". The Markovian model is presented, in
which the probability of changes in health of the operator in the process of
liquidation of the accident is found using the principle of maximizing the
information entropy. The stability time of the process and the value of
changing the dynamic model to stationary one are estimated. The safety criterion of situation that is the ratio of the average time between failures and mean time of recovery is introduced and investigated.
Keywords: Markov chain , Kolmogorov equations , Maximum entropy
Here we model the
behavior of the system when the intensity of the incoming stream of events
depends on time . For
this case the system of Kolmogorov equations is set up. The probability for the human to become
disable is found using the maximum information entropy principle, by numerical solving
the optimization problem.
Let the human
perform five operations in sequence to eliminate the accident, that is . This means that the diagram
of the system will look, as shown in Fig. 1
Let the intensity of
input , as well as all the
state probabilities be functions of the time. Here we consider a time unit,
that corresponds to approximately two hours in the field.
2 Standard graph of the function
Now consider the
intensity m(t) of a human operator in
the procedure to eliminate accidents. It can be assumed that the maximum
efficiency of the operator is obtained at about the middle of the work period.
Then gradual decline starts to its initial level. By the end of shift
efficiency can rise again, due to the haste and desire to get the job done
quickly. Based on these considerations, we present the common shape function of
operations’ intensity as shown in Fig.3
We use the principle of maximum
information entropy and form the optimization problem:
The solution of this problem with Matlab gives
the following values:
@ 2/3 , p2 @ 1/3; here , for all operations .
The result is a graph in time for probability of efficient state. The
calculations show that for the intensity of the incoming stream of events, that
is no longer changes with time, the system reaches a steady state.
расчету марковской модели эргатической системы / Наумейко И.В., Сова А.В. –
Сб.науч.труд. 5-й Юбилейной Международной научной конференции
"Функциональная база наноэлектроники" – Харьков-Крым, 2012. С. 236-239.
А. Я. Работы по математической теории массового обслуживания / Под редакцией Б.
В. Гнеденко. М.: Физматгиз, 1963, 236 с.