RT&A EditorIAl Board Members
The 80th Birthday of Vladimir Rykov
The Editor-in-chief of our journal and
full member of the Informatization Academy, Professor
Vladimir Rykov became eighty on January 2018. Rykov got his
bachelor and master degree in 1960 from the Lomonosov Moscow
State University (MSU). In his diploma project, supervised
by A.N. Kolmogorov, Rykov studied the properties of
trajectories of random processes and simultaneously with R.
Dobrushin found the condition for absence of jumps in them.
After the graduation in 1960 Rykov has begun his career in
the MSU Computer Center, then he has worked for ten years at
the Central Research and Development Institute of Complex
Automation (CRICA), and for more than 35 year he is
Professor at the department of Applied Mathematics and
Computer Modeling in Gubkin State University of Oil and Gas.
At the same time, he gives lectures at the Department of
Applied Probability and Informatics of the Peoples’
Friendship University of Russia and has actively
collaborated before with the RAS Kharkevich Institute for
Information Transmission Problems. During two years he has
been teaching as invited professor at the mathematical
department in Kettering University (USA). The Editorial
Board of “Reliability: Theory and Applications”
congratulates Vladimir Rykov on his eighty anniversary and
wishes him good health and further creative advances.
B. V. Gnedenko (Publication and notes
by D. B. Gnedenko)
Two A. N.
Kolmogorov's Early Letters About Mathematics Education
It is well known that A.N. Kolmogorov
made a great contribution to the development of Russian
mathematics pedagogy. Mr. Kolmogorov became increasingly
interested in pedagogical issues in early 1962, when he came
up with many new ideas that encouraged teachers and
mathematicians to use their creativity in search of ways to
solve these issues. Those ideas were set forth in the
letters I received from Mr. Kolmogorov in 1962. My son came
across two of them while sorting out books and papers, and
both of them deserve publication. We will present the part
of the letters devoted to the topic of our discussion in
full. The publication takes the reader to the early 1960s
and introduces him or her to Andrey Nikolaevich Kolmogorov's
vision of mathematics education at schools and universities
(particularly at the faculties of mathematics, physics,
chemistry, and at physics and technology institutes, as well
as at engineering and physics institutes).
DOI:
https://doi.org/10.24411/1932-2321-2018-00001
News
Memorial board
On December 5, at 12:00, with the
participation of representatives of the Kyiv City State
Administration, the memorial plaque was unveiled to
academician of the National Academy of Sciences of Ukraine,
Director of the Institute of Mathematics of the National
Academy of Sciences of Ukraine Gnedenko Boris Vladimirovich.
The board is installed on the house in which Gnedenko lived
in Kiev. In the photo, the middle balcony in the middle row
of balconies is the balcony of his apartment. Two hundred
meters further down the street - Khreshchatyk. Another two
hundred meters to the left on Khreshchatyk - Maidan.
Irina Gadolina
Application of SMED
(Single Minutes Exchange of Die) for Production Optimization
For optimization of engineering
production, it is proposed to use a system of quick
changeover (SMED). The introduction of this approach will
enhance, in particular, the increment of the coefficient of
technical use of equipment A (availability factor) by
reducing non-productive time downtime. In this case, A is
used as the optimization parameter. Examples of technical
decisions applying SMED are presented.
Keywords: Single minutes
exchange of die (SMED), maintenance and repair system,
availability coefficient, series volume
DOI:
https://doi.org/10.24411/1932-2321-2018-00002
Boyan Dimitrov, Sahib Esa
Interval Dependence
Structures of Two Bivariate Distributions in Risk and
Reliability
We follow the ideas of measuring
strength of dependence between random events, presented at
two previous MMR conferences in South Africa and Tokyo. In
our work here we apply it for analyzing local dependence
structure of some popular bivariate distributions. At the
Grenoble conference presentation we focus on the Bivariate
Normal distributions with various correlation coefficients,
and on the Marshal-Olkin distribution with various
parameter’s combinations. We draw the surface z = gii(x,y),
i=1,2 of dependence of i-th component on the other component
j≠i within the squares [x, x +1]x[y,y+1], and [x, x +.5]x[y,y+.5].
The points (x,y) run within the square [-3.5, 3.5]x[-3.5,
3.5] for Bivariate Normal distribution, and in [0.10]x[0,10]
for the Marshal-Olkin distribution.
Keywords: Local dependence,
local regression coefficients, strength of dependence,
strength of dependence, surface of dependence, Bivariate
normal, Marshal-Olkin distributions
DOI:
https://doi.org/10.24411/1932-2321-2018-00003
Dmitry Kozyrev, Vladimir Rykov, Nikolai
Kolev
Reliability Function
of Renewable System under Marshall-Olkin Failure Model
In this note we obtain reliability
function of two-component system under the Marshall-Olkin
failure model in terms of Laplace transform. The problem of
its sensitivity to the shape of the system components repair
times is investigated as well.
Keywords: Heterogeneous
reliability systems, Laplace transform, Marshall-Olkin
bivariate failure model, reliability function, sensitivity
analysis.
DOI:
https://doi.org/10.24411/1932-2321-2018-00004
Maria Rachinskaya, Mikhail Fedotkin
Research of a
Multidimensional Markov Chain as a Model for the Class of
Queueing Systems Controlled by a Threshold Priority
Algorithm
A class of controlled queueing systems
with several heterogeneous conflicting input flows is
investigated. A model of such systems is a time-homogeneous
multidimensional Markov chain with a countable state space.
Classification of the chain states is made: a closed set of
recurrent aperiodic states and a set of transient states are
determined. An ergodic theorem for the Markov chain is
formulated and proved.
Keywords: controlled queueing
system, threshold priority, multidimensional Markov chain,
recurrent state, stationary distribution
DOI:
https://doi.org/10.24411/1932-2321-2018-00005
Gurami Tsitsiashvili, Marina Osipova
Generalization and
Extension of Burke Theorem
A simplification of Burke theorem proof
[1] and its generalizations for queuing systems and networks
are considered. The proof simplification is based on the
fact that points in output flow take place in moments when
Markov process of customers number in queuing system has
jumps down. In such way it is possible to obtain a property
of the mutual independence of the flow into disjoint periods
of time and to calculate intensity of output flow.
Keywords: an output Poisson
flow, the Jackson network, the Burke theorem
DOI:
https://doi.org/10.24411/1932-2321-2018-00006
Larisa G. Afanasyeva, Andrey Tkachenko
Stability of
Discrete Multi-Server Queueing Systems with Heterogeneous
Servers, Interruptions and Regenerative Input Flow
In the paper we study a discrete-time
multichannel queueing system with heterogeneous servers,
regenerative input flow, and interruptions. The breakdowns
of servers may occur at any time even if they are not
occupied by customers. Consecutive moments of breakdowns are
defined by a renewal process, but we do not assume blocked
and available periods to be independent. We consider the
preemptive repeat different service discipline as well as
preemptive resume service discipline. We exploit the
regeneration property of the input flow and renewal
structure of the processes describing the servers’
breakdowns to organise synchronisation of the input and
service flows. This approach helps to establish the
necessary and sufficient stability condition of the system.
Generally, for preemptive repeat different service
discipline this stability condition can not be expressed it
terms of moments of service and interruption processes.
Therefore, we derive the sufficient but not necessary
condition, which can be expressed through these moments, and
show that it coincides with condition obtained in existing
literature for simpler queueing systems.
Keywords: Multichannel system,
Regenerative input flow, Ergodicity, Interruption, Vacation,
Unreliable servers
DOI:
https://doi.org/10.24411/1932-2321-2018-00007
