HIGH TECH IN EARTH SPACE RESEARCH

Calculation of waiting time distribution in multi-channel non-markovian queuing systems with “cooling” and “heat-up”

Khomonenko A.D., Lokhvitskiy V.A., Khalil M.M.

The approach to calculation of distribution of waiting time of requests in the multi-channel non-Markov queuing systems with “cooling”, “heat-up” and distributions of phase type is developed. The characteristic of methods of calculation of distribution of waiting time for non-Markov queuing systems is given.

At the heart of calculation of probable characteristics of multi-channel non-Markov queuing systems with approximating distributions of phase type (the hyperexponential, the Erlang, Cox) the Takakhashi-Takami's iterative method is lies. When calculating distribution of waiting time of multi-channel QS with “cooling” and “heat-up” transitions between microstates are considered. The main result is a method for calculating the waiting time distribution in a multichannel non-Markov queuing system. The method is based on the weighted convolution of the Laplace-Stieltjes transformations of the transit times of each of the components of the exponential phases of the microstates of the system. The knowledge of the Laplace-Stieltjes transformation of the waiting time distribution of the application in the queue makes it possible, by numerically differentiating this transformation at the point s = 0, to calculate the initial moments of the required distribution, from which to construct the approximation of the distribution function. The example of calculation of waiting time in queue for model of multi-channel QS M/M/E2/n with the Poisson input flow, exponentially distributed duration of service and with the "cooling" distributed under the generalized law of the Erlang of the 2nd order is considered. From the presented results it follows that with an increase in the average “cooling” duration, the average waiting time increases. In addition, the duration of “cooling” has a very significant effect on the average waiting time. The Kolmogorov distance for the distributions of the number of requests received by the numerical method and using the simulation model was {0.0014; 0.0013; 0.0038; 0.0024; 0.012} for a different intensity of “cooling”, respectively, which indicates the correctness of the analytical model.  Thus, a generalization of the classical Little’s formula is achieved. The proposed approach can be useful in probabilistic modeling of nodes of distributed data processing centers, modeling and justification of the architecture of cloud computing systems with the Web interface, and evaluating the impact of costs on updating the context.

The subject of published articles on the nomenclature of specialties

2.2.15 Systems, networks and telecommunications (technical sciences)

2.3.1 System analysis, management and processing of information (technical sciences)

2.3.5 Mathematical and software of computing systems, complexes and computer networks (technical sciences)

2.3.6 Methods and information protection systems, information security (technical sciences)

2.5.13 Design, design and production of aircraft (technical sciences)

2.5.16 Dynamics, ballistics, the movement of aircraft (technical sciences)

Editorial board

Bobrowsky V.I.
(Ph.D., Associate Professor, Head of Department of "INTELTEH")

Borisov V.V.
(Ph.D., Professor, Actual Member of the Academy of Military Sciences, Professor, Department of Computer Science of MPEI)

Budko P.A.
(Ph.D., Professor, Department of Technical communication and automation in S.M. Budjonny Military Academy of the Signal Corps)

Budnikov S.A.
(Ph.D., associate professor, Actual Member of the Academy of Education Informatization, Head of the automated control systems Department in Russian Air Force Military Educational and Scientific Center “Air Force Academy named after Professor N.E. Zhukovsky and Y.A. Gagarin”)

Verhova G.V.
(Ph.D., Professor, Head of Department of Automation communication companies In the Bonch-Bruevich Saint Petersburg State University of Telecommunications)

Goncharevsky V.S.
(Ph.D., Professor, Honored Worker of Science and Technology of the Russian Federation, Professor of technologies and technical support and maintenance of the automated control systems in Military Space Academy of A.F. Mozhaysky)

Komashinskiy V.I.
(Ph.D., Professor, professor of processing and transmission discrete messages in the Bonch-Bruevich Saint Petersburg State University of Telecommunications)

Kirpanev A.V.
(Ph.D., Associate Professor, Head of JSC "Scientific Production Enterprise "Radar MMS")

Kurnosov V.I.
(Ph.D., Professor, Academician of Academy of Sciences of the Arctic, Academician of the International Academy of Informatization, International Academy of defense, security, law and order, corresponding member of the Academy of Natural Sciences, Senior Researcher" Open Joint Stock Company "Scientific Research Institute "Rubin")

Manuilov Y.S.
(Ph.D., Professor, Department of automated control systems space complexes in Military Space Academy of A.F. Mozhaysky)

Morozov A.V.
(Ph.D., Professor, Actual Member of the Academy of Military Sciences, Head of the Department of automated command and control systems in Military Аcademy of troops of antiaircraft defense)

Moshak N.N.
(Ph.D., Associate Professor, head of the department of "INTELTEH")

Prorok V.Y.
(Ph.D., Professor, professor of automatic control systems in Military Space Academy of A.F. Mozhaysky)

Semenov S.S.
(Ph.D., associate professor, professor of technical communication and automation in S.M. Budjonny Military Academy of the Signal Corps)

Sinicyn E.A.
(Ph.D., Professor, Head of the Research Department of JSC "The All-Russian research institute of radio equipment")

Shatrakov Y.G.
(Ph.D., Professor, Honored Worker of Science, Scientific Secretary of JSC "The All-Russian research institute of radio equipment")