Infinite Linear Systems M/G/\(\infty\) and Multilinear Systems with M/G/n/0 Losses

A. M. Popov *

Mechanical Engineering Research Institute of the Russian Academy of Sciences (IMASH RAN), Moscow, Russia.

R. M. Valiev

All-Russian Academy of Foreign Trade, Moscow, Russia.

*Author to whom correspondence should be addressed.


The method based on the description of the probabilities of states using a non-stationary Poisson flow allows using elementary reasoning to find not only a stationary, but also a non-stationary distribution of the number of requirements in the system.

To find a stationary distribution of the number of requirements in queuing systems (QS), the method of introducing additional variables leading to a piecewise linear Markov process is used.

The fact of invariance is shown: the stationary probabilities of pi states in queuing systems (QS) M/G/n/0 depend only on the average service time of the requirement and do not depend on the type of distribution G(x).

Keywords: Infinitely Linear System, multilinear system, unsteady poisson flow, CFR requirement, distribution, intensity, probability of states, erlang system

How to Cite

Popov , A. M., and R. M. Valiev. 2023. “Infinite Linear Systems M/G/\(\infty\) and Multilinear Systems With M/G/N/0 Losses”. Current Journal of Applied Science and Technology 42 (31):15-20.


Download data is not yet available.


Gnedenko BV, Kovalenko IN. Vvedenie v teoriyu queuing / M.: Nauka; 1966.

L Mills. Statistical methods/ Trans. see –M.: Gosstatisdat; 1965.

Wentzel ES. Introduction to operations research: Textbook, Moscow: Sovetskoe Radio Publ. 1964:390.

Ventzel ES, Ovcharov LA. Applied problems of probability theory. 1983;416.

I Likesha, Lyaga Y. Basic tables of mathematical statistics/ Trans. from Czech- M.: Finance and Statistics; 1985.

Popov AM, Sotnikov VN. Die ekonomiko-mathematischen methoden und die modelle. Die monografie. Monograph / Germany; 2015.

Kokren GU. Metody selektivnogo issledovaniya [Methods of selective research]; 1990.

G Kramer. Mathematical methods of statistics/ Trans. see – M.: Mir; 1975.

Raifa G, Shleifer R. Prikladnaya teoriya statisticheskikh resheniy [Applied theory of statistical solutions]; 1992.

G. Cochran.U. Methods of selective research / Trans. see – M.: Statistics; 1976.

Wentzel ES, Ovcharov LA. Probability theory and its engineering applications. 2nd ed. – Moscow: Higher School. 2000;480.

Wentzel ES. Operations research: tasks, principles, methodology. 2nd ed. – Moscow: Nauka, 1988;208.

Gini K. Average values/ Trans. from Italian. – M.: Statistics; 1970.

Popov AM, Sotnikov VN, Valiev RM. Ekonomiko-matematicheskie metody i modeli v mashinostroenii [Economic and mathematical methods and models in mechanical engineering]. Monograph. / M.: OOO "Nauka-Inform; 2017.

Popov AM, Sotnikov VN. Probability theory and mathematical statistics. Textbook and workshop. 2nd ed., ispr. and add. / Moscow: Yurayt; 2017.

Draper N, Smith G. Applied regression analysis/ Translated from English – M.: Finance and Statistics; 1987.

Finni D. Vvedenie v teoriyu planirovaniya eksperimentov [Introduction to the theory of experiment planning]; 1992.

Dubrovsky SA. Applied multidimensional statistical analysis.– M.: Finance and Statistics; 1982.