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.
Abstract
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