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30PLenary session 27
4. Buizza R., Miller M., Palmer T. Stochastic representation of model uncertainties in the ECMWF Ensemble
Prediction System. ECMWF Tech.Memo. V. 279. 1999.
Alternative designs of highload queuingsystems withsmall queue
G. Sh. Tsitsiashvili
Institute for Applied Mathematics FEB RAS
Email: guram@iam.dvo.ru
DOI 10.24412/cl.35065.2021.1.02.35
In this paper, two alternative designs are constructing for queuing systems with a large load and a small
queue.These modes are convenient from an economic point of view, since the service device is almost fully
loaded. On the other hand, this mode is also convenient for users who will not be idle in the queue for a long
time. The first design is an aggregation of a large number of single.channel systems into a multi.channelsys.
tem. The second design is basing on the model of a single.channelsystem, in which random fluctuations are
defining as the degree of tending to zero difference between the unit and the load factor. The exponent of this
degree has a critical value, above which the stationary waiting time tends to zero, and below which it tends to
infinity. A similar phase transition is founding in the multi.channel queuing system. The methods of the
sources [1.4] are using.
References
1. Borovkov A.A. Asymptotic methods in queueing theory.M.: Nauka, 1980.
2. Borovkov A.A. Stochastic processes in queuing theory.M.: Nauka, 1972.
3. Tsitsiashvili G.Sh., Osipova M.A. Phase Transitions in Multiserver Queuing Systems // Information Technologies
and Mathematical Modelling. Queueing Theory and Applications. 2016.V. 638. P. 341.353.
4.Boxma O.J., Cohen, J.W. Heavy.traffic analysis for the GI/G/l queue with heavy.tailed distributions // Queueing
Systems. 1999. V. 33. P. 177.204.
Taking into account a priori information is the most important stage in solving ill.posed problems
V. V. Vasin, A. L. Ageev
1Institute of Mathematics and Mechanics UB RAS
Ural FederalUniversity,Ekaterinburg
Email: vasin@imm.uran.ru
DOI 10.24412/cl.35065.2021.1.02.18
What is a problem with a priori information? It is a problem, in which together with the basic statement
there is an additional information on a solution (namely, constraints) that isabsent in the original statement.
But thisinformation might contain important data on some properties of a solution. It should be noted that in
the case of a non.uniqueness solution, (when a prioriinformation is not used in the algorithm of the problem
to be solved), the approximate solutions could not satisfy to physical reality. In the case of uniqueness of solution,
attraction of the additional constraints permits to localize the desired solution and to raise its stability
w.r.t. the errors in the input data. Majority of a priori constraints that arise in the applied problems can be
presentedin the form of the linear relations or systems of the linear and convex inequalities. We investigate
various methods of taking into account a priori constraints, in particular, the most general and economical
method on the basis of the Fejer mappings.Also, we consider the ill.posed problems, for whichthe solutions
are found by the high.precision algorithms using a priori information [1�3].
