Asymptotic analysis of the closed queueing structure with time-dependent service parameters and single-type messages

• Autorzy: Matalytski M. , Rusilko T. , Pankov A.
• Języki publikacji: EN

Abstrakty

EN

A closed queueing structure is considered in the paper; the number of single-type messages is not constant and depends on time. The route of messages is given by an arbitrary stochastic matrix of transition probabilities. An asymptotic analysis of this structure in case of large number of service requests is conducted. The service parameters of each queueing system of this structure, as well as the probability of messages transition between systems, depend on time. A system of ordinary differential equations to calculate the average relative number of messages in each queueing system, depending on the time, was obtained.

Słowa kluczowe

EN

queueing network; differential equation; asymptotic analysis

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2013
• Tom: Vol. 12, nr 2
• Strony: 73--80
• Opis fizyczny: Bibliogr. 3 poz., rys.

Twórcy

autor

Matalytski M.

• Institute of Mathematics, Czestochowa University of Technology Czestochowa, Poland

autor

Rusilko T.

• Grodno State University, Grodno, Belarus

autor

Pankov A.

• Grodno State University, Grodno, Belarus

Bibliografia

• [1] Matalytski M., Rusilko T., Mathematical Analysis of Stochastic Models of Claims Processing in Insurance Companies, GrSU, Grodno 2007.
• [2] Rusilko T., Research of stochastic model of insurance company’s customer claims with time-dependent servicing parameters, Vestnik GrSU 2011, 3, 167-174.
• [3] Medvedev G., On optimization of closed queueing system, Proceedings of the Academy of Sciences of the USSR, Technical Cybernetics 1975, 6, 65-73.