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

Matalytski M., Rusilko T., Pankov A.

Journal of Applied Mathematics and Computational Mechanics

2013

Vol. 12, nr 2

73--80

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.

The network probability model of one-type customer requests processing in an insurance company

Matalytski M., Rusilko T.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

2012

Vol. 11, nr 1

73-83

The subject of this paper is the stochastic model of client requests processed by an insurance company. The model takes into account the limited duration of insurance contracts and the dependence on time of requests service rate. A closed exponential queueing network with single-type messages is used as the model. The goal of the study is to solve the problem of finding the optimal number of employees of the insurance company on certain time intervals. The study is conducted in the asymptotic case of high network load. The results of this paper could be applied to optimize the functioning of insurance companies.

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

Matalytski M., Rusilko T., Pankov A.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

2012

Vol. 11, nr 4

105-112

A queueing network of any structure with single-type messages is considered in the paper. An asymptotic analysis of the network in case of large number of service requests conducted. It is suggested that the service parameters of each queueing system of the network, 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. There is one calculated example in the article.