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Analysis of an M|G|1|R queue with batch arrivals and two hysteretic overload control policies

Yuliya Gaidamaka;  Alexander Pechinkin;  Rostislav Razumchik;  Konstantin Samouylov;  Eduard Sopin — 2014

International Journal of Applied Mathematics and Computer Science

Hysteretic control of arrivals is one of the most easy-to-implement and effective solutions of overload problems occurring in SIP-servers. A mathematical model of an SIP server based on the queueing system M [ X ] | G | 1 ⟨ L , H ⟩ | ⟨ H , R ⟩ with batch arrivals and two hysteretic loops is being analyzed. This paper proposes two analytical methods for studying performance characteristics related to the number of customers in the system. Two control policies defined by instants when it is decided to change the system’s mode are considered....

Ergodicity and perturbation bounds for inhomogeneous birth and death processes with additional transitions from and to the origin

Alexander Zeifman;  Anna Korotysheva;  Yacov Satin;  Victor Korolev;  Sergey Shorgin;  Rostislav Razumchik — 2015

International Journal of Applied Mathematics and Computer Science

Service life of many real-life systems cannot be considered infinite, and thus the systems will be eventually stopped or will break down. Some of them may be re-launched after possible maintenance under likely new initial conditions. In such systems, which are often modelled by birth and death processes, the assumption of stationarity may be too strong and performance characteristics obtained under this assumption may not make much sense. In such circumstances, timedependent analysis is more meaningful....

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