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

100%

Gaidamaka Y., Pechinkin A., Razumchik R., Samouylov K., Sopin E.

International Journal of Applied Mathematics and Computer Science

2014

tom 24

nr 3

519-534

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. The expression for an important performance characteristic of each policy (the mean time between changes in the system mode) is presented. Numerical examples that allow comparison of the efficiency of both policies are given.

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

86%

Zeifman A., Korotysheva A., Satin Y., Korolev V., Shorgin S., Razumchik R.

International Journal of Applied Mathematics and Computer Science

2015

tom 25

nr 4

787-802

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. In this paper, transient analysis of one class of Markov processes defined on non-negative integers, specifically, inhomogeneous birth and death processes allowing special transitions from and to the origin, is carried out. Whenever the process is at the origin, transition can occur to any state, not necessarily a neighbouring one. Being in any other state, besides ordinary transitions to neighbouring states, a transition to the origin can occur. All possible transition intensities are assumed to be non-random functions of time and may depend (except for transition to the origin) on the process state. To the best of our knowledge, first ergodicity and perturbation bounds for this class of processes are obtained. Extensive numerical results are also provided.

Ograniczanie wyników

2 International Journal of Applied Mathematics and Computer Science

2 Razumchik R.

1 Gaidamaka Y.

1 Korolev V.

1 Korotysheva A.

1 Pechinkin A.

1 Samouylov K.

1 Satin Y.

1 Shorgin S.

1 Sopin E.

1 Zeifman A.

1 2015

1 2014

Wyniki wyszukiwania

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

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