Queuing system with infinite buffer and stepwise inflow intensity

Authors:
N. I. Golovko;V. O. Karetnik;O. V. Peleshok
Affiliations:
Pacific State Economic University, Vladivostok, Russia;Pacific State Economic University, Vladivostok, Russia;Pacific State Economic University, Vladivostok, Russia
Venue:
Automation and Remote Control
Year:
2009

Citing 3
Cited 0

Markov-modulated queueing systems

Proceedings of the workshop held at the Mathematical Sciences Institute Cornell University on Mathematical theory of queueing systems
A Markov-modulated M/M/1 queue with group arrivals

Queueing Systems: Theory and Applications
Queueing system with finite memory and jump intensity of the arrival process

Automation and Remote Control

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Abstract

The queuing system with infinite buffer, single server, and exponential servicing was considered. A double stochastic Poisson flow whose intensity 驴(t) is a stepwise process with exponentially distributed constancy intervals arrives to it. It was assumed that the values of process 驴(t) to the left and right of the discontinuity point were independent. The nonstationary and stationary characteristics were determined using the method of generating functions. Existence and uniqueness of the stationary mode and stabilization of the nonstationary queuing system mode were proved. The results of numerical analysis and application of the considered queuing system were discussed.