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Consideration is given to a discrete-time queueing system with inverse discipline, service interruption and repeat again service, second-order geometrical demand arrival, arbitrary (discrete) distribution of demand length and finite storage. Each demand entering the queue has random volume besides its length. The total volume of the demands in the queue is limited by a certain number. Formulae for...
A two-priority queueing system with trunk reservation, Poisson input flows of both priorities customers, infinite buffers and different exponential distributions of both priorities customers service times is considered. Trunk reservation means that there are some channels which can be used only by customers of high priority. Analytic relations to calculate the main stationary distributions of both...
Threshold load control is one of the key tools in preventing overload in telecommunication networks. Its implementation as hysteretic control mechanism is used for detecting and mitigating congestion in Next Generation Networks, where session initiation protocol is the main signalling protocol. In this paper single-server finite capacity queuing system with constant service time, poisson input flows...
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 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...
In this paper, we present analytical results of the analysis of the queueing system that models signalling hop-by-hop load control mechanism for SIP server. The so-called hop-by-hop overload control, known from recent IETF drafts and RFCs, is based on hysteretic load control with two thresholds for reducing potential oscillations between the control-on and control-off states under certain loading...
A discrete time single-line queueing system with independent geometric streams of regular and negative claims, infinite buffer, and geometric service is considered. A negative claim pushes a regular claim out of the buffer queue and moves it to a bunker of infinite capacity. If the buffer is empty, a negative claim leaves the system without any effect. After servicing a claim, the system receives...
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