Ruslana Nekrasova

Asymptotic Analysis of Queueing Systems with Finite Buffer Space

In the paper, we consider a single-server loss system in which each customer has both service time and a random volume. The total volume of the customers present in the system is limited by a finite constant (the system’s capacity). For this system, we apply renewal theory and regenerative processes to establish a relation which connects the stationary idle probability P 0 with the limiting fraction of the lost volume, Q loss, provided the service time and the volume are proportional. Moreover, we use the inspection paradox to deduce an asymptotic relation between Q loss and the stationary loss probability P loss. An accuracy of this approximation is verified by simulation.

STABILITY ANALYSIS AND SIMULATION OF N-CLASS RETRIAL SYSTEM WITH CONSTANT RETRIAL RATES AND POISSON INPUTS

In this paper, we study a new retrial queueing system with N classes of customers, where a class-i blocked customer joins orbit i. Orbit i works like a single-server queueing system with (exponential) constant retrial time (with rate

A Regeneration-Based Estimation of High Performance Multiserver Systems

\mu_{0}^{(i)}

On the ergodicity bounds for a constant retrial rate queueing model

) regardless of the orbit size. Such a system is motivated by multiple telecommunication applications, for instance wireless multi-access systems, and transmission control protocols. First, we present a review of some corresponding recent results related to a single-orbit retrial system. Then, using a regenerative approach, we deduce a set of necessary stability conditions for such a system. We will show that these conditions have a very clear probabilistic interpretation. We also performed a number of simulations to show that the obtained conditions delimit the stability domain with a remarkable accuracy, being in fact the (necessary and sufficient) stability criteria, at the very least for the 2-orbit M/M/1/1-type and M/Pareto/1/1-type retrial systems that we focus on.

Optimal and Equilibrium Retrial Rates in Single-Server Multi-orbit Retrial Systems

In this paper we develop a novel approach to confidence estimation of the stationary measures in high performance multiserver queueing systems. This approach is based on construction of the two processes which are, respectively, upper and lower (stochastic) bounds for the trajectories of the basic queue size process in the original system. The main feature of these envelopes is that they have classical regenerations. This approach turns out to be useful when the original process is not regenerative or regenerations occur extremely rare to be applied in estimation. We apply this approach to construct confidence intervals for the steady-state queue size in classical multiserver systems and also for the novel high performance cluster (HPC) model, a multiserver system with simultaneous service. Simulation based on a real HPC dataset shows that this approach allows to estimate stationary queue size in a reasonable time with a given accuracy.

Performance Evaluation of Finite Buffer Queues through Regenerative Simulation

We consider a Markovian single-server retrial queueing system with a constant retrial rate. Conditions of null ergodicity and exponential ergodicity for the corresponding process, as well as bounds on the rate of convergence are obtained.

Stability analysis of retrial systems with constant retrial rates

We consider a single-server retrial system with one and several classes of customers. In the case of several classes, each class has its own orbit for retrying customers. The retrials from the orbits are generated with constant retrial rates. In the single class case, we are interested in finding an optimal retrial rate. Whereas in the multi-class case, we use game theoretic framework and find equilibrium retrial rates. Our performance criteria balance the number of retrials per retrying customer with the number of unhappy customers.

Upper bounds on the rate of convergence for constant retrial rate queueing model with two servers

In this paper we discuss the estimation of the loss probability in a queueing system with finite buffer fed by Brownian traffic, the Gaussian counterpart of the well-known Poisson process. The independence among arrivals in consecutive time slots allows the application of regenerative simulation technique, combined with the so-called Delta-method to construct confidence intervals for the stationary loss probability. Numerical simulation are carried out to verify the efficiency of the regenerative approach for different values of the queue parameters (buffer size and utilization) as well as simulation settings (digitization step and generalizations of the regeneration cycle).