Oleg Lukashenko

On Convergence Rate to Stationarity of Queues with General Gaussian Input

The paper studies the rate of convergence to stationarity of the fluid queueing system with a constant service rate which is fed by a Gaussian process with stationary increments. It is assumed that variance of the input process is regularly varying with index \(2H\in (1,\,2)\). It is proved that the convergence rate is exactly the same that has been obtained for the fluid system fed by the corresponding fractional Brownian motion.

On Conditional Monte Carlo Estimation of Busy Period Probabilities in Gaussian Queues

Due to the self-similar nature of broadband traffic, the arrival rate can persist on relatively high values for a considerable amount of time. Such a behavior, closely related to the duration of busy periods, has a deep impact on queueing performance in terms of loss probability and distribution of losses. In the paper we consider the probability that the normalized cumulative workload grows at least as the length T of the considered interval in case of Gaussian input traffic. As T increases, the event becomes rare and standard Monte Carlo simulation would require a large number of generated sample paths to get an accurate estimate. To cope with this problem, we propose a variant of the well-known conditional Monte Carlo method, in which conditioning is expressed in terms of the bridge process. We derive the analytical expression of the estimator and verify its effectiveness through simulations.

Regenerative analysis of a finite buffer fluid queue

We discuss the application of the regenerative simulation of estimate the loss probability in a queueing system with finite buffer which is fed by a Gaussian input. We mainly consider queue with Brownian input. Stability analysis is discussed and some numerical examples are also included.

On the Use of a Bridge Process in a Conditional Monte Carlo Simulation of Gaussian Queues

In spite of their low frequency, rare events often play a major role in determining systems performance. In most cases they can be analysed only through simulation with ad-hoc techniques since traditional Monte Carlo approaches are quite inefficient in terms of simulation length and/or estimation accuracy. Among rare event simulation techniques, conditional Monte Carlo is an interesting approach as it always leads to variance reduction. Unfortunately, it is often impossible, or at least very difficult, to find a suitable conditioning strategy. To tackle this issue, the applicability of a bridge process is proposed in the case of queueing systems with Gaussian inputs. In more detail, overflow probability and busy-period length are investigated and the analytical expressions of the corresponding estimators are derived. Finally, the effectiveness of the proposed approach is investigated through simulations.

On the Effective Envelopes for Fluid Queues with Gaussian Input

Thanks to their flexibility and compact characterization, Gaussian processes have emerged as popular models to describe the traffic dynamics in a wide class of the modern telecommunication networks. A relatively new characterization of traffic flows is based on the effective envelopes, which represent a probabilistic generalization of the arrival curve of Network Calculus. In this paper, we analyse the effective envelopes for a general Gaussian process and use these results to derive non-asymptotic performance bounds for a fluid queuing system. To highlight the effectiveness of the proposed approach, numerical results are shown taking into account heterogeneous traffic flows as well as different correlation structures.

Performance Evaluation of Finite Buffer Queues through Regenerative Simulation

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).