In this paper, the asymptotic behaviour of the distribution tail of the stationary waiting time W in the GI/GI/2 FCFS queue is studied. Under subexponential-type assumptions on the service time distribution, bounds and sharp asymptotics are given for the probability P{W > x}. We also get asymptotics for the distribution tail of a stationary two-dimensional workload vector and of a stationary qu...

In this paper, we discuss an exponential integrator scheme, based on spatial discretization and time discretization, for a class of stochastic partial differential equations. We show that the scheme has a unique stationary distribution whenever the stepsize is sufficiently small, and that the weak limit of the stationary distribution of the scheme as the stepsize tends to zero is in fact the st...

In this paper, the asymptotic behaviour of the distribution tail of the stationary waiting time W in the GI/GI/2 FCFS queue is studied. Under subexponential-type assumptions on the service time distribution, bounds and sharp asymptotics are given for the probability P{W > x}. We also get asymptotics for the distribution tail of a stationary two-dimensional workload vector and of a stationary qu...

This paper proposes a linear programming algorithm for computing the stationary distribution of semimartingale reflected Brownian motion (SRBM), which arises as an approximation of certain queueing networks operating in heavy-traffic. Our algorithm is based on a Basic Adjoint Relationship (BAR) which characterizes the stationary distribution. Approximating the state space with a finite grid of ...

We consider the problem of minimum energy steering of a linear stochastic system to a final prescribed distribution over a finite horizon and the problem to maintain a stationary distribution over an infinite horizon. For both problems the control and noise channels are allowed to be distinct, thereby, placing the results of this paper outside of the scope of previous work both in probability a...

Spectral analysis considers the problem of determining (the art of recovering) the spectral content (i.e., the distribution of power over frequency) of a stationary time series from a finite set of measurements, by means of either nonparametric or parametric techniques. This paper introduces the spectral analysis problem, motivates the definition of power spectral density functions, and reviews...

Quasi-stationary distributions have been used to model the long-term behaviour of stochastic systems which in some sense terminate, but appear to be stationary over any reasonable time scale. Imagine population is observed to be extant at some time t. What is the chance of there being precisely i individuals present? If we were equipped with the full set of state probabilities, we would evaluat...

This paper develops a theoretical framework based on Markov chains for the simple genetic algorithm (operators of reproduction, crossover, and mutation). We prove the existence of a unique stationary distribution for the Markov chain when mutation probability is used as a control parameter. We also show that there is a stationary distribution limit when the control parameter approaches zero. Fi...

Abstract The stationary distribution of the number of customers in the infinite-server system with nonPoissonian arrivals is dependent on the form of the service time distribution. In particular, when the interarrival time is a hyperexponential random variable that is more variable than an exponential random variable, the stationary state distribution becomes stochastically less variable, as th...

The goal is to identify the class of distributions to which the distribution of the maximum of a Lévy process with no negative jumps and negative mean (equivalently, the stationary distribution of the reflected process) belongs. An explicit new distributional identity is obtained for the case where the Lévy process is an independent sum of a Brownian motion and a general subordinator (nondecrea...