We consider the cyclic polling system with two queues. One queue is served according to the exhaustive discipline, and the other queue is served according to the 1-limited discipline. At least one of the service and/or switchover times has a regularly varying tail. We obtain the tail behavior of the waiting time distributions. When one of the service and/or switchover times has an infinite seco...

In this paper we extend some results about the probability that the sum of n dependent subexponential random variables exceeds a given threshold u. In particular, the case of non-identically distributed and not necessarily positive random variables is investigated. Furthermore we establish criteria how far the tail of the marginal distribution of an individual summand may deviate from the other...

We present upper and lower bounds for the tail distribution of the stationary waiting time D in the stable GI/GI/s FCFS queue. These bounds depend on the value of the traffic load ρ which is the ratio of mean service and mean interarrival times. For service times with intermediate regularly varying tail distribution the bounds are exact up to a constant, and we are able to establish a “principl...

Abstract. We consider a dynamical system in R driven by a vector field −U ′, where U is a multi-well potential satisfying some regularity conditions. We perturb this dynamical system by a Lévy noise of small intensity and such that the heaviest tail of its Lévy measure is regularly varying. We show that the perturbed dynamical system exhibits metastable behaviour i.e. on a proper time scale it ...

Logarithmic asymptotics are proved for the tail of the supremum of a stochastic process, under the assumption that the process satisfies a restricted large deviation principle on regularly varying scales. The formula for the rate of decay of the tail of the supremum, in terms of the underlying rate function, agrees with that stated by Duffield and O’Connell [Math. Proc. Cambridge Philos. Soc. (...

In this article we study a channel with arbitrarily varying channel probability functions in the presence of a noiseless feedback channel (a. v. ch. f.). We determine its capacity by proving a coding theorem and its strong converse. Our proof of the coding theorem is constructive; we give explicitly a coding scheme which performs at any rate below the capacity with an arbitrarily small decoding...

In a recent paper, Opasanon and Miller-Hooks study multicriteria adaptive paths in stochastic time-varying networks. They propose a label correcting algorithm for finding the full set of efficient strategies. In this note we show that their algorithm is not correct, since it is based on a property that does not hold in general. Opasanon and Miller-Hooks also propose an algorithm for solving a p...

Time-varying networks describe a wide array of systems whose constituents and interactions evolve over time. They are defined by an ordered stream of interactions between nodes, yet they are often represented in terms of a sequence of static networks, each aggregating all edges and nodes present in a time interval of size Δt. In this work we quantify the impact of an arbitrary Δt on the descrip...

Abstruct-The random-code capacity region of the multiple-access arbitrarily varying channel subject to both state and input constraints is determined. Consideration of a simple erasure channel shows that the capacity region is not convex in general.