Related papers: Some reflected autoregressive processes with depen…
We study termination time and recurrence time in programs with unbounded recursion, which are either randomized or operate on some statistically quantified inputs. As the underlying formal model for such programs we use probabilistic…
Resampling methods such as the bootstrap have proven invaluable in the field of machine learning. However, the applicability of traditional bootstrap methods is limited when dealing with large streams of dependent data, such as time series…
We consider a point process $i+\xi_i$, where $i\in \bZ$ and the $\xi_{i}$'s are i.i.d. random variables with variance $\sigma^{2}$. This process, with a suitable rescaling of the distribution of $\xi_i$'s, converges to the Poisson process…
We investigate reflected random walks in the quarter plane, with particular emphasis on the time spent along the reflection boundary axes. Assuming the drift of the random walk lies within the cone, the local time converges -- without the…
This paper presents a wp-style calculus for obtaining expectations on the outcomes of (mutually) recursive probabilistic programs. We provide several proof rules to derive one-- and two--sided bounds for such expectations, and show the…
Multiclass open queueing networks find wide applications in communication, computer and fabrication networks. Often one is interested in steady-state performance measures associated with these networks. Conceptually, under mild conditions,…
In this paper we consider a single-server, cyclic polling system with switch-over times and Poisson arrivals. The service disciplines that are discussed, are exhaustive and gated service. The novel contribution of the present paper is that…
This note aims to verify a Laplace transform pair, previously published without proof, concerning the expected stock-out that may occur in a production-inventory systems when demand is Poisson, and the time horizon is finite. Stock-out, or…
We consider the problem of defining and fitting models of autoregressive time series of probability distributions on a compact interval of $\mathbb{R}$. An order-$1$ autoregressive model in this context is to be understood as a Markov…
This paper analyses a system subject to multiple dependent degradation processes. Degradation processes start at random times following a non homogeneous Poisson process and next dependently propagate. The growth of these degradation…
Proper management of resources whose arrival and consumption are subject to environmental randomness is an intrinsic process in both natural and artificial systems. This phenomenon can be modeled as a queuing process whose arrival…
We study regenerative processes time-changed by state-dependent inverse subordinators. The construction assigns possibly different independent subordinators to measurable classes of excursions and builds a random clock from the…
We calculate asymptotics of the distribution of the number of customers in orbit in a two-class priority retrial $M/G/1$-type queueing model. In this model, priority customers wait in line while non-priority customers join an orbit and…
Independent or i.i.d. innovations is an essential assumption in the literature for analyzing a vector time series. However, this assumption is either too restrictive for a real-life time series to satisfy or is hard to verify through a…
Tandem queues with finite buffer capacity commonly exist in practical applications. By viewing a tandem queue as an integrated system, an innovative approach has been developed to analyze its performance through the insight from reduction…
Intermittent demand, where demand occurrences appear sporadically in time, is a common and challenging problem in forecasting. In this paper, we first make the connections between renewal processes, and a collection of current models used…
This article deals with asynchronous server vacation and customer retrial facility in a multi-server queueing-inventory system. The Poisson process governs the arrival of a customer. The system is comprised of c identical servers, a…
We consider a general polling model with $N$ stations. The stations are served exhaustively and in cyclic order. Once a station queue falls empty, the server does not immediately switch to the next station. Rather, it waits at the station…
Intermittency is a common and challenging problem in demand forecasting. We introduce a new, unified framework for building intermittent demand forecasting models, which incorporates and allows to generalize existing methods in several…
Under some mild condition, a random walk in the plane is recurrent. In particular each trajectory is dense, and a natural question is how much time one needs to approach a given small neighborhood of the origin. We address this question in…