In this paper, we study the behavior of a discrete-time multiserver buffer system with infinite buffer size. Packets arrive at the system according to a two-state Markovian arrival process. The service times of the packets are assumed to be constant, equal to multiple slots. The behavior of the system is analyzed by means of an analytical technique based on probability generating functions (PGF...

In this paper we consider a large deviations problem for a discrete-time polling system consisting of two-parallel queues and a single server. The arrival process of each queue is a superposition of traffic streams generated by a number of mutually independent and identical Markovian on/off sources, and the single server serves the two queues according to the so-called Bernoulli service schedul...

We consider a single-server discrete-time queueing system with N sources, where each source is modelled as a correlated Markovian customer arrival process, and the customer service times are generally distributed. We focus on the analysis of the number of customers in the queue, the amount of work in the queue, and the customer delay. For each of these quantities, we will derive an expression f...

A non-Markovian model of quantum repeated interactions between a small quantum system and an infinite chain of quantum systems is presented. By adapting and applying usual projection operator techniques in this context, discrete versions of the integro-differential and time-convolutioness Master equations for the reduced system are derived. Next, an intuitive and rigorous description of the ind...

In this paper, we identify the batch Markovian arrival process (BMAP) as analytically tractable model of choice for aggregated traffic modeling of IP networks. The key idea of this aggregated traffic model lies in customizing the batch Markovian arrival process such that the different lengths of IP packets are represented by rewards (i.e., batch sizes of arrivals) of the BMAP. The utilization o...

A generalized semi-Markov process provides a stochastic process model for a discrete-event simulation. This representation is particularly useful for non-Markovian systems where it is nontrivial to obtain recurrence properties of the underlying stochastic processes. We develop ‘geometric trials” arguments which can be used to obtain results on recurrence and regeneration in this setting. Such p...

We use a discrete time analysis, giving necessary and sufficient conditions for the almost sure convergence of ARCH(1) and GARCH(1,1) discrete time models, to suggest an extension of the (G)ARCH concept to continuous time processes. Our “COGARCH” (continuous time GARCH) model, based on a single background driving Lévy process, is different from, though related to, other continuous time stochast...

Several paradigms exist for modeling causal graphical models for discrete variables that can handle latent variables without explicitly modeling them quantitatively. Applying them to a problem domain consists of different steps: structure learning, parameter learning and using them for probabilistic or causal inference. We discuss two well-known formalisms, namely semi-Markovian causal models a...

We consider simple Markovian games, in which several states succeed each other over time, following an exogenous discrete-time Markov chain. In each state, a different simple static game is played by the same set of players. We investigate the approximation of the Shapley–Shubik power index in simple Markovian games (SSM). We prove that an exponential number of queries on coalition values is ne...

This paper addresses the robust filtering problem for a class of discrete time-varying Markovian jump systems with randomly occurring nonlinearities and sensor saturation. Two kinds of transition probability matrices for the Markovian process are considered, namely, the one with polytopic uncertainties and the one with partially unknown entries. The nonlinear disturbances are assumed to occur r...