Related papers: Reversibility in Queueing Models
We develop randomized modifications of Markov chains and apply these modifications to the routing chains of customers in Jacksonian stochastic networks. The aim of our investigations is to find new rerouting schemes for non standard Jackson…
Traditionally stationarity refers to shift invariance of the distribution of a stochastic process. In this paper, we rediscover stationarity as a path property instead of a distributional property. More precisely, we characterize a set of…
The concepts of probability, statistics and stochastic theory are being successfully used in structural engineering. Markov Chain modelling is a simple stochastic process model that has found its application in both describing stochastic…
We introduce a rate balance principle for general (not necessarily Markovian) stochastic processes. Special attention is given to processes with birth and death like transitions, for which it is shown that for any state $i$, the rate of two…
We study randomized experiments in a service system when stochastic congestion can arise from temporarily limited supply or excess demand. Such congestion gives rise to cross-unit interference between the waiting customers, and analytic…
We consider a stochastic fluid queue served by a constant rate server and driven by a process which is the local time of a certain Markov process. Such a stochastic system can be used as a model in a priority service system, especially when…
Reversible Markov chains play a central role in stochastic modelling and in algorithms such as Markov chain Monte Carlo (MCMC). Motivated by the fundamental importance of reversibility in classical settings, this paper develops a…
We consider a single server system with infinite waiting room in a random environment. The service system and the environment interact in both directions. Whenever the environment enters a prespecified subset of its state space the service…
We investigate congestion-aware control of quantum repeater nodes operating under stochastic traffic and finite memory coherence. Entanglement generation is modeled as a probabilistic process producing Werner states subject to depolarizing…
We study the stochastic dynamics of a system of interacting species in a stochastic environment by means of a continuous-time Markov chain with transition rates depending on the state of the environment. Models of gene regulation in systems…
By modeling the interaction of a system with an environment through a renewal approach, we demonstrate that completely positive non-Markovian dynamics may develop some unexplored non-standard statistical properties. The renewal approach is…
We attempt to characterize irreversibility of a dynamical system from the existence of different forward and backward mathematical representations depending on the direction of the time arrow. Such different representations have been…
The quantum strategy (or quantum combs) framework is a useful tool for reasoning about interactions among entities that process and exchange quantum information over the course of multiple turns. We prove a time-reversal property for a…
We propose a new approach concerning the introduction of time-irreversibility in statistical mechanics. It is based on a transition function defined in terms of path integral and verifying a time-irreversible equation. We show first how…
Queueing networks are systems of theoretical interest that find widespread use in the performance evaluation of interconnected resources. In comparison to counterpart models in genetics or mathematical biology, the stochastic (jump)…
We introduce the notion of time reversal in open quantum systems as represented by linear quantum operations, and a related generalization of classical entropy production in the environment. This functional is the ratio of the probability…
Queueing networks are notoriously difficult to analyze sans both Markovian and stationarity assumptions. Much of the theoretical contribution towards performance analysis of time-inhomogeneous single class queueing networks has focused on…
Statistical Mechanics deals with ensembles of microstates that are compatible with fixed constraints and that on average define a thermodynamic macrostate. The evolution of a small system is normally subjected to changing constraints and…
Stochastic reaction networks are mathematical models with a wide range of applications in biochemistry, ecology, and epidemiology, and are often complex to analyze. Except for some special cases, it is generally difficult to predict how the…
This paper focuses on modeling the dynamic attributes of a dynamic network with a fixed number of vertices. These attributes are considered as time series which dependency structure is influenced by the underlying network. They are modeled…