相关论文: Multiclass processes, dual points and M/M/1 queues

It is interesting and challenging to study double-ended queues with First-Come-First-Match discipline under customers' impatient behavior and non-Poisson inputs. The system stability can be guaranteed by the customers' impatient behavior,…

We study the generic non-equilibrium steady states in asymmetric exclusion processes on a closed network with bottlenecks. To this end we proposes and study closed simple networks with multiply-connected non-identical junctions. Depending…

We classify all functions which, when applied term by term, leave invariant the sequences of moments of positive measures on the real line. Rather unexpectedly, these functions are built of absolutely monotonic components, or reflections of…

Contemporary machine learning applications often involve classification tasks with many classes. Despite their extensive use, a precise understanding of the statistical properties and behavior of classification algorithms is still missing,…

For a class of piecewise deterministic Markov processes, the supports of the invariant measures are characterized. This is based on the analysis of controllability properties of an associated deterministic control system. Its invariant…

Temporal point processes offer a powerful framework for sampling from discrete distributions, yet they remain underutilized in existing literature. We show how to construct, for any target multivariate count distribution with…

We present a study of exclusion process on a peculiar topology of network with two intersected lanes, competing for the particles in a reservoir with finite capacity. To provide a theoretical ground for our findings, we exploit mean-field…

We prove a duality between the asymmetric simple exclusion process (ASEP) with non-conservative open boundary conditions and an asymmetric exclusion process with particle-dependent hopping rates and conservative reflecting boundaries. This…

We consider optimizing average queueing delay and average power consumption in a nonpreemptive multi-class M/G/1 queue with dynamic power control that affects instantaneous service rates. Four problems are studied: (1) satisfying per-class…

The large-time behavior of a nonlinearly coupled pair of measure-valued transport equations with discontinuous boundary conditions, parameterized by a positive real-valued parameter $\lambda$, is considered. These equations describe the…

Numerous studies grounded on Hawkes processes have been carried out in many fields including finance, biology and social network. Hawkes processes form a class of selfexciting simple point processes. In this article, we consider a general…

Stochastic driven flow along a channel can be modeled by the asymmetric simple exclusion process. We confirm numerically the presence of a dynamic queuing phase transition at a nonzero obstruction strength, and establish its scaling…

We study a multiclass M/M/1 queueing control problem with finite buffers under heavy-traffic where the decision maker is uncertain about the rates of arrivals and service of the system and by scheduling and admission/rejection decisions…

We show that bootstrap methods based on the positivity of probability measures provide a systematic framework for studying both synchronous and asynchronous nonequilibrium stochastic processes on infinite lattices. First, we formulate…

In this paper, we prove a conjecture by Aas and Linusson on the two-point correlations of adjacent particles in a continuous multispecies TASEP on a ring (AIHPD, 2018). We use the theory of multiline queues as devised by Ferrari and Martin…

We extend classic characterisations of posterior distributions under Dirichlet process and gamma random measures priors to a dynamic framework. We consider the problem of learning, from indirect observations, two families of time-dependent…

In this paper, the notion of measure complexity is introduced for a topological dynamical system and it is shown that Sarnak's M\"{o}bius disjointness conjecture holds for any system for which every invariant Borel probability measure has…

We study the flux of totally asymmetric simple exclusion processes (TASEPs) on a twin co-axial square tracks. In this biologically motivated model the particles in each track act as mobile bottlenecks against the movement of the particles…

When a second-order phase transition is crossed at fine rate, the evolution of the system stops being adiabatic as a result of the critical slowing down in the neighborhood of the critical point. In systems with a topologically nontrivial…

We consider a pair of causally independent processes, modelled as the tensor product of two channels, acting on a possibly correlated input to produce random outputs X and Y. We show that, assuming the processes produce a sufficient amount…