Related papers: A note on the stability of multiclass Markovian qu…
Stability is an important issue in order to characterize the performance of a network, and it has become a major topic of study in the last decade. Roughly speaking, a communication network system is said to be stable if the number of…
In this article, we consider a continuous review (s, S) inventory system with failures of demand fulfillment (service) modeled as a Markov-modulated retrial queueing system. The inventory system features a single product that experiences…
In this paper, we present a stability criterion for Processor Sharing queues, in which the throughput may depend on the number of customers in the system (in such cases such as interferences between the users). Such a system is represented…
With the development of real-time networks such as reactive embedded systems, there is a need to compute deterministic performance bounds. This paper focuses on the performance guarantees and stability conditions in networks with cyclic…
We derive a sufficient condition for a $k$-th order homogeneous Markov chain $\mathbf{Z}$ with finite alphabet $\mathcal{Z}$ to have a unique invariant distribution on $\mathcal{Z}^k$. Specifically, let $\mathbf{X}$ be a first-order,…
Stabilization of non-stationary linear systems over noisy communication channels is considered. Stochastically stable sources, and unstable but noise-free or bounded-noise systems have been extensively studied in information theory and…
For a stochastically monotone Markov chain taking values in a Polish space, we present a number of conditions for existence and for uniqueness of its stationary regime, as well as for closeness of its transient trajectories. In particular,…
Classical conditions for ensuring the robust stability of a linear system in feedback with a sector-bounded nonlinearity include small gain, circle, passivity, and conicity theorems. In this work, we present a similar stability condition,…
We consider a heterogeneous queueing system consisting of one large pool of $O(r)$ identical servers, where $r\to\infty$ is the scaling parameter. The arriving customers belong to one of several classes which determines the service times in…
We establish heavy traffic limit theorems for queue-length processes in critically loaded single class queueing networks with state dependent arrival and service rates. A distinguishing feature of our model is non-Markovian state…
This paper studies the stability of sampled and networked control systems with sampling and communication times governed by probabilistic clocks. The clock models have few restrictions, and can be used to model numerous phenomena such as…
We develop a robust queueing network analyzer algorithm to approximate the steady-state performance of a single-class open queueing network of single-server queues with Markovian routing. The algorithm allows non-renewal external arrival…
We analyze the performance of redundancy in a multi-type job and multi-type server system. We assume the job dispatcher is unaware of the servers' capacities, and we set out to study under which circumstances redundancy improves the…
We consider a heterogeneous distributed service system, consisting of $n$ servers with unknown and possibly different processing rates. Jobs with unit mean and independent processing times arrive as a renewal process of rate $\lambda n$,…
This paper studies the mean stability of positive semi-Markovian jump linear systems. We show that their mean stability is characterized by the spectral radius of a matrix that is easy to compute. In deriving the condition we use a certain…
We construct a generic, simple, and efficient scheduling policy for stochastic processing networks, and provide a general framework to establish its stability. Our policy is randomized and prioritized: with high probability it prioritizes…
We study multiclass many-server queues for which the arrival, service and abandonment rates are all modulated by a common finite-state Markov process. We assume that the system operates in the "averaged" Halfin-Whitt regime, which means…
Markovian network equilibrium generalizes the classical Wardrop equilibrium in network games. At a Markovian network equilibrium, each player of the game solves a Markov decision process instead of a shortest path problem. We propose two…
We introduce a multiclass single-server queueing system in which the arrival rates depend on the current job in service. The system is characterized by a matrix of arrival rates in lieu of a vector of arrival rates. Our proposed model…
We define a wide class of Markovian load balancing networks of identical single-server infinite-buffer queues. These networks may implement classic parallel server or work stealing load balancing policies, and may be asymmetric, for…