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A novel Markovian network evolution model is introduced and analysed by means of information theory. It will be proved that the model, called Network Evolution Chain, is a stationary and ergodic stochastic process. Therefore, the Asymptotic…
This paper studies the steady-state properties of the Join the Shortest Queue model in the Halfin-Whitt regime. We focus on the process tracking the number of idle servers, and the number of servers with non-empty buffers. Recently,…
In this paper we revisit the results of Loynes (1962) on stability of queues for ergodic arrivals and services, and show examples when the arrivals are bounded and ergodic, the service rate is constant, and under stability the limit…
One of the key performance measures in queueing systems is the exponential decay rate of the steady-state tail probabilities of the queue lengths. It is known that if a corresponding fluid model is stable and the stochastic primitives have…
We present the explicit construction of a stable queue with several servers and impatient customers, under stationary ergodic assumptions. Using a stochastic comparison of the (multivariate) workload sequence with two monotonic stochastic…
We consider processing networks where multiple dispatchers are connected to single-server queues by a bipartite compatibility graph, modeling constraints that are common in data centers and cloud networks due to geographic reasons or data…
We are concerned with an $M/M$-type join the shortest queue ($M/M$-JSQ for short) with $k$ parallel queues for an arbitrary positive integer $k$, where the servers may be heterogeneous. We are interested in the tail asymptotic of the…
Consider a countably infinite collection of interacting queues, with a queue located at each point of the $d$-dimensional integer grid, having independent Poisson arrivals, but dependent service rates. The service discipline is of the…
This paper shows how the application of stochastic geometry to the analysis of wireless networks is greatly facilitated by (i) a clear separation of time scales, (ii) the abstraction of small-scale effects via ergodicity, and (iii) an…
In the context of communication networks, the framework of stochastic event graphs allows a modeling of control mechanisms induced by the communication protocol and an analysis of its performances. We concentrate on the logarithmic tail…
Randomized load balancing networks arise in a variety of applications, and allow for efficient sharing of resources, while being relatively easy to implement. We consider a network of parallel queues in which incoming jobs with independent…
A network belongs to the monotone separable class if its state variables are homogeneous and monotone functions of the epochs of the arrival process. This framework contains several classical queueing network models, including generalized…
We propose and study a novel continuous space-time model for wireless networks which takes into account the stochastic interactions in both space through interference and in time due to randomness in traffic. Our model consists of an…
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,…
We consider a dynamical process in a network which distributes all particles (tokens) located at a node among its neighbors, in a round-robin manner. We show that in the recurrent state of this dynamics (i.e., disregarding a polynomially…
A network belongs to the monotone separable class if its state variables are homogeneous and monotone functions of the epochs of the arrival process. This framework, which was first introduced to derive the stability region for stochastic…
In this paper, we introduce ergodic sets, subsets of nodes of the networks that are dynamically disjoint from the rest of the network (i.e. that can never be reached or left following to the network dynamics). We connect their definition to…
Using elementary methods, we prove that for a countable Markov chain $P$ of ergodic degree $d > 0$ the rate of convergence towards the stationary distribution is subgeometric of order $n^{-d}$, provided the initial distribution satisfies…
In this paper we solve a particular stochastic recursion in the stationary ergodic framework, and propose some applications of this result to the study of regenerativity (that is, finiteness of busy cycles) and stationarity of some queueing…
In this work, we focus on the stationary analysis of a specific class of continuous time Markov-modulated reflected random walks in the quarter plane with applications in the modelling of two-node Markov-modulated queueing networks with…