Related papers: The max-plus algebra approach in modelling of queu…
Inspired by quantum switches, we consider a discrete-time multi-way matching system with two classes of arrivals: requests for entangled pair of qubits between two nodes, and qubits from each node that can be used to serve the requests. An…
Evolving multiplex networks are a powerful model for representing the dynamics along time of different phenomena, such as social networks, power grids, biological pathways. However, exploring the structure of the multiplex network time…
The max-plus algebra $\mathbb{R}\cup \{-\infty \}$ is defined in terms of a combination of the following two operations: addition, $a \oplus b := \max(a,b)$, and multiplication, $a \otimes b := a + b$. In this study, we propose a new method…
Let us extend the pair of operations (max,+) over real numbers to matrices in the same way as in conventional linear algebra. We study integer images of max-plus linear mappings. The question whether Ax (in the max-plus algebra) is an…
Dynamic processes on networks are fundamental to understanding modern-day phenomena such as information diffusion and opinion polarization on the internet or epidemics spreading through society. However, such processes are notoriously…
The MIMO wireless channel offers a rich ground for quality of service analysis. In this work, we present a stochastic network calculus analysis of a MIMO system, operating in spatial multiplexing mode, using moment generating functions…
We consider an infinite-server queue into which customers arrive according to a Cox process and have independent service times with a general distribution. We prove a functional large deviations principle for the equilibrium queue length…
The dynamics of competing opinions in social network play an important role in society, with many applications in diverse social contexts as consensus, elections, morality and so on. Here we study a model of interacting agents connected in…
It is shown that bandwidth estimation in packet networks can be viewed in terms of min-plus linear system theory. The available bandwidth of a link or complete path is expressed in terms of a {\em service curve}, which is a function that…
Network growth as described by the Duplication-Divergence model proposes a simple general idea for the evolution dynamics of natural networks. In particular it is an alternative to the well known Barab\'asi-Albert model when applied to…
We consider a service system with an infinite number of exponential servers sharing a finite service capacity. The servers are ordered according to their speed, and arriving customers join the fastest idle server. A capacity allocation is…
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…
This paper introduces and analyzes the notion of throughput suboptimality for many-server queueing systems in heavy traffic. The queueing model under consideration has multiple customer classes, indexed by a finite set $\mathcal{I}$, and…
We present a new model of neural networks called Min-Max-Plus Neural Networks (MMP-NNs) based on operations in tropical arithmetic. In general, an MMP-NN is composed of three types of alternately stacked layers, namely linear layers,…
It is well known that building analytical performance models in practice is difficult because it requires a considerable degree of proficiency in the underlying mathematics. In this paper, we propose a machine-learning approach to derive…
We consider a tandem queue with coupled processors, which is subject to global breakdowns. When the network is in the operating mode and both queues are non empty, the total service capacity is shared among the stations according to fixed…
We consider the problem of designing models to leverage a recently introduced approximate model averaging technique called dropout. We define a simple new model called maxout (so named because its output is the max of a set of inputs, and…
We show that for a certain class of dynamics at the nodes the response of a network of any topology to arbitrary inputs is defined in a simple way by its response to a monotone input. The nodes may have either a discrete or continuous set…
The rise of e-hailing taxis has significantly altered urban transportation and resulted in a competitive taxi market with both traditional street-hailing and e-hailing taxis. The new mobility services provide similar door-to-door rides as…
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…