Metastability of Queuing Networks with Mobile Servers

We study symmetric queuing networks with moving servers and FIFO service discipline. The mean-field limit dynamics demonstrates unexpected behavior which we attribute to the meta-stability phenomenon. Large enough finite symmetric networks on regular graphs are proved to be transient for arbitrarily small inflow rates. However, the limiting non-linear Markov process possesses at least two stationary solutions. The proof of transience is based on martingale techniques

Distributed Resource Allocation for Stream Data Processing

Abstract. Data streaming applications are becoming more and more common due to the rapid development in the areas such as sensor net-works, multimedia streaming, and on-line data mining, etc. These ap-plications are often running in a decentralized, distributed environment. The requirements for processing large volumes of streaming data at real time have posed many great design challenges. It is critical to optimize the ongoing resource consumption of multiple, distributed, cooperating, processing units. In this paper, we consider a generic model for the gen-eral stream data processing systems. We address the resource alloca-tion problem for a collection of processing units so as to maximize the weighted sum of the throughput of different streams. Each processing unit may require multiple input data streams simultaneously and pro-duce one or many valuable output streams. Data streams flow through such a system after processing at multiple processing units. Based on this framework, we develop distributed algorithms for finding the best resource allocation schemes in such data stream processing networks. Performance analysis on the optimality and complexity of these algo-rithms are also provided

Towards a generalisation of formal concept analysis for data mining purposes

In this paper we justify the need for a generalisation of Formal Concept Analysis for the purpose of data mining and begin the synthesis of such theory. For that purpose, we first review semirings and semimodules over semirings as the appropriate objects to use in abstracting the Boolean algebra and the notion of extents and intents, respectively. We later bring to bear powerful theorems developed in the field of linear algebra over idempotent semimodules to try to build a Fundamental Theorem for K-Formal Concept Analysis, where K is a type of idempotent semiring. Finally, we try to put Formal Concept Analysis in new perspective by considering it as a concrete instance of the theory developed

Single-cell and multi-cell performance analysis of OFDM index modulation

This study addresses the achievable rate of single cell and sum rate of multi-cell orthogonal frequency division multiplexing (OFDM) index modulation (IM). The single-cell achievable rate of OFDM-IM with Gaussian input is calculated using a multi-ary symmetric channel. Then, the cumulative distribution function of multi-cell OFDM-IM is investigated by stochastic geometry. Furthermore, it is proved in this study that the probability density function of noise plus inter-cell interference in multicell OFDM-IM with quadrature-amplitude modulation follows a mixture of Gaussians (MoGs) distribution. Next, parameters of the MoG distribution are estimated using a simplified expectation maximisation algorithm. Upper bound of sum rates of multi-cell OFDM-IM is derived. Furthermore, analytic and simulated results are compared and discussed

TCP is Max-Plus Linear and what it tells us on its throughput

Projet MCRWe give a representation of the packet-level dynamical behavior of the Reno and Tahoe variants of TCP over a single end-to-end connection. This representation allows one to consider the case when the connection involves a network made of several, possibly heterogeneous, deterministic or random routers in series. It is shown that the key features of the protocol and of the network can be expressed via a linear dynamical system in the so called max-plus algebra. This opens new ways of both analytical evaluation and fast simulation based on products of matrices in this algebra. This also leads to closed form formulas for the throughput allowed by TCP under natural assumptions on the behavior of the routers and on the detection of losses and timeouts; these new formulas are shown to refine those obtained from earlier models which either assume that the network could be reduced to a single bottleneck router and/or approximate the packets by a fluid

Separation of Circulating Tokens

Self-stabilizing distributed control is often modeled by token abstractions. A system with a single token may implement mutual exclusion; a system with multiple tokens may ensure that immediate neighbors do not simultaneously enjoy a privilege. For a cyber-physical system, tokens may represent physical objects whose movement is controlled. The problem studied in this paper is to ensure that a synchronous system with m circulating tokens has at least d distance between tokens. This problem is first considered in a ring where d is given whilst m and the ring size n are unknown. The protocol solving this problem can be uniform, with all processes running the same program, or it can be non-uniform, with some processes acting only as token relays. The protocol for this first problem is simple, and can be expressed with Petri net formalism. A second problem is to maximize d when m is given, and n is unknown. For the second problem, the paper presents a non-uniform protocol with a single corrective process.Comment: 22 pages, 7 figures, epsf and pstricks in LaTe

Reachability problems for products of matrices in semirings

We consider the following matrix reachability problem: given $r$ square matrices with entries in a semiring, is there a product of these matrices which attains a prescribed matrix? We define similarly the vector (resp. scalar) reachability problem, by requiring that the matrix product, acting by right multiplication on a prescribed row vector, gives another prescribed row vector (resp. when multiplied at left and right by prescribed row and column vectors, gives a prescribed scalar). We show that over any semiring, scalar reachability reduces to vector reachability which is equivalent to matrix reachability, and that for any of these problems, the specialization to any $r\geq 2$ is equivalent to the specialization to $r=2$. As an application of this result and of a theorem of Krob, we show that when $r=2$, the vector and matrix reachability problems are undecidable over the max-plus semiring $(Z\cup\{-\infty\},\max,+)$. We also show that the matrix, vector, and scalar reachability problems are decidable over semirings whose elements are ``positive'', like the tropical semiring $(N\cup\{+\infty\},\min,+)$.Comment: 21 page