: This paper discusses some aspects of selecting and testing random and pseudorandom number generators. The outputs of such generators may he used in many cryptographic applications, such as the generation of key material. Generators suitable for use in cryptographic applications may need to meet stronger requirements than for other applications. In particular, their outputs must he unpredictable in the absence of knowledge of the inputs. Some criteria for characterizing and selecting appropriate generators are discussed in this document. The subject of statistical testing and its relation to cryptanalysis is also discussed, and some recommended statistical tests are provided. These tests may he useful as a first step in determining whether or not a generator is suitable for a particular cryptographic application. The design and cryptanalysis of generators is outside the scope of this paper.

/pdf/a-statistical-test-suite-for-random-and-pseudorandom-number-xf8s068cdk.pdf

A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications

This paper investigates two fundamental characteristics of a wireless multi -hop network: its minimum node degree and its k--connectivity Both topology attributes depend on the spatial distribution of the nodes and their transmission range Using typical modeling assumptions :--- :a random uniform distribution of the nodes and a simple link model :--- :we derive an analytical expression that enables the determination of the required range r0 that creates, for a given node density ρ, an almost surely k--connected network Equivalently, if the maximum r0 of the nodes is given, we can find out how many nodes are needed to cover a certain area with a k--connected network We also investigate these questions by various simulations and thereby verify our analytical expressions Finally, the impact of mobility is discussedThe results of this paper are of practical value for researchers in this area, eg, if they set the parameters in a network--level simulation of a mobile ad hoc network or if they design a wireless sensor network

/pdf/on-the-minimum-node-degree-and-connectivity-of-a-wireless-gd91chp0fp.pdf

On the minimum node degree and connectivity of a wireless multihop network

We consider a communication system in which status updates arrive at a source node, and should be transmitted through a network to the intended destination node. The status updates are samples of a random process under observation, transmitted as packets, which also contain the time stamp to identify when the sample was generated. The age of the information available to the destination node is the time elapsed, since the last received update was generated. In this paper, we model the source-destination link using the queuing theory, and we assume that the time it takes to successfully transmit a packet to the destination is an exponentially distributed service time. We analyze the age of information in the case that the source node has the capability to manage the arriving samples, possibly discarding packets in order to avoid wasting network resources with the transmission of stale information. In addition to characterizing the average age, we propose a new metric, called peak age, which provides information about the maximum value of the age, achieved immediately before receiving an update.

On the Age of Information in Status Update Systems With Packet Management

Applied Probability and Queues.

From social networks such as Facebook, the World Wide Web and the Internet, to the complex interactions between proteins in the cells of our bodies, we constantly face the challenge of understanding the structure and development of networks. The theory of random graphs provides a framework for this understanding, and in this book the authors give a gentle introduction to the basic tools for understanding and applying the theory. Part I includes sufficient material, including exercises, for a one semester course at the advanced undergraduate or beginning graduate level. The reader is then well prepared for the more advanced topics in Parts II and III. A final part provides a quick introduction to the background material needed. All those interested in discrete mathematics, computer science or applied probability and their applications will find this an ideal introduction to the subject.

/pdf/introduction-to-random-graphs-3cfvwg09nu.pdf

Introduction to random graphs

Introduction to Queuing Theory

Several practical approaches have been used to estimate the probabilities of rare events occurring in queueing processes. Rare events of practical interest can be considered as large deviations for a fixed queueing process (such as level crossing by the waiting time, or the queue length) or as those for a limiting triangular scheme. This paper is a survey of the literature devoted to the regenerative analysis of rare events. Because of the importance of busy period parameters, rare events within a busy period are discussed. A number of small parameter theorems useful in rare events analysis are outlined, including singular states aggregation theorems. Simulation methods for rare events analysis and other numerical methods are also presented.

Rare events in queueing systems—A survey

Consideration is given to a queueing model that describes the deployment of emergency medical service along a highway. Two heuristic methods are proposed for the approximate evaluation of stationary loss probability and utilization of ambulance cars. The high accuracy of these methods is demonstrated by several examples.

Heuristic methods for the analysis of a queuing system describing emergency medical service deployed along a highway

Einführung in die Bedienungstheorie

Theory of random graphs

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