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In complex networks, the rich-get-richer effect (nodes with high degree at one point in time gain more degree in their future) is commonly observed. In practice this is often studied on a static network snapshot, for example, a preferential attachment model assumed to explain the more highly connected nodes or a rich-club}effect that analyses the most highly connected nodes. In this paper, we consider temporal measures of how success (measured here as node degree) propagates across time. By analogy with social mobility (a measure people moving within a social hierarchy through their life) we define hierarchical mobility to measure how a node's propensity to gain degree changes over time. We introduce an associated taxonomy of temporal correlation statistics including mobility, philanthropy and community. Mobility measures the extent to which a node's degree gain in one time period predicts its degree gain in the next. Philanthropy and community measure similar properties related to node neighbourhood. We apply these statistics both to artificial models and to 26 real temporal networks. We find that most of our networks show a tendency for individual nodes and their neighbourhoods to remain in similar hierarchical positions over time, while most networks show low correlative effects between individuals and their neighbourhoods. Moreover, we show that the mobility taxonomy can discriminate between networks from different fields. We also generate artificial network models to gain intuition about the behaviour and expected range of the statistics. The artificial models show that the opposite of the "rich-get-richer" effect requires the existence of inequality of degree in a network. Overall, we show that measuring the hierarchical mobility of a temporal network is an invaluable resource for discovering its underlying structural dynamics., Comment: 10 pages, 5 figures, 3 pages supplemental material. Accepted for Nature Scientific Reports

This survey uncovers the tension between AI techniques designed for energy saving in mobile networks and the energy demands those same techniques create. We compare modeling approaches that estimate power usage cost of current commercial terrestrial next-generation radio access network deployments. We then categorize emerging methods for reducing power usage by domain: time, frequency, power, and spatial. Next, we conduct a timely review of studies that attempt to estimate the power usage of the AI techniques themselves. We identify several gaps in the literature. Notably, real-world data for the power consumption is difficult to source due to commercial sensitivity. Comparing methods to reduce energy consumption is beyond challenging because of the diversity of system models and metrics. Crucially, the energy cost of AI techniques is often overlooked, though some studies provide estimates of algorithmic complexity or run-time. We find that extracting even rough estimates of the operational energy cost of AI models and data processing pipelines is complex. Overall, we find the current literature hinders a meaningful comparison between the energy savings from AI techniques and their associated energy costs. Finally, we discuss future research opportunities to uncover the utility of AI for energy saving., Comment: 16 pages, 4 figures, Accepted for publication in IEEE Access

Recent sustainability drives place energy-consumption metrics in centre-stage for the design of future radio access networks (RAN). At the same time, optimising the trade-off between performance and system energy usage by machine-learning (ML) is an approach that requires large amounts of granular RAN data to train models, and to adapt in near realtime. In this paper, we present extensions to the system-level discrete-event AIMM (AI-enabled Massive MIMO) Simulator, generating realistic figures for throughput and energy efficiency (EE) towards digital twin network modelling. We further investigate the trade-off between maximising either EE or spectrum efficiency (SE). To this end, we have run extensive simulations of a typical macrocell network deployment under various transmit power-reduction scenarios with a range of difference of 43 dBm. Our results demonstrate that the EE and SE objectives often require different power settings in different scenarios. Importantly, low mean user CPU execution times of 2.17 $\pm$ 0.05 seconds (2~s.d.) demonstrate that the AIMM Simulator is a powerful tool for quick prototyping of scalable system models which can interface with ML frameworks, and thus support future research in energy-efficient next generation networks., Comment: 6 pages, 3 figures, Accepted for 2024 IEEE Wireless Communications and Networking Conference (WCNC)

In the dynamic landscape of the Web, we are witnessing the emergence of the Web3 paradigm, which dictates that platforms should rely on blockchain technology and cryptocurrencies to sustain themselves and their profitability. Cryptocurrencies are characterised by high market volatility and susceptibility to substantial crashes, issues that require temporal analysis methodologies able to tackle the high temporal resolution, heterogeneity and scale of blockchain data. While existing research attempts to analyse crash events, fundamental questions persist regarding the optimal time scale for analysis, differentiation between long-term and short-term trends, and the identification and characterisation of shock events within these decentralised systems. This paper addresses these issues by examining cryptocurrencies traded on the Ethereum blockchain, with a spotlight on the crash of the stablecoin TerraUSD and the currency LUNA designed to stabilise it. Utilising complex network analysis and a multi-layer temporal graph allows the study of the correlations between the layers representing the currencies and system evolution across diverse time scales. The investigation sheds light on the strong interconnections among stablecoins pre-crash and the significant post-crash transformations. We identify anomalous signals before, during, and after the collapse, emphasising their impact on graph structure metrics and user movement across layers. This paper pioneers temporal, cross-chain graph analysis to explore a cryptocurrency collapse. It emphasises the importance of temporal analysis for studies on web-derived data and how graph-based analysis can enhance traditional econometric results. Overall, this research carries implications beyond its field, for example for regulatory agencies aiming to safeguard users from shocks and monitor investment risks for citizens and clients.

Distributed ledger technologies have opened up a wealth of fine-grained transaction data from cryptocurrencies like Bitcoin and Ethereum. This allows research into problems like anomaly detection, anti-money laundering, pattern mining and activity clustering (where data from traditional currencies is rarely available). The formalism of temporal networks offers a natural way of representing this data and offers access to a wealth of metrics and models. However, the large scale of the data presents a challenge using standard graph analysis techniques. We use temporal motifs to analyse two Bitcoin datasets and one NFT dataset, using sequences of three transactions and up to three users. We show that the commonly used technique of simply counting temporal motifs over all users and all time can give misleading conclusions. Here we also study the motifs contributed by each user and discover that the motif distribution is heavy-tailed and that the key players have diverse motif signatures. We study the motifs that occur in different time periods and find events and anomalous activity that cannot be seen just by a count on the whole dataset. Studying motif completion time reveals dynamics driven by human behaviour as well as algorithmic behaviour.

An important concept in organisational behaviour is how hierarchy affects the voice of individuals, whereby members of a given organisation exhibit differing power relations based on their hierarchical position. Although there have been prior studies of the relationship between hierarchy and voice, they tend to focus on more qualitative small-scale methods and do not account for structural aspects of the organisation. This paper develops large-scale computational techniques utilising temporal network analysis to measure the effect that organisational hierarchy has on communication patterns within an organisation, focusing on the structure of pairwise interactions between individuals. We focus on one major organisation as a case study - the Internet Engineering Task Force (IETF) - a major technical standards development organisation for the Internet. A particularly useful feature of the IETF is a transparent hierarchy, where participants take on explicit roles (e.g. Area Directors, Working Group Chairs). Its processes are also open, so we have visibility into the communication of people at different hierarchy levels over a long time period. We utilise a temporal network dataset of 989,911 email interactions among 23,741 participants to study how hierarchy impacts communication patterns. We show that the middle levels of the IETF are growing in terms of their dominance in communications. Higher levels consistently experience a higher proportion of incoming communication than lower levels, with higher levels initiating more communications too. We find that communication tends to flow "up" the hierarchy more than "down". Finally, we find that communication with higher-levels is associated with future communication more than for lower-levels, which we interpret as "facilitation". We conclude by discussing the implications this has on patterns within the wider IETF and for other organisations.

Raphtory is a platform for building and analysing temporal networks. The library includes methods for creating networks from a variety of data sources; algorithms to explore their structure and evolution; and an extensible GraphQL server for deployment of applications built on top. Raphtory's core engine is built in Rust, for efficiency, with Python interfaces, for ease of use. Raphtory is developed by network scientists, with a background in Physics, Applied Mathematics, Engineering and Computer Science, for use across academia and industry.

Recent years have witnessed the availability of richer and richer datasets in a variety of domains, where signals often have a multi-modal nature, blending temporal, relational and semantic information. Within this context, several works have shown that standard network models are sometimes not sufficient to properly capture the complexity of real-world interacting systems. For this reason, different attempts have been made to enrich the network language, leading to the emerging field of higher-order networks. In this work, we investigate the possibility of applying methods from higher-order networks to extract information from the online trade of Non-fungible tokens (NFTs), leveraging on their intrinsic temporal and non-Markovian nature. While NFTs as a technology open up the realms for many exciting applications, its future is marred by challenges of proof of ownership, scams, wash trading and possible money laundering. We demonstrate that by investigating time-respecting non-Markovian paths exhibited by NFT trades, we provide a practical path-based approach to fraud detection., Comment: Abstract accepted as a workshop presentation at Complex Data Blocks, a satellite of the 2022 Conference of Complex Systems

Often, due to prohibitively large size or to limits to data collecting APIs, it is not possible to work with a complete network dataset and sampling is required. A type of sampling which is consistent with Twitter API restrictions is uniform edge sampling. In this paper, we propose a methodology for the recovery of two fundamental network properties from an edge-sampled network: the degree distribution and the triangle count (we estimate the totals for the network and the counts associated with each edge). We use a Bayesian approach and show a range of methods for constructing a prior which does not require assumptions about the original network. Our approach is tested on two synthetic and three real datasets with diverse sizes, degree distributions, degree-degree correlations and triangle count distributions., Comment: Extended version of the paper accepted in Complex Networks 2022

The centrality of a node within a network, however it is measured, is a vital proxy for the importance or influence of that node, and the differences in node centrality generate hierarchies and inequalities. If the network is evolving in time, the influence of each node changes in time as well, and the corresponding hierarchies are modified accordingly. However, there is still a lack of systematic study into the ways in which the centrality of a node evolves when a graph changes. In this paper we introduce a taxonomy of metrics of equality and hierarchical mobility in networks that evolve in time. We propose an indicator of equality based on the classical Gini Coefficient from economics, and we quantify the hierarchical mobility of nodes, that is, how and to what extent the centrality of a node and its neighbourhood change over time. These measures are applied to a corpus of thirty time evolving network data sets from different domains. We show that the proposed taxonomy measures can discriminate between networks from different fields. We also investigate correlations between different taxonomy measures, and demonstrate that some of them have consistently strong correlations (or anti-correlations) across the entire corpus. The mobility and equality measures developed here constitute a useful toolbox for investigating the nature of network evolution, and also for discriminating between different artificial models hypothesised to explain that evolution.

Gab is an online social network often associated with the alt-right political movement and users barred from other networks. It presents an interesting opportunity for research because near-complete data is available from day one of the network's creation. In this paper, we investigate the evolution of the user interaction graph, that is the graph where a link represents a user interacting with another user at a given time. We view this graph both at different times and at different timescales. The latter is achieved by using sliding windows on the graph which gives a novel perspective on social network data. The Gab network is relatively slowly growing over the period of months but subject to large bursts of arrivals over hours and days. We identify plausible events that are of interest to the Gab community associated with the most obvious such bursts. The network is characterised by interactions between `strangers' rather than by reinforcing links between `friends'. Gab usage follows the diurnal cycle of the predominantly US and Europe based users. At off-peak hours the Gab interaction network fragments into sub-networks with absolutely no interaction between them. A small group of users are highly influential across larger timescales, but a substantial number of users gain influence for short periods of time. Temporal analysis at different timescales gives new insights above and beyond what could be found on static graphs., Comment: 10 pages, 9 figures

Motion sensors embedded in wearable and mobile devices allow for dynamic selection of sensor streams and sampling rates, enabling several applications, such as power management and data-sharing control. While deep neural networks (DNNs) achieve competitive accuracy in sensor data classification, DNNs generally process incoming data from a fixed set of sensors with a fixed sampling rate, and changes in the dimensions of their inputs cause considerable accuracy loss, unnecessary computations, or failure in operation. We introduce a dimension-adaptive pooling (DAP) layer that makes DNNs flexible and more robust to changes in sensor availability and in sampling rate. DAP operates on convolutional filter maps of variable dimensions and produces an input of fixed dimensions suitable for feedforward and recurrent layers. We also propose a dimension-adaptive training (DAT) procedure for enabling DNNs that use DAP to better generalize over the set of feasible data dimensions at inference time. DAT comprises the random selection of dimensions during the forward passes and optimization with accumulated gradients of several backward passes. Combining DAP and DAT, we show how to transform non-adaptive DNNs into a Dimension-Adaptive Neural Architecture (DANA), while keeping the same number of parameters. Compared to existing approaches, our solution provides better classification accuracy over the range of possible data dimensions at inference time and does not require up-sampling or imputation, thus reducing unnecessary computations. Experiments on seven datasets (four benchmark real-world datasets for human activity recognition and three synthetic datasets) show that DANA prevents significant losses in classification accuracy of the state-of-the-art DNNs and, compared to baselines, it better captures correlated patterns in sensor data under dynamic sensor availability and varying sampling rates., Comment: Proc. ACM Interact. Mob. Wearable Ubiquitous Technol., Vol. 5, No. 3, Article 120. Publication date: September 2021

Sensitive inferences and user re-identification are major threats to privacy when raw sensor data from wearable or portable devices are shared with cloud-assisted applications. To mitigate these threats, we propose mechanisms to transform sensor data before sharing them with applications running on users' devices. These transformations aim at eliminating patterns that can be used for user re-identification or for inferring potentially sensitive activities, while introducing a minor utility loss for the target application (or task). We show that, on gesture and activity recognition tasks, we can prevent inference of potentially sensitive activities while keeping the reduction in recognition accuracy of non-sensitive activities to less than 5 percentage points. We also show that we can reduce the accuracy of user re-identification and of the potential inference of gender to the level of a random guess, while keeping the accuracy of activity recognition comparable to that obtained on the original data., Comment: Accepted to appear in Pervasive and Mobile computing (PMC) Journal, Elsevier

Alternative paths in a network play an important role in its functionality as they can maintain the information flow under node/link failures. In this paper we explore the navigation of a network taking into account the alternative paths and in particular how can we describe this navigation in a concise way. Our approach is to simplify the network by aggregating into groups the nodes that do not contribute to alternative paths. We refer to these groups as super-nodes, and describe the post-aggregation network with super-nodes as the skeleton network. We present a method to describe with the least amount of information the paths in the super--nodes and skeleton network. Applying our method to several real networks we observed that there is scaling behaviour between the information required to describe all the paths in a network and the minimal information to describe the paths of its skeleton. We show how from this scaling we can evaluate the information of the paths for large networks with less computational cost., Comment: 18 pages, 8 figures

Discriminating between competing explanatory models as to which is more likely responsible for the growth of a network is a problem of fundamental importance for network science. The rules governing this growth are attributed to mechanisms such as preferential attachment and triangle closure, with a wealth of explanatory models based on these. These models are deliberately simple, commonly with the network growing according to a constant mechanism for its lifetime, to allow for analytical results. We use a likelihood-based framework on artificial data where the network model changes at a known point in time and demonstrate that we can recover the change point from analysis of the network. We then use real datasets and demonstrate how our framework can show the changing importance of network growth mechanisms over time.

Getting good statistical models of traffic on network links is a well-known, often-studied problem. A lot of attention has been given to correlation patterns and flow duration. The distribution of the amount of traffic per unit time is an equally important but less studied problem. We study a large number of traffic traces from many different networks including academic, commercial and residential networks using state-of-the-art statistical techniques. We show that the log-normal distribution is a better fit than the Gaussian distribution commonly claimed in the literature. We also investigate a second heavy-tailed distribution (the Weibull) and show that its performance is better than Gaussian but worse than log-normal. We examine anomalous traces which are a poor fit for all distributions tried and show that this is often due to traffic outages or links that hit maximum capacity. We demonstrate the utility of the log-normal distribution in two contexts: predicting the proportion of time traffic will exceed a given level (for service level agreement or link capacity estimation) and predicting 95th percentile pricing. We also show the log-normal distribution is a better predictor than Gaussian or Weibull distributions., Comment: Accepted for INFOCOM 2019

Motion sensors such as accelerometers and gyroscopes measure the instant acceleration and rotation of a device, in three dimensions. Raw data streams from motion sensors embedded in portable and wearable devices may reveal private information about users without their awareness. For example, motion data might disclose the weight or gender of a user, or enable their re-identification. To address this problem, we propose an on-device transformation of sensor data to be shared for specific applications, such as monitoring selected daily activities, without revealing information that enables user identification. We formulate the anonymization problem using an information-theoretic approach and propose a new multi-objective loss function for training deep autoencoders. This loss function helps minimizing user-identity information as well as data distortion to preserve the application-specific utility. The training process regulates the encoder to disregard user-identifiable patterns and tunes the decoder to shape the output independently of users in the training set. The trained autoencoder can be deployed on a mobile or wearable device to anonymize sensor data even for users who are not included in the training dataset. Data from 24 users transformed by the proposed anonymizing autoencoder lead to a promising trade-off between utility and privacy, with an accuracy for activity recognition above 92% and an accuracy for user identification below 7%., Comment: 10 pages

There is growing concern about how personal data are used when users grant applications direct access to the sensors of their mobile devices. In fact, high resolution temporal data generated by motion sensors reflect directly the activities of a user and indirectly physical and demographic attributes. In this paper, we propose a feature learning architecture for mobile devices that provides flexible and negotiable privacy-preserving sensor data transmission by appropriately transforming raw sensor data. The objective is to move from the current binary setting of granting or not permission to an application, toward a model that allows users to grant each application permission over a limited range of inferences according to the provided services. The internal structure of each component of the proposed architecture can be flexibly changed and the trade-off between privacy and utility can be negotiated between the constraints of the user and the underlying application. We validated the proposed architecture in an activity recognition application using two real-world datasets, with the objective of recognizing an activity without disclosing gender as an example of private information. Results show that the proposed framework maintains the usefulness of the transformed data for activity recognition, with an average loss of only around three percentage points, while reducing the possibility of gender classification to around 50\%, the target random guess, from more than 90\% when using raw sensor data. We also present and distribute MotionSense, a new dataset for activity and attribute recognition collected from motion sensors., Comment: 6 pages

An increasing number of sensors on mobile, Internet of things (IoT), and wearable devices generate time-series measurements of physical activities. Though access to the sensory data is critical to the success of many beneficial applications such as health monitoring or activity recognition, a wide range of potentially sensitive information about the individuals can also be discovered through access to sensory data and this cannot easily be protected using traditional privacy approaches. In this paper, we propose a privacy-preserving sensing framework for managing access to time-series data in order to provide utility while protecting individuals' privacy. We introduce Replacement AutoEncoder, a novel algorithm which learns how to transform discriminative features of data that correspond to sensitive inferences, into some features that have been more observed in non-sensitive inferences, to protect users' privacy. This efficiency is achieved by defining a user-customized objective function for deep autoencoders. Our replacement method will not only eliminate the possibility of recognizing sensitive inferences, it also eliminates the possibility of detecting the occurrence of them. That is the main weakness of other approaches such as filtering or randomization. We evaluate the efficacy of the algorithm with an activity recognition task in a multi-sensing environment using extensive experiments on three benchmark datasets. We show that it can retain the recognition accuracy of state-of-the-art techniques while simultaneously preserving the privacy of sensitive information. Finally, we utilize the GANs for detecting the occurrence of replacement, after releasing data, and show that this can be done only if the adversarial network is trained on the users' original data., Comment: 12 pages, 11 figures

This paper describes TARDIS (Traffic Assignment and Retiming Dynamics with Inherent Stability) which is an algorithmic procedure designed to reallocate traffic within Internet Service Provider (ISP) networks. Recent work has investigated the idea of shifting traffic in time (from peak to off-peak) or in space (by using different links). This work gives a unified scheme for both time and space shifting to reduce costs. Particular attention is given to the commonly used 95th percentile pricing scheme. The work has three main innovations: firstly, introducing the Shapley Gradient, a way of comparing traffic pricing between different links at different times of day; secondly, a unified way of reallocating traffic in time and/or in space; thirdly, a continuous approximation to this system is proved to be stable. A trace-driven investigation using data from two service providers shows that the algorithm can create large savings in transit costs even when only small proportions of the traffic can be shifted., Comment: 12 pages 9 figures. This is the full paper for the two page paper of the same name accepted as a short paper for SIGMETRICS 2014

We present a system for streaming live entertainment content over the Internet originating from a single source to a scalable number of consumers without resorting to centralised or provider- provisioned resources. The system creates a peer-to-peer overlay network, which attempts to optimise use of existing capacity to ensure quality of service, delivering low start-up delay and lag in playout of the live content. There are three main aspects of our solution. Firstly, a swarming mechanism that constructs an overlay topology for minimising propagation delays from the source to end consumers. Secondly, a distributed overlay anycast system that uses a location-based search algorithm for peers to quickly find the closest peers in a given stream. Finally, a novel incentives mechanism that encourages peers to donate capacity even when the user is not actively consuming content., Comment: 11 pages, 6 figures

In this paper we present the \emph{Distributed Overlay Anycast Table}, a structured overlay that implements application-layer anycast, allowing the discovery of the closest host that is a member of a given group. One application is in locality-aware peer-to-peer networks, where peers need to discover low-latency peers participating in the distribution of a particular file or stream. The DOAT makes use of network delay coordinates and a space filling curve to achieve locality-aware routing across the overlay, and Bloom filters to aggregate group identifiers. The solution is designed to optimise both accuracy and query time, which are essential for real-time applications. We simulated DOAT using both random and realistic node distributions. The results show that accuracy is high and query time is low., Comment: 7 pages, 4 figures

Many researchers have hypothesised models which explain the evolution of the topology of a target network. The framework described in this paper gives the likelihood that the target network arose from the hypothesised model. This allows rival hypothesised models to be compared for their ability to explain the target network. A null model (of random evolution) is proposed as a baseline for comparison. The framework also considers models made from linear combinations of model components. A method is given for the automatic optimisation of component weights. The framework is tested on simulated networks with known parameters and also on real data., Comment: Published in INFOCOM NetSciCom Workshop 2009. http://dl.acm.org/citation.cfm?id=1719896

This paper takes a critical look at the usefulness of power law models of the Internet. The twin focuses of the paper are Internet traffic and topology generation. The aim of the paper is twofold. Firstly it summarises the state of the art in power law modelling particularly giving attention to existing open research questions. Secondly it provides insight into the failings of such models and where progress needs to be made for power law research to feed through to actual improvements in network performance., Comment: To appear Computer Communications

This paper criticises the notion that long-range dependence is an important contributor to the queuing behaviour of real Internet traffic. The idea is questioned in two different ways. Firstly, a class of models used to simulate Internet traffic is shown to have important theoretical flaws. It is shown that this behaviour is inconsistent with the behaviour of real traffic traces. Secondly, the notion that long-range correlations significantly affects the queuing performance of traffic is investigated by destroying those correlations in real traffic traces (by reordering). It is shown that the longer ranges of correlations are not important except in one case with an extremely high load., Comment: Presented at the PMECT 2009 workshop (part of ICCCN 2009) in San Francisco

A problem which has recently attracted research attention is that of estimating the distribution of flow sizes in internet traffic. On high traffic links it is sometimes impossible to record every packet. Researchers have approached the problem of estimating flow lengths from sampled packet data in two separate ways. Firstly, different sampling methodologies can be tried to more accurately measure the desired system parameters. One such method is the sample-and-hold method where, if a packet is sampled, all subsequent packets in that flow are sampled. Secondly, statistical methods can be used to ``invert'' the sampled data and produce an estimate of flow lengths from a sample. In this paper we propose, implement and test two variants on the sample-and-hold method. In addition we show how the sample-and-hold method can be inverted to get an estimation of the genuine distribution of flow sizes. Experiments are carried out on real network traces to compare standard packet sampling with three variants of sample-and-hold. The methods are compared for their ability to reconstruct the genuine distribution of flow sizes in the traffic.

This paper examines a discrete-time queuing system with applications to telecommunications traffic. The arrival process is a particular Markov modulated process which belongs to the class of discrete batched Markovian arrival processes. The server process is a single server deterministic queue. A closed form exact solution is given for the expected queue length and delay. A simple system of equations is given for the probability of the queue exceeding a given length., Comment: to appear Performance Evaluation

This paper describes, in detail, techniques for measuring the Hurst parameter. Measurements are given on artificial data both in a raw form and corrupted in various ways to check the robustness of the tools in question. Measurements are also given on real data, both new data sets and well-studied data sets. All data and tools used are freely available for download along with simple ``recipes'' which any researcher can follow to replicate these measurements., Comment: 12 pages, 3 figures, 4 tables

This paper describes a framework for analysing matches in multiple data sets. The framework described is quite general and can be applied to a variety of problems where matches are to be found in data surveyed at a number of locations (or at a single location over a number of days). As an example, the framework is applied to the problem of false matches in licence plate survey data. The specific problem addressed is that of estimating how many vehicles were genuinely sighted at every one of a number of survey points when there is a possibility of accidentally confusing two vehicles due to the nature of the survey undertaken. In this paper, a method for representing the possible "types of match" is outlined using set theory. The phrase "types of match" will be defined and formalised in this paper. A method for enumerating the set of all types of match over n survey sites, is described. The method is applied to the problem of correcting survey data for false matches using a simple probabalistic method. An algorithm is developed for correcting false matches over multiple survey sites and its use is demonstrated with simulation results., Comment: 13 pages, 1 figure

The aim of this paper is to use a very simple queuing model to compare a number of models from the literature which have been used to replicate the statistical nature of internet traffic and, in particular, the long-range dependence of this traffic. The four models all have the form of discrete time Markov-modulated processes (two other models are introduced for comparison purposes). While it is often stated that long-range dependence has a critical effect on queuing performance, it appears that the models used here do not well replicated the queuing performance of real internet traffic. In particular, they fail to replicate the mean queue length (and hence the mean delay) and the probability of the queue length exceeding a given level., Comment: 33 pages, 13 figures. Revised after comments and changed format. Added diagrams about queue overflow probabilities

This paper describes a model for generating time series which exhibit the statistical phenomenon known as long-range dependence (LRD). A Markov Modulated Process based upon an infinite Markov chain is described. The work described is motivated by applications in telecommunications where LRD is a known property of time-series measured on the internet. The process can generate a time series exhibiting LRD with known parameters and is particularly suitable for modelling internet traffic since the time series is in terms of ones and zeros which can be interpreted as data packets and inter-packet gaps. The method is extremely simple computationally and analytically and could prove more tractable than other methods described in the literature, Comment: 8 pages, 2 figures