. We discuss how long range dependence can influence the characteristics of a single server queue. We take the analogue of the G/M/1 queue except that the input stream is altered to exhibit long range dependence. The equilibrium queue size and equilibrium waiting time distributions each have heavy tails. By suitably selecting the parameters of the inputs, the queue size or waiting time can be made to possess infinite variance and even infinite mean. Some simulations dramatically illustrate the potential for undetected long range dependence to significantly alter the queueing behavior compared to what is anticipated with traditional inputs. 1. Introduction. Long range dependence is a property of stationary time series models whose current state has a strong dependency on the remote past. Definitions vary from author to author but a commonly accepted definition in covariance stationary time series is that a process fXng has long range dependence if 1 X j=1 jcorr(X 0 ; X j )j = 1 (cf...

INTRODUCTION There now exist several large teletraffic data sets exhibiting non-standard features incompatible with classical assumtions of short range dependence and rapidly decreasing tails. For instance, it is worth exploring the variety of data catalogued at the ITA web site www.acm.org/sigcomm/ITA/. These data sets exhibit the phenomena of heavy-tailed marginal distributions and long range dependence. Tails can be so heavy that only infinite variance models are possible (eg, [43]), and sometimes, as in file size data, even first moments are infinite. See [1]. Heavy tails have been fit to file lengths ([1], [9],[10]) cpu time to complete a job, call holding times, inter-arrival times between packets in a network ([39]), lengths of on/off cycles ([43], [42]). Other areas where heavy tails abound are finance and economics ([12], [13], [20], [6], [7]) and insurance analysis ([30], [32]). Of course, long range dependence was originially consider

. - The problem of optimal filtering is investigated in a continuous time linear Gaussian system where the signal is a fixed random variable and the noise driving the observation process is a fractional Brownian motion with Hurst parameter H 2 (1=2; 1). Closed form expressions are derived both for the optimal filter and the variance of the filtering error. Then an application to the determination of the best linear unbiased estimator in a related parameter estimation problem is discussed. Finally integral transformations which change a fractional Brownian motion to martingales are identified and an elementary approach to a Girsanov type formula is developed which shows that the estimator is in fact the maximum likelihood estimator. Key Words and Phrases: Fractional Brownian motion; Optimal filter; Best linear unbiased estimator; Maximum likelihood estimator. AMS 1991 Subject Classification: Primary 60G35, 62M20; Secondary 60G15, 93E11. 1. Introduction. - It is now widely accepted t...

With the ever increasing deployment and usage of gigabit networks, traditional network anomaly detection based Intrusion Detection Systems (IDS) have not scaled accordingly. Most, if not all, intrusion detection systems (IDS) assume the availability of complete and clean audit data. We contend that this assumption is not valid. Factors like noise, mobility of the nodes and the large amount of network traffic make it difficult to build a traffic profile of the network that is complete and immaculate for the purpose of anomaly detection. In this paper, we attempt to address these issues by presenting an anomaly detection scheme, called SCAN (Stochastic Clustering Algorithm for Network anomaly detection), that has the capability to detect intrusions with high accuracy even with incomplete audit data. To address the threats posed by network-based denial-of-service attacks in high speed networks, SCAN consists of two modules: an anomaly detection module that is at the core of the design and an adaptive packet sampling scheme that intelligently samples packets to aid the anomaly detection module. The noteworthy features of SCAN include: (a) it intelligently samples the incoming network traffic to decrease the amount of audit data being sampled while retaining the intrinsic characteristics of the network traffic itself; (b) it computes the missing elements of the sampled audit data by utilizing an improved Expectation-Maximization (EM) algorithm-based clustering algorithm; and (c) it improves the speed of convergence of the clustering process by employing Bloom filters and data summaries.

This paper exmines evidence of long-term memory in the yen/dollar price change as well as in the daily estimate of volatility of the exchange rate series. The methodology used is due to Lo (1989) which is robust to the presence of heteroscedasticity and is applied to a ten year data set. The result shows no evidence of long-term memory in the price change series indicating efficient pricing by the market participants. The volatility series, however, shows evidence of long-term memory which may have implications for traders dealing with long lived assets.

Abstract. The notion of long range dependence is discussed from a variety of points of view, and a new approach is suggested. A number of related topics is also discussed, including connections with non-stationary processes, with ergodic theory, self-similar processes and fractionally differenced processes, heavy tails and light tails, limit theorems and large deviations. 1.

A Hilb alued stochastic integration is defined for an integrator that is acylindrical fractional Brownian motion in a Hilbert space. Since the integrator is not a semimartingale for the fractional Brownian motions considered, a di#erent definition of integration is required. Both deterministic and stochastic operatoralued integrands are used. The approach to integration has an analogue with Skorokhod integrals for Brownian motion by the basic use of a derivative of some functionals of Brownianmotion. An Ito formula is given for some processes obtained by this stochastic integration. 1 Int7 duct91 Fractional Brownian motion is afamil# of Gaussian processes that are indexed by the Hurst parameter H (0, 1). In a finitedimensional Eucl#nsio space these processes were introduced by Kol#6q=fi9 v [10] and some properties of these processes were given byMandel#94# and van Ness [13]. Hurst [8], [9] used this approach to describe the l#efi term capacity of reservoirs al#sfi the Nil# River which was theinitial indication that these processescoul# be used as model# of physical phenomena. Mandel#na. [12] used these processes to model some economic data and, most recentl# , these processes have been noted for model# oftel#66q7 unication tra#c (e.g., [11]). To enhance theanal#q7# and theappl#kT4fi9T4 y of these processes, a stochastic cal#icfiT has been devel#fi ed in recent years for these processes in finite dimensional spaces (e.g., [1], [3], [4]). The stochasticcal#icfi# given here uses a di#erent approach than the one used in [1], [3] or [4]. Since afractional Brownian motion, for H #=1/2, not a semimartingal## it is necessary to define a stochasticcal#icfi#6 These processes have a sel#kfi9SkqTfil# y inprobabil#k yl aw and, for H (1/2, 1), al##6 range dependence property d...

Allocating resources to variable bitrate (VBR) teletraffic sources is not a trivial task because the impact of such sources on a buffered switch is difficult to predict. This problem has repercussions for call admission control (CAC) on asynchronous transfer mode (ATM) networks. In this thesis we report on investigations into the nature of several types of VBR teletraffic. The purpose of these investigations is to identify parameters of the traffic that may assist in the development of CAC algorithms. As such we concentrate on the correlation structure and marginal distribution; the two aspects of a teletraffic source that affect its behaviour through a buffered switch. The investigations into the correlation structure consider whether VBR video is selfsimilar or non-stationary. This question is significant as the exponent of self-similarity has been identified as being useful for characterising VBR teletraffic. Although results are inconclusive with regards to the original question, t...