Robert McGorman

Approximating Lognormal Sum Distributions With Power Lognormal Distributions

In wireless communications, cochannel interference is usually characterized by a sum of lognormal random variables. Since the characteristic function of a lognormal distribution lacks explicit expression, and numerical calculation of a lognormal sum distribution is very challenging, lognormal distributions are often used to approximate lognormal sum distributions. However, it has been shown that a lognormal distribution can only capture a certain part of the body of a lognormal sum distribution. To improve the accuracy of approximation of lognormal sum distributions, one must resort to non-lognormal approximations. In this paper, we propose the use of power lognormal distributions to approximate lognormal sum distributions. To illustrate the superiority of the proposed model, some numerical experimental results are provided.

Online EM algorithm for mixture with application to internet traffic modeling

Since histograms of many real network traces show strong evidence of mixture, this paper uses mixture distributions to model Internet traffic and applies the EM algorithm to fit the models. Making use of the fact that at each iteration of the EM algorithm the parameter increment has a positive projection on the gradient of the likelihood function, this paper proposes an online EM algorithm to fit the models and the Bayesian Information Criterion is applied to select the best model. Experimental results on real traces are provided to illustrate the efficiency of the proposed algorithm.

Mixture Lognormal Approximations to Lognormal Sum Distributions

In wireless communication, co-channel interference is usually characterized by a sum of lognormal random variables. Since calculating the exact distribution of a lognormal sum has a lot of challenges, lognormal distributions are often used to approximate lognormal sum distributions. However, it has been shown that lognormal approximations can only capture a certain part of the body of a lognormal sum distribution, which implies that to accurately approximate a lognormal sum distribution, one has to resort to non-lognormal approximations. In this paper we propose to use a two-component mixture lognormal model to approximate lognormal sum distributions. Numerical examples are provided to compare the proposed mixture lognormal approximation with the existing ones.

Traffic Estimation and Power Saving Mechanism Optimization of IEEE 802.16e Networks

In order to save power to prolong battery life of subscriber stations (SSs) in IEEE 802.16e networks, the standard defines a sleep mode for SS. When there is no traffic for an SS to transmit or to receive, the SS switches to sleep mode periodically. The sleep interval is doubled each time until a maximum sleep interval threshold Tmax is reached. Obviously, the performance of this power saving mechanism depends on the idle period distribution, which is user-specific. In network traffic modeling, it is commonly accepted that frame interarrival times have heavy-tailed distributions. Since heavy-tailed distributions make analysis and design challenging, in this paper we propose to use mixtures of exponentials to approximate heavy-tailed idle times. With a mixture of exponentials approximating the idle times, performance can be explicitly derived and optimized. An online EM algorithm is proposed to fit the mixture of exponential distributions to the idle times. Numerical examples show the effectiveness of the proposed procedures.

A long-range dependent model for Internet traffic with power transformation

Internet traffic has been shown to have long-range dependence, and is often modeled by using the fractional Gaussian noise model. The fractional Gaussian noise model can capture the autocorrelation of a real trace, but cannot fit the marginal distribution when the trace has a non-Gaussian marginal distribution. In this letter, we use the inverted Box-Cox transformation to establish a long-range dependent Internet traffic model that can simultaneously capture both the long-range dependence parameter and the marginal distribution of a real trace

A Traffic Modeling Based Power Saving Mechanism for Mobile Devices in Wireless Systems

In wireless communication networks, power saving is a critical issue. Sleep mode is usually applied to save power in mobile devices; when there is no data to transmit or receive, a mobile device can switch to sleep mode periodically. Evidently, there is a trade-off between power saving and response delay, and the performance of a power saving mechanism depends on user traffic characteristics and how well the power saving mechanism can predict the termination time of an idle period. In the literature, it is commonly accepted that traffic on a highspeed network is self-similar, resulting from heavy-tailed on-off periods. In this paper, we model the on-off durations by generalized Pareto distributions and apply the Xp inspection policy of operational research to power saving mechanism design for wireless communication devices. Numerical examples are provided to show the usefulness of the proposed scheme.

Recursive EM algorithm for finite mixture models with application to Internet traffic modeling

In the past decade, many quantities characterizing high-speed telecommunication network performance have been reported to have heavy-tailed distributions, namely, with tails decreasing hyperbolically rather than exponentially. Since mixture distributions can approximate many heavy-tailed distributions with high precision, the paper uses mixture distributions to model Internet traffic and applies the EM algorithm to fit the models. Making use of the fact that, at each iteration of the EM algorithm, the parameter increment has a positive projection on the gradient of the likelihood function, the paper proposes a recursive EM algorithm to fit the models, and the Bayesian information criterion is applied to select the best model. To illustrate the efficiency of the proposed algorithm, numerical results and experimental results on real traffic are provided.

Traffic modeling with gamma mixtures and dynamical bandwidth provisioning

Dynamic bandwidth provisioning for data service is an efficient way to optimize network resource utilization. For the purpose of dynamical bandwidth provisioning, we need a model that can capture online the traffic characteristics and facilitate mathematical analysis. A mixture of gamma distributions can approximate any distribution with nonnegative support as closely as desired. It can not only characterize field data well, but also facilitate analytically tractable results far performance evaluation. This paper uses a Gamma mixture to model Internet traffic and proposes an online algorithm to fit the model to actual Internet traffic. The fitted model is applied to provision bandwidth dynamically, and many simulation and experimental results are also provided

Empirical bandwidth provisioning models for high speed Internet traffic

This paper develops formulas to provision bandwidth for any number of high speed internet subscribers at a given probability that load exceeds available capacity. Formulas are based on Gamma models fitted to traffic loads generated over 1-sec intervals by various subscriber aggregations. We assume loads are i.i.d. and use characteristic function properties to extrapolate load distributions for any aggregation size. The provisioning formulas show that economies of scale exist. Results apply to initial system provisioning and to growth planning in existing networks. Sensitivity analysis is performed. Findings may interest telephone and cable companies

Similarities between voice and high speed Internet traffic provisioning

The paper finds similarities between voice traffic and high speed Internet data traffic characteristics from a facility provisioning perspective. Telephone switch traffic measurements are used to show that self-similarity is present in a voice traffic time series, to identify the factor associated with self-similarity, and then to demonstrate that traditional voice traffic provisioning methods remove self-similarity. Voice traffic methods and models are then applied with some modifications to a high speed Internet traffic series for various subscriber aggregations and time scale resolutions. Voice traffic models are found to be applicable to data traffic when it is processed in a similar way to that for voice traffic. The conclusions are based on model fitting results and goodness-of-fit tests for weekday busy hour Internet data traffic loads. The similarities appear to be strong enough that telephone company operations support systems and provisioning methods may require only relatively small modifications and extensions to support both voice and high speed Internet services. The findings can also benefit cable companies offering voice and data services.