Donald C. McNickle

Distributed stochastic discrete-event simulation in parallel time streams

Quantitative stochastic simulation suffers from the fact that sound simulation studies require very long runlength to obtain the results with sufficient accuracy. We look at traditional approaches to distributed quantitative stochastic simulation and propose a new scenario, Multiple Replications in Parallel Time Streams (MRIP), that solves the problem in an efficient way. An implementation of MRIP in a simulation package AKAROA is also described. AKAROA accepts ordinary (non-parallel), simulation models and creates automatically the environment required for running MRIP on workstations of a local area network. Presented results show that MRIP offers linear speedup of simulation. Limitations of this scenario for running distributed quantitative stochastic simulation are also discussed.

THE EFFECT OF CORRELATED ARRIVALS ON QUEUES

Using Markov renewal arrival processes, a study of the effect of serial correlations in the arrival process on the mean queueing performance has been done. We show that positive serial correlations may have major impact on the mean queue lengths (and consequently on other performance measures).

Coverage of confidence intervals in sequential steady-state simulation☆

Abstract Stochastic discrete-event simulation has become one of the most-used tools for performance evaluation in science and engineering. But no innovation can replace the responsibility of simulators for obtaining credible results from their simulation experiments. In this paper we address the problem of the statistical correctness of simulation output data analysis, in the context of sequential steady-state stochastic simulation, conducted for studying long run behavior of stable systems. Such simulations are stopped as soon as the relative precision of estimates, defined as the relative half-width of confidence intervals at a specified confidence level, reaches the required level. We formulate basic rules for the proper experimental analysis of the coverage of steady-state interval estimators. Our main argument is that such an analysis should be done sequentially. The numerical results of our coverage analysis of the method of non-overlapping batch means and spectral analysis are presented, and compared with those obtained by the traditional, non-sequential approach. Two scenarios for stochastic simulation are considered: traditional sequential simulation on a single processor, and fast concurrent simulation based on multiple replications in parallel (MRIP), with multiple processors cooperating in the production of output data.

Accuracy of the line intersect method of post-logging sampling under orientation bias

Abstract The Line Intersect Method of Post-Logging Residue Sampling is used extensively as a means of estimating waste volume on a clearfelled stand. Whilst the performance of the method under non-random spatial log arrangement conditions has been examined in the literature, similar examinations of method performance when the logs have a non-random orientation distribution have not been rigorously attempted. Thus, a corrected analytic approach to the calculation of expected sampling error under conditions of log orientation angle bias is presented, along with a correction to the Line Intersect Method literature. A simulation model is also used to calculate the standard deviation of the sampling error under orientation bias conditions. The two models are then used to examine the Line Intersect Method in the context of a typical New Zealand stand of Pinus radiata , comparing and evaluating the performance of the method under four patterns of line arrangements and varying line lengths. Our principal conclusion is that the fan and L arrangement provide considerable protection against the effects of orientation bias, although the presence of an orientation bias can considerably increase the size of the likely measurement error.

Comparison of various estimators in simulated FGN

Abstract The Hurst parameter is the simplest numerical characteristic of self-similar long-range dependent stochastic processes. Such processes have been identified in many natural and man-made systems. In particular, since they were discovered in the Internet and other multimedia telecommunication networks a decade ago, they have been the subject of numerous investigations. Typical quantitative assessment of self-similarity and long-range dependency, begins with the estimation of the Hurst parameter H. There have been a number of techniques proposed for this. This paper reports results of a comparative analysis of the six most frequently used estimators of H. To set up a credible framework for this, the minimal acceptable sample size is first determined. The Hurst parameter estimators are then compared for bias and variance. Our experimental results have confirmed that the Abry–Veitch Daubechies Wavelet-Based (DWB) and the Whittle ML (Maximum Likelihood) estimators of H are the least biased. However, the latter has significantly smaller variance and can be applied to shorter data samples than the Abry–Veitch DWB estimator. On the other hand, the Abry–Veitch DWB estimator is computationally simpler and faster than the Whittle ML estimator.

Experimental evaluation of confidence interval procedures in sequential steady-state simulation

Sequential analysis of simulation output is generally accepted as the most efficient way for securing representativeness of samples of collected observations. In this scenario a simulation experiment is stopped when the relative precision of estimates, defined as the relative width of confidence intervals at an assumed confidence level, reaches the required level. This paper deals with the statistical correctness of the methods proposed for estimating confidence intervals for mean values in sequential steady-state stochastic simulation. We formulate basic rules that should be followed in proper experimental analysis of coverage of different steady state interval estimators. Our main argument is that such analysis should be done sequentially. The numerical results of our preliminary coverage analysis of the method of Spectral Analysis (SA/HW) and Non overlapping Batch Means are presented, and compared with those obtained by traditional, non-sequential approaches.

The role of the Weibull distribution in Internet traffic modeling

This paper highlights the important role played by the two parameter Weibull distribution in Internet traffic modeling. Internet traffic structurally consists of sessions, flows and packets; and traverses through different tiers of service providers during its end-to-end journey. Observation of invariant heavy tails in access traffic patterns of individual users has motivated us to investigate traffic transformation/aggregation as it traverses from access to core network. We found that the flexible nature of the Weibull distribution can capture this transformation at inter-arrival level. We also present and justify our hypothesis that given a suitable scale parameter specific to a certain access media or tier, the Weibull shape parameter can be used to zoom in from session to flow and to the packet level inter-arrivals.

Distributed steady-state simulation of telecommunication networks with self-similar teletraffic

Abstract Recent measurement studies of teletraffic data in modern telecommunication networks have shown that self-similar processes may provide better models of teletraffic than Poisson processes. If this is not taken into account, it can lead to inaccurate conclusions about performance of telecommunication networks. We show how arrival processes with self-similar input influences the run-length of a distributed steady-state simulation of queueing systems in telecommunication networks. For this purpose, the simulation run-length of SSM/M/1/∞ queueing systems in the method based on the batch means, conducted for estimating steady-state mean waiting times is compared with the results obtained from simulations of M/M/1/∞ queueing systems when a single processor and multiple processors are used. We also investigate speedup conducted stochastic simulation of SSM/M/1/∞ queueing systems on multiple processors under a scenario of distributed stochastic simulation known as MRIP (Multiple Replications In Parallel) in a local area network (LAN) environment on Solaris operating system. We show that, assuming self-similar inter-event processes (i.e., SSM/M/1/∞ queueing systems), many more observations are required to obtain the final simulation results with a required precision, as the value of the Hurst parameter H increases, than when assuming Poisson models, exhibiting short-range dependence (i.e., M/M/1/∞ queueing systems) on a single processor and multiple processors. Our results show that the time for collecting many numbers of observations under the MRIP scenario is clearly reduced as traffic intensity and the value of the Hurst parameter increase, and as the engaged processor increases one to four. In particular, the value of H influences much more the speedup than traffic intensity and the engaged processor.

Self-Similar Properties of Spam

We often receive unwanted information from a variety of electronic systems mainly through emails, electronic boards and messengers, called spam. Spam is the use of electronic messaging systems to send unsolicited bulk messages indiscriminately. Widely varying estimates of the cost associated with spam are available in the literature. However, a stochastic and quantitative analysis of the determinant characteristics of spam traffic is still an open problem. This work fills this gap. A 4-year data sample of real-time inbound traffic between May 2005 and July 2009 was collected to investigate and analyze characteristics of spam traffic through JIRANSOFTs Spam Sniper on the network at Korean Bible University. Our major findings of a statistical analysis of spam traffic are that (i) real-time inbound spam traffic is statistically more correlated (self-similar) when compared to normal traffic, and (ii) the degree of self-similarity measured in terms of the Hurst parameter H and obtained from different estimation techniques is very high.

Generation of self-similar processes for simulation studies of telecommunication networks

It is generally accepted that self-similar processes may provide better models for teletraffic in modern telecommunication networks than Poisson processes. If stochastic self-similarity of teletraffic is not taken into account, it can lead to inaccurate conclusions about the performance of networks. Thus, an important requirement for conducting simulation studies of networks is the ability to generate long synthetic self-similar sequences of incremental processes, to transform them into interevent time intervals, and to do this accurately and quickly. A fast generator for count processes based on wavelets is described. Then a method for transformation of count processes into interevent processes proposed by Leroux and Hassan [1] and an alternative method, that is, inverting the empirical distribution directly, are studied. A case study is discussed to show how long sequences are needed in the steady-state simulation of queueing models with self-similar input processes. This is compared with simulation run lengths of the same queueing models fed by Poisson processes.