• Usually we don’t have enough trace data to collect meaningful system measurements (statistically significant ones). • Sometimes we might purposely want to generate a Poisson arrival process, so that we can study effects of other variables. • If you’ve used empirical data to create closed-form analytic curve-fit, that analytic distribution can be very accurate. For example: the SURGE Web workl...

We provide a new version of our ziggurat method for generating a random variable from a given decreasing density. It is faster and simpler than the original, and will produce, for example, normal or exponential variates at the rate of 15 million per second with a C version on a 400MHz PC. It uses two tables, integers ki and reals wi. Some 99% of the time, the required x is produced by: Generate...

Some History • Earliest methods were manual – throwing dice, dealing cards, drawing balls from an urn • Mechanized devices in early 1900’s • Later, methods based on electric circuits • Many other schemes based on phone books, π etc. • Advent of computing led to interest in numerical and arithmetic methods – such methods generate numbers sequentially and are easily programmed – the most commonly...

Impressive development of computer networks has been required precise evaluation of efficiency of these networks for users and especially internet service providers. Considering the extent of these networks, there has been numerous factors affecting their performance and thoroughly investigation of these networks needs evaluation of the effective parameters by using suitable tools. There are se...

There are several theorical results about order statistics and copulas in the literature that have  been mentioned also by Nelsen cite{p20}. The present study after reviewing some of these results, relies on  simulation technique to investigate the mentioned results about order statistics and copulas. The study concentrates on two well known Archimedean Gumbel and Frank families in the case tha...

Communicated by Jerzy Neyman, August 1, 1966 1. All random variables considered in this note are nonnegative and integervalued. Generically, the probability generating functions (P. G. F.) of such variables are denoted by G with subscripts identifying the random variables concerned. The argument, or arguments of the P. G. F., denoted by either u or v, will be assumed to have their moduli less t...

The probability generating function is a powerful technique for studying the law of finite sums of independent discrete random variables taking integer positive values. For real valued discrete random variables, the well known elementary theory of Dirichlet series and the symbolic computation packages available nowadays, such as Mathematica 5 TM, allows us to extend to general discrete random v...