# simEd (Simulation Education)

This package contains various functions to be used for simulation education, including: simple Monte Carlo simulation functions; queueing simulation functions with optional animation; variate generation functions capable of producing independent streams and antithetic variates; separate functions for visualizing/animating (a) event-driven simulation details of a single-server queue model, (b) a Lehmer random-number generator, (c) random variate generation via acceptance-rejection, (d) generation of a non-homogeneous Poisson process via thinning, and (e) random variate generation for various discrete and continuous distributions; and functions to compute time-persistent statistics. The package also contains two queueing data sets (one fabricated, one real-world) to facilitate input modeling.

Request From Authors: If you adopt and use this package for your simulation course, we would greatly appreciate were you to email us (`blawson<at>richmond<dot>edu` or `leemis<at>math<dot>wm<dot>edu`) to let us know, as we would like to maintain a list of adopters. Please include your name, university/affiliation, and course name/number. Thanks!

## Example

This is an example showing use of the `ssq` function in our package to simulate a simple M/M/1 queue, passing in a custom exponential interarrival function defined using our `vexp` variate generator, and then plotting the number in the system across time, with superimposed time-averaged statistics computed using `meanTPS` and `sdTPS`:

``````## ssq example code
library(simEd)
myArrFcn <- function() { vexp(1, rate = 1 / 0.95, stream = 1) }
output <- ssq(maxArrivals = 100, seed = 8675309, interarrivalFcn = myArrFcn,
saveNumInSystem = TRUE, showOutput = FALSE)
avg <- meanTPS(output\$numInSystemT, output\$numInSystemN)
sd <- sdTPS(output\$numInSystemT, output\$numInSystemN)
plot(output\$numInSystemT, output\$numInSystemN, type = "s", main = "M/M/1 Queue",
bty = "l", las = 1, xlab = "time", ylab = "number in system")
abline(h = avg, lwd = 2, col = "red")
abline(h = c(avg - sd, avg + sd), lwd = 2, lty = "dotted", col = "red")``````

## Installing

Install the current version of `simEd` from CRAN using `install.packages("simEd")`.

Note that the `simEd` package depends on Josef Leydold’s `rstream` package, a wrapper of Pierre L’Ecuyer’s “mrg32k3a” random number generator, to provide independent streams of uniform(0,1) random numbers. The `simEd` package also depends on the `shape` package, used in producing animations. If either of the `rstream` or `shape` package is not already installed, the previous step will install them automatically.

## Details

The goal of this package is to facilitate use of R for an introductory course in discrete-event simulation.

This package contains animation functions for visualizing:

• event-driven details of a single-server queue model: `ssqvis`;
• a Lehmer random number generator: `lehmer`;
• variate generation via acceptance-rejection: `accrej`;
• generation of a non-homogeneous Poisson process via thinning: `thinning`.

This package contains variate generators capable of independent streams (based on Josef Leydold’s `rstream` package) and antithetic variates for four discrete and eleven continuous distributions:

• discrete: `vbinom`, `vgeom`, `vnbinom`, `vpois`,
• continuous: `vbeta`, `vcauchy`, `vchisq`, `vexp`, `vgamma`, `vlnorm`, `vlogis`, `vnorm`, `vt`, `vunif`, `vweibull`

All of the variate generators use inversion, and are therefore monotone and synchronized.

The package contains functions to visualize variate generation for the same four discrete and eleven continuous distributions:

• discrete: `ibinom`, `igeom`, `inbinom`, `ipois`,
• continuous: `ibeta`, `icauchy`, `ichisq`, `iexp`, `igamma`, `ilnorm`, `ilogis`, `inorm`, `it`, `iunif`, `iweibull`

The package contains functions that implement Monte Carlo simulation approaches for estimating probabilities in two different dice games:

• Galileo’s dice problem: `galileo`
• craps: `craps`

The package also contains functions that are event-driven simulation implementations of a single-server single-queue system and of a multiple-server single-queue system:

• single-server: `ssq`
• multiple-server: `msq`

Both queueing functions are extensible in allowing the user to provide custom arrival and service process functions. Both functions provide animation.

The package contains four functions primarily for visualizing simulation concepts:

• event-driven details of a single-server queuing system: `ssqvis`
• Lehmer random number generator: `lehmer`
• variate generation via acceptance-rejection: `accrej`
• generating a non-homogeneous Poisson process via thinning: `thinning`

The package contains three functions for computing time-persistent statistics:

• time-average mean: `meanTPS`
• time-average standard deviation: `sdTPS`
• time-average quantiles: `quantileTPS`

The package also masks two functions from the `stats` package:

• `set.seed`, which explicitly calls the `stats` version in addition to setting up seeds for the independent streams in the package;
• `sample`, which provides capability to use independent streams and antithetic variates.

Finally, the package provides two queueing data sets to facilitate input modeling:

• `queueTrace`, which contains 1000 arrival times and 1000 service times (all fabricated) for a single-server queueing system;
• `tylersGrill`, which contains 1434 arrival times and 110 (sampled) service times corresponding to actual data collected during one business day at Tyler’s Grill at the University of Richmond.