R/bmfree2.R

In cartools: Tools for Understanding Highway Performance

#' The \code{bmfree2} function returns a \code{tux} matrix of time \code{t}, speed \code{u} (fps)
#'  and location \code{x} (feet).
#'
#' @param umn mean speed (mph), a number
#' @param usd standard deviation of \code{usd} (mph), a number
#' @param tstart simulation start time, a number
#' @param tend simulation end time, a number
#' @param xstart location (feet), a number
#' @param type logical for plotting where TRUE creates a plot
#' @param step time-step size, a number
#' @usage bmfree2(umn, usd, tstart, tend, xstart, step, type)
# #' @examples
# #' bmfree2(41, 11, 16.5, 30, 10, 0.25, TRUE)
bmfree2  <- function(umn, usd, tstart, tend, xstart, step, type) {
  t     <- seq(tstart, tend, step)
  N     <- length(t)
  W     <- numeric(N)
  usd   <- 5280/3600*usd
  for(i in 2:(N)) W[i] <- W[i-1] + usd * sqrt(step) * rnorm(1)
  x     <- 5280/3600*umn
  y     <- 5280/3600*umn
  u     <- x + (W - (t - tstart)/(tend - tstart) * (W[N] - y + x))
  for(i in 1:N) if(u[i] <= 0) u[i] = 0
  if(type == TRUE) {
    plot(t, u, typ = "l")
    abline(h = x, col = gray(0.8))
  }
  x     <- rep(0, length(t))
  x[1]  <- xstart
  for(i in 2:N) x[i] <- x[i-1] + step * u[i-1]
  tux   <- as.matrix(data.frame(t, u, x))
  return(tux)
}