The gravity model relies on a function called alternately the "impedance", "friction factor", "utility function", "propensity function".

Wikipedia: http://en.wikipedia.org/wiki/Trip_distribution
Gravity function here: http://www.metropolisplan.org/SectionII_Modeling.pdf
  Points out a fairly general function they call "Log Linear + Log" which I cannot for the life of me find any details on
Also here: http://dspace.mit.edu/handle/1721.1/32414
  Here poses a function "1.08438 / [1+0.08438*exp(0.076223*t)]" which applies to transit trips - not exactly what I'm looking for
MIT paper here: http://www.google.com/url?sa=t&source=web&ct=res&cd=3&ved=0CA0QFjAC&url=http%3A%2F%2Fdspace.mit.edu%2Fbitstream%2Fhandle%2F1721.1%2F33691%2F64636849.pdf%3Fsequence%3D1&ei=M6b4SunLHYuGtgO71uimBQ&usg=AFQjCNE0X4G5HbGrf3c820IBFS-K8whyFA&sig2=CsLYWBQDFjwzoLMmKb9YMA
  Impedance function for automobile travel time: exp(-5.556 - 0.421*t^0.5), and for transit travel time: exp(-3.281 - 0.859*t^0.5)
  Assuming that travel impedance is the same _per unit time_ in automobiles and walking, a walking rate of 20 minutes per mile, normalizing such that f(0)=1, the impedance function per mile is exp(-5.556 - 0.421*(d*20)^0.5)/0.0038642

Recent paper here: http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6VG8-4W207DG-4&_user=10&_rdoc=1&_fmt=&_orig=search&_sort=d&_docanchor=&view=c&_rerunOrigin=scholar.google&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=c6428a46c837b078f3110af9fbb13e89
  Gives actual pedestrian impedance at about 0.486*exp(-1.683x) where x is distance in kilometers. Normalize f(0)=1 and using miles, exp(-1.5*(d*1.609344)) works