erlang.js

var MAX_AGENTS_TO_TEST = 200;

function determineAgents(callDuration, calls, periodLength, answerTarget, serviceLevelTarget) {
  if(calls === 0) return(0);
  for (var agents = 1; agents <= MAX_AGENTS_TO_TEST; agents++) {
    if(serviceLevel(callDuration, calls, periodLength, agents, answerTarget) >= serviceLevelTarget) break;
  }
  return(agents);
}  


function agentOccupancy(callDuration, calls, periodLength, agents) {
  return(callDuration * calls / (periodLength * agents))
}

function averageSpeedOfAnswer(callDuration, calls, periodLength, agents) {
  var U = callDuration * calls / periodLength;
  var o = U / agents;
  var ec = PoissonTerm(U, agents)/(PoissonTerm(U, agents) + (1-o)*PoissonP(U,agents-1));
  return(ec * callDuration /(agents * (1 - o)));
}

function serviceLevel(callDuration, calls, periodLength, agents, answerTarget) {
  var U = callDuration * calls / periodLength;
  var o = U / agents;
  var ec = PoissonTerm(U, agents)/(PoissonTerm(U, agents) + (1-o)*PoissonP(U,agents-1));
  return(1 - ec * Math.exp(-(agents-U)*answerTarget/callDuration));
}

// Helper functions

function g( x ) {
   // Peizer & Pratt 1968, JASA 63: 1416-1456
   var  switchlev = 0.1, z;

   if (x == 0)  z = 1;
   else
      if (x == 1)  z = 0;
      else {

         var d = 1 - x;

         if (Math.abs(d) > switchlev)
            z = (1 - (x * x) + (2 * x * Math.log(x))) / (d * d);
         else {

            z = d / 3;  // first term
            var di = d;  // d**1

            for (var i = 2; i <= 7; i++) {
               di *= d;  // d**i
               z += (2 * di) / ((i+1) * (i+2));
               }
            }
         }
   return z;
}

function NormalP( x ) {
   // Abramowitz & Stegun 26.2.19
   var
      d1 = 0.0498673470,
      d2 = 0.0211410061,
      d3 = 0.0032776263,
      d4 = 0.0000380036,
      d5 = 0.0000488906,
      d6 = 0.0000053830,
      a = Math.abs(x),
      t;

   t = 1.0 + a*(d1+a*(d2+a*(d3+a*(d4+a*(d5+a*d6)))));

   // to 16th power
   t *= t;  t *= t;  t *= t;  t *= t;
   t = 1.0 / (t+t);  // the MINUS 16th

   if (x >= 0)  t = 1-t;
   return t;
}


function LnFact( x ) {
   // ln(x!) by Stirling's formula
   //   see Knuth I: 111
   if (x <= 1)  x = 1;

   if (x < 12)
      return Math.log( Fact(Math.round(x)) );
   else {
      var invx = 1 / x;
      var invx2 = invx * invx;
      var invx3 = invx2 * invx;
      var invx5 = invx3 * invx2;
      var invx7 = invx5 * invx2;

      var sum = ((x + 0.5) * Math.log(x)) - x;
      sum += Math.log(2*Math.PI) / 2;
      sum += (invx / 12) - (invx3 / 360);
      sum += (invx5 / 1260) - (invx7 / 1680);

      return sum;
      }
}

function Fact( x ) {
   // x factorial
   var  t=1;
   while (x > 1)
      t *= x--;
   return t;
}


function PoissonPD( u, k ) {
   // Peizer & Pratt 1968, JASA 63: 1416-1456

   var s = k + (1/2);

   var d1 = k + (2/3) - u;
   var d2 = d1 + 0.02/(k+1);

   var z = (1 + g(s/u)) / u;
   z = d2 * Math.sqrt(z);
   z = NormalP( z );

   return z;
}

function PoissonTerm( u, k ) {
   // by logs
   return  Math.exp( (k * Math.log(u)) - u - LnFact(k) );
}

function PoissonP( u, k ) {
   // term-by-term summation
   if (k >= 20) return  PoissonPD( u, k );
   else {
      var  sum = 0.0, j = 0;
      while (j <= k)
         sum += PoissonTerm( u, j++ );
      if (sum > 1)  sum = 1;
      return  sum;
      }
}