public ActionResult ComputeErlangC(long numberOfCalls, long ahtInSeconds, decimal requiredServiceLevel,
long targetAnswerTimeInSeconds, decimal shrinkage)
{
string msg = string.Empty;
ErlangCViewModel erlangModel = new ErlangCViewModel();
try
{
erlangModel = _erlangService.Calculate(numberOfCalls, ahtInSeconds, requiredServiceLevel, targetAnswerTimeInSeconds, shrinkage);
}
catch (Exception ex)
{
msg = ex.Message;
}
ErlangCCalculatorResult model = new ErlangCCalculatorResult()
{
ErlangCViewModel = erlangModel,
Message = msg
};
return(Json(model, JsonRequestBehavior.AllowGet));
}
public ErlangCViewModel Calculate(long numberOfCalls, long ahtInSeconds, decimal requiredServiceLevel,
long targetAnswerTimeInSeconds, decimal shrinkage, long?newN = null)
{
ErlangCViewModel model = new ErlangCViewModel();
#region Declare Variable(s)
long a = 0;
long n = 0;
long numberOfCallsPerHour = 0;
decimal x = 0;
decimal y = 0;
decimal pw = 0;
decimal pwPerc = 0;
decimal sl = 0;
decimal slPerc = 0;
decimal asa = 0;
decimal immediateAnswerPerc = 0;
decimal occupancyPerc = 0;
long numberOfAgentsRequired = 0;
#endregion Declare Variable(s)
#region 2. Work Out the Number of Calls Per Hour
numberOfCallsPerHour = numberOfCalls;
#endregion 2. Work Out the Number of Calls Per Hour
#region 3. Work Out the Traffic Intensity (A)
long ahtInMinutes = ahtInSeconds / 60;
a = (numberOfCalls * ahtInMinutes) / 60;
#endregion 3. Work Out the Traffic Intensity (A)
#region 4. Estimate the Raw Number of Agents Required (N)
//Initial value is A+1
if (newN == null)
{
n = (a + 1);
}
else
{
n = (long)newN;
}
//n = newN ?? (a+1);
#endregion 4. Estimate the Raw Number of Agents Required (N)
// --5.Calculate the Erlang Formula for Probability a Call Waits(SKIP)
// --6.Work Out N!(N Factorial) (SKIP)
// --7.Be Careful With Large Factorials (SKIP)
//-- n
//--8.Work Out the Powers – A(SKIP)
//--9.Let’s Simplify the Erlang C Formula
//-- X / (Y + X)
#region 10. Let’s Work Out the Top Row of the Erlang Formula (X)
// --NUMERATOR FIRST(X)
//-- n
//-- A* N
// --___ ___
// -- N!N-A
decimal numeratorA, numeratorB;
numeratorA = (decimal)Math.Pow(a, n) / this.Factorial(n);
numeratorB = (decimal)n / ((decimal)n - (decimal)a);
x = numeratorA * numeratorB;
#endregion 10. Let’s Work Out the Top Row of the Erlang Formula (X)
#region 11. Work Out the Sum of a Series (Y) or ΣApowerofI/i!
//loop n
decimal i = 0;
decimal eaPowOfiDivIFact = 0;
List <TableY> tblY = new List <TableY>();
while (i <= (n - 1))
{
decimal iFact, aPowI, aPowOfiDivIFact;
iFact = i == 0 ? 1 : this.Factorial(i);
aPowI = (decimal)Math.Pow(a, (double)i);
aPowOfiDivIFact = aPowI / iFact;
eaPowOfiDivIFact = eaPowOfiDivIFact + aPowOfiDivIFact;
tblY.Add(new TableY()
{
i = i,
iFactorial = iFact,
aPowerOfi = aPowI,
aPowerOfiDivideIFactorial = aPowOfiDivIFact,
SumOfAPowerofIDivideIFactorial = eaPowOfiDivIFact
});
i++;
}
y = tblY.OrderByDescending(s => s.SumOfAPowerofIDivideIFactorial).FirstOrDefault().SumOfAPowerofIDivideIFactorial;
#endregion 11. Work Out the Sum of a Series (Y) or ΣApowerofI/i!
#region 12. Put X and Y into the Erlang C Formula (The probability a call has to wait)
pw = x / (x + y);
pwPerc = pw * 100;
#endregion 12. Put X and Y into the Erlang C Formula (The probability a call has to wait)
#region 13. Calculate the Service Level
#region 13.1 Let’s work out -(N – A) * (TargetTime / AHT)
double exponent = 0;
exponent = -((n - a) * ((double)targetAnswerTimeInSeconds / (double)ahtInSeconds));
#endregion 13.1 Let’s work out -(N – A) * (TargetTime / AHT)
sl = 1 - (pw * (decimal)Math.Exp(exponent));
slPerc = sl * 100;
if (slPerc < requiredServiceLevel)
{
long nIncrement = n + 1;
model = this.Calculate(numberOfCalls, ahtInSeconds, requiredServiceLevel, targetAnswerTimeInSeconds, shrinkage, nIncrement);
}
else
{
#region 15. Average Speed of Answer (ASA)
//ASA = Pw(AHT)/(No.of Agents-Traffic Intesity)
asa = (pw * ahtInSeconds) / (n - a);
#endregion 15. Average Speed of Answer (ASA)
#region 16. Percentage of Calls Answered Immediately
//Immediate Answer = (1-Pw)x100
immediateAnswerPerc = (1 - pw) * 100;
#endregion 16. Percentage of Calls Answered Immediately
#region 17. Check Maximum Occupancy
//Occupancy = (([TrafficIntensity or A])/[RawAgents or N] )* 100
occupancyPerc = ((decimal)a / (decimal)n) * 100;
if (occupancyPerc > 85)
{
occupancyPerc = (decimal)a / (occupancyPerc / 100);
}
#endregion 17. Check Maximum Occupancy
#region 18. Factor In Shrinkage
//DECLARE @ShrinkagePerc NUMERIC(18,3) = 30 --The industry average is around 30–35%, in this case we used 30%. Note that we can change it
//NumberOfAgentsRequired = [Raw Agents or N]/(1-(Shrinkage/100))
numberOfAgentsRequired = (long)Math.Ceiling((decimal)n / (1 - (shrinkage / 100)));
#endregion 18. Factor In Shrinkage
model.NumberOfAgentsRequired = numberOfAgentsRequired;
model.ServiceLevel = sl;
model.ServiceLevelPerc = Math.Round(slPerc, 2);
model.PwErlang = pw;
model.PwErlangPerc = Math.Round(pwPerc, 2);
model.ASA = Math.Round(asa, 2);
model.ImmediateAnswerPerc = Math.Round(immediateAnswerPerc, 2);
model.TargetAnswerTimeInSecond = targetAnswerTimeInSeconds;
model.AHTSec = ahtInSeconds;
model.RequiredServiceLevelPerc = Math.Round(requiredServiceLevel, 2);
model.N = n;
model.X = x;
model.Y = y;
model.A = a;
model.OccupancyPerc = Math.Round(occupancyPerc, 2);
}
#endregion 13. Calculate the Service Level
return(model);
}
