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Erlang Library for Excel Function Reference |
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Erlang Library for Excel Function Reference |
Returns the traffic load in erlangs that can be carried by a given number of servers, with a given average handle time, and with a given average wait time. Assumes the Erlang C queueing model.
ErlcTrafFromWait( nsrv, ahtSeconds, averageWaitSeconds)
nsrv number of servers, and can be any non-negative number
ahtSeconds is the average handle time (average duration of service), and can be any positive number.
averageWaitSeconds is the desired average wait time to be experience by calls.
| Formula | Description | Return Value |
|---|---|---|
| =ErlcTrafFromWait( 20, 300, 5) | Calculates the traffic load in erlangs that we can support if there are 20 servers, an average handle time of 300 seconds, and we want calls to experience an average wait time of 5 seconds. | 14.089485 |
| =ErlcTrafFromWait( 20, 300, 60) | Same as the preceding, except that we relax the average wait time to 60 seconds. | 17.600246 |
Public Function ErlcTrafFromWait(nsrv As Double, ahtSeconds
As Double, averageWaitSeconds As Double) As Double ErlcFractionDelayed ErlcWait ErlcNsrvFromFractionOk ErlcNSrv4 ErlcNsrvFromFractionOk ErlcNsrvFromFractionOk5
If this function is not available, and returns the #NAME? error, then you must install and load the Erlang Library for Excel from Abstract Micro Systems.
How?
Suppose that your call center uses average wait time as its measure of service quality. Then you might ask: given a certain number of agents, and given a certain type of traffic, how much of that traffic can the center handle without driving the average wait over 10 seconds? 30 seconds? 60 seconds? Etc.
Here is a concrete example. Suppose that for this call center we have:
| Maximum number of calls that can be waiting: | Very large |
| Period length: | 30 minutes |
| Number of agents: | 50 |
| Average Handle Time | 600 seconds |
Assume further that the calls arrive in a Poisson process, that the handle times are exponentially distributed, and that the queue of waiting calls is processed in a FIFO manner. Finally, assume that if a caller finds that all agents are busy, then the caller will wait until an agent picks up the call.
Question: How many erlangs x of traffic can this center handle with an average wait t = 10 seconds? t = 30 seconds? t = 60 seconds? t = 600 seconds?
As a first observation, we note that x will always be less than 50, because the traffic load that can be carried in any call center is always bounded above by the number of agents. Furthermore, as we increase the allowable average wait t, we expect that the carrying capacity x will approach 50 as a limit. Now let's compute the exact answers to our problem. We find:
| t | Formula for x | Value of x |
| 10 seconds | ErlcTrafFromWait( 50, 600, 10) | 41.51 |
| 30 seconds | ErlcTrafFromWait( 50, 600, 30) | 44.13 |
| 60 seconds | ErlcTrafFromWait( 50, 600, 60) | 45.71 |
| 600 seconds | ErlcTrafFromWait( 50, 600, 600) | 49.14 |
(Note that the period length, 30 minutes, is not used in the computation and does not affect the result.)