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Erlang Library for Excel Function Reference |
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Erlang Library for Excel Function Reference |
Returns the average number of waiting customers (also called the average queue length) in the Erlang C queueing model, for a given number of servers and given traffic load.
ErlcNwaiting( nsrv, trafficInErlangs)
nsrv is the number of servers (a non-negative number).
trafficInErlangs is the offered traffic, measured in erlangs (a non-negative number).
| Formula | Description | Return Value |
|---|---|---|
| =ErlcNwaiting(10, 8) | Returns the average number waiting for 10 servers and an offered load of 8 erlangs | 1.63672 |
| =ErlcNwaiting(10, 9) | Same as above, except offered load increases to 9 erlangs | 6.01858 |
| =ErlcNwaiting(10,10) | Same as above, except offered load increases to 10 erlangs. In this case, the function returns a very large number. (See remarks) | 1 E+50 |
Public Function ErlcNwaiting(nsrv As Double, trafficInErlangs
As Double) As Double Please supply a value for nsrv that is greater than trafficInErlangs. In the Erlang C queueing model, the number of servers must always be greater than the offered traffic. If trafficInErlangs is greater than or equal to nsrv, then the ErlcNwaiting returns 1E+50, that is, 1050.
In call center applications, the closely-related function erlcNwaiting4 is often more convenient to use than erlcNwaiting.
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?
You may use ErlcNwaiting to estimate the average queue lenth for incoming calls in a call center. Suppose that we have a call center with these parameters during a certain period of time:
| Maximum number of calls that can be waiting: | Very large |
| Period length: | 30 minutes |
| Number of agents: | 140 |
| Incoming calls offered during the period: | 1000 |
| Average handle time: | 240 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.
We are interested in estimating the number NW, defined as the average number of waiting callers. We first compute the offered traffic, x, as follows:
x = 1000 * 240 / 1800 = 133.3333 erlangs
Then we use ErlcNwaiting as follows.
NW = ErlcNwaiting( 140, 133.3333) = 9.187
Thus, we estimate the average queue length to be a little over 9 customers. In other words, the average number of waiting customers will be a little more than 9.
Note that this computation would be a little easier if we use ErlcNwaiting4 instead of ErlcNwaiting. This is because we avoid the intermediate step of computing the offered traffic x.