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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.
ErlcNwaiting4( nsrv, secondsPerPeriod, callsPerPeriod, ahtSeconds)
nsrv is the number of servers (a non-negative number).
secondsPerPeriod is the length in seconds of the reporting period.
callsPerPeriod is the number of incoming calls during the reporting period.
ahtSeconds is the average handle time (average duration of service) measured in seconds.
| Formula | Description | Return Value |
|---|---|---|
| =ErlcNwaiting4(20, 1800, 60, 540) | Returns the average number of waiting callers for 20 servers, period length = 1800 seconds, 60 calls per period, average handle time = 540 seconds | 4.95692 |
| =ErlcNwaiting4(20, 1800, 60, 580) | Same as above, except average handle time is increased to 580 seconds. | 24.14167 |
| =ErlcNwaiting4(20, 1800, 60, 700) | Same as above, except average handle time is increased to 700 seconds. See "Caution" under Remarks below. | 1 E+50 (a very large number) |
Public Function ErlcNwaiting4(nsrv As Double, secondsPerPeriod
As Double, callsPerPeriod As Double, ahtSeconds As Double) As Double
This function is similar to ErlcNwaiting, but is often more convenient to use in call center applications.
Caution: it is easy to supply arguments to
ErlcNwaiting4 that result in an offered traffic load that is greater than or
equal to the number of servers. This happens when
(callsPerPeriod * ahtSeconds)/secondsPerPeriod is greater than
or equal to nsrv. In this case, it is physically impossible
for the specified number of servers to carry the traffic, and the Erlang Queueing
model does not apply. The function ErlcNwaiting returns
a very large number in this case, namely, 1E+50, that is., 10+50.
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 ErlcNwaiting4 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 use ErlcNwaiting4 as follows.
NW = ErlcNwaiting4( 140, 1800, 1000, 240) = 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.