The following lists and explains all the arguments used in the functions in the Queueing ToolPak. The arguments are classified as common (required by almost all functions), optional, and advanced (only required by some functions).

All functions require the **
Arrival Rate** and ** Service Rate** arguments and most require the ** Servers**
argument.

Arrival Rate:Average rate at which customers arrive to the system. Has units of "customers / time unit". The time unit used must be the same as forService Rate. TheArrival Ratemust be greater than or equal to zero.

Service Rate:The average rate at which an individual server can serve customers. Has units of "customers / time unit" and is the reciprocal of the average time it takes to serve one customer. The time unit used must be the same as for theArrival Rate. TheService Ratemust be greater than zero.

Servers:The number of servers available to serve customers entering a queueing system. The number of servers must be a whole number that is greater than or equal to one.

**Important: **The first three arguments must satisfy:

Arrival Rate/ (Service Rate*Servers) < 100%

This is required for the queueing system to be *stable*, that is, to prevent the queue from growing indefinitely.

(If the optional Queue Capacity argument is set to a finite value, then the condition above is not necessary -- the system will be stable regardless.)

Queue Capacity:The maximum number of customers that can wait in a queue. Must be a whole number that is greater than or equal to zero.Example: If a call center has 20 lines and 16 agents on duty, then 4 callers can be kept on hold and the

Queue Capacityis 4. It is assumed that customers that arrive when the queue is filled to capacity will balk. If theQueue Capacityargument is "infinity", then it is assumed that there is no limit on the capacity of the queue.

System Capacity:The total number of customers that can be in the system, either waiting or being served. Must be a whole number that is greater than or equal to one.

Note that **System Capacity**
= ** Queue Capacity** + ** Servers**

If the value of the argument
is typed inside the function, such as QTPMMS_L(10,12,1,"Infinity"), then the quotation marks around
"Infinity" are needed. If "Infinity" is typed in a cell and a reference to that cell is
used as an argument to a QTP function, such as QTPMMS_L(10,12,1,A1), then
the quotation marks are * not* needed.

Instead of "Infinity" one can use any string that begins with "inf", "Inf" or "INF".

Threshold Time:A threshold time is used to specify a level of service of the form "80% of customers should wait 20 seconds or less before being served." In this example, theThreshold Timeis 20 seconds.

The **Threshold Time** must be expressed in the same
time units as used for the **Arrival Rate** and **Service Rate**.
If that time unit is an hour, then a 20-second **Threshold Time** can be
expressed as 20 / (60 * 60)

Service Level:A probability used to specify a level of service in the form "80% of customers should wait 20 seconds or less before being served". In this example, theService Levelis 80% or 0.8. TheService Levelmust be greater than or equal to zero and less than one.

State:The number of customers in a system, including both customers being served and customers waiting. TheStatemust be a whole number that is greater than or equal to zero.

The next two arguments are required by the QTPGGS functions.

StDevArrivals:The standard deviation of the distribution of interarrival times.

StDevService:The standard deviation of the distribution of service times.

The following argument is only needed for the QTP_NORMSDIST function.

z: z-score for which the cumulative distribution function for a standard normal random variable is required.