Queueing Function Arguments

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).

Common Arguments

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 for Service Rate. The Arrival Rate must 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 the Arrival Rate. The Service Rate must 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.)

Optional Arguments

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 Capacity is 4. It is assumed that customers that arrive when the queue is filled to capacity will balk. If the Queue Capacity argument 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

Representing infinite capacity: if the optional Queue Capacity and System Capacity arguments are omitted then they are assumed infinite.  If these arguments are provided, then an infinite value can be represented by the string "Infinity."

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".

Advanced Arguments

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, the Threshold Time is 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, the Service Level is 80% or 0.8.  The Service Level must 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.  The State must 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.

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