How to Compute the Finite Calling Population

Queuing models simulate lines and line-like situations such as waiting for a customer service representative to help you onthe phone. In many situations, researchers mightwish to know the size of the population that the model is built to serve. In real-world situations, this population is finite, hence the name: finite calling population. Calculating the finite calling population is done through a few mathematical techniques based on specific knowledge of the model of interest.

Instructions

    • 1

      Add the model's arrival rate to its service rate. The arrival rate is the rate at which new calls or customers enter the system. The service rate is the rate at which calls or customers are served or handled successfully. Add these two values. Call the result "a."

    • 2

      Divide "a" by the arrival rate. You will yield a number greater than 1. Call this number "b."

    • 3

      Subtract the probability that no customers or calls are in the system from 1. If the model does not clearly display this probability, it will display it as the "average time in which there are no customers." Subtract this probability (a number between 0 and 1) from 1, yielding again a number between zero and 1. Call this value "c."

    • 4

      Multiply "b" by "c." Call the result "d."

    • 5

      Subtract "d" from the average number of customers in the queue or calls in the system. The resulting value should be a number that is usually much larger than 1. Call this value "n."

    • 6

      Round "n" to the nearest integer (whole number). This resulting number is the finite calling population.

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