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Waiting Lines: A step-by-step solution

Waiting line theories are valuable tools in operations. One model is based on the Poisson arrival distribution, FIFO line discipline, and customers arrive at the rate of two per minute. This is a single phase operation and each server operates at the average rate of 160 customers served per hour. Management is concerned by the higher than desirable average time spent in the waiting line, Ws. Management needs to know what effect adding a second service line will have on the average time spent in the waiting line.

a) Identify the queuing models in each scenario
b) Calculate the average number of customers in line for both scenarios
c) Find the average wait time in each queue
d) What benefit is available by adding the second service line? What other factors should management consider?

Solution Preview

The computations showed the following results:

Statistics table with a Single Service Line

Equations Description Value
L Number of clients in the system 2.98 or 3
W Average minutes client spends in the ...

Solution Summary

The solution shows how to solve waiting line problems. Formula and step-by-step guide are shown in the attached five-page file.