PROBLEM 4 In a factory, there is a Social Security office where the workers can go during working hours. The Chief of Staff, who has observed the inflow of workers to the office, has asked to perform a study of this service. A specialist has been appointed to determine the average waiting time of the workers and the average duration of the conversation with QUEUEING THEORY November 2019 the office employee. This analyst reaches the conclusion that in the first and last half hours of the shift the inflow is very reduced and fluctuating, but during the remaining seven hours of the shift the phenomenon can be considered in steady state. From the analysis of 100 periods of 5 minutes, consecutive or not, but in the steady state phase, it can be deduced that the mean number of workers going to the office was 1.25 per period and the inter-arrival time followed an exponential distribution. A similar study about the duration of the conversations concluded that its distribution was exponential with a mean duration of 3.33 minutes. Determine: a) Average number of workers waiting b) Average waiting time c) Compare the time spent by the workers and the time spent by the office employee. Determine the cost for the company if an hour of the office employee is 250 and one hour of the worker 400 . Would it be profitable to open another office?

In a factory, there is a Social Security office where the workers can go during working hours. The Chief of Staff, who has observed the inflow of workers to the office, has asked to perform a study of this service. A specialist has been appointed to determine the average waiting time of the workers and the average duration of the conversation with QUEUEING THEORY November 2019 the office employee. This analyst reaches the conclusion that in the first and last half hours of the shift the inflow is very reduced and fluctuating, but during the remaining seven hours of the shift the phenomenon can be considered in steady state. From the analysis of 100 periods of 5 minutes, consecutive or not, but in the steady state phase, it can be deduced that the mean number of workers going to the office was 1.25 per period and the inter-arrival time followed an exponential distribution. A similar study about the duration of the conversations concluded that its distribution was exponential with a mean duration of 3.33 minutes. Determine: a) Average number of workers waiting b) Average waiting time c) Compare the time spent by the workers and the time spent by the office employee. Determine the cost for the company if an hour of the office employee is 250 and one hour of the worker 400. Would it be profitable to open another office