ServiceOntario is investigating their quality of service and customer satisfacti

Question

ServiceOntario is investigating their quality of service and customer satisfaction. Employees of ServiceOntario are thus required to record the metrics of providing services. Donald Wardell works at the counter for driver licensing. According to his report, Mr. Wardell could process 60 visitors per hour and visitors are coming every 1.5 minutes. The arrival rate of visitors follows a Poisson distribution, and the processing time by Donald is exponentially distributed. Given the information above, can you help the investigators calibrate Mr. Wardell's performance by answering the questions as follows?

b) What fraction of time will Mr. Wardell spend interacting with visitor coming for services?

c) How many visitors will be expected to line up at the counter?

d) How long will an average visitor spend waiting in line?

Explanation / Answer

This is a M/M/1 queue model with following parameters

Arrival rate, = 60/1.5 = 40 per hour

Service rate, = 60 per hour

b) Fraction of time that Mr Wardell spend interacting with visitor coming for services = = / = 40/60 = 66.7 %

c) Number of visitors expected to line up at the counter, (length of waiting line) Lq = = 2/(*(-)) = 402/(60*(60-40)) = 1.33

d) Average time visitor spend waiting in line, Wq = Lq/ = 1.33/40 = 0.033 hour = 2 minutes

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