Question

For questions 1-3

Customers arrive at the Cox Store at an average of one every 15 minutes and their requests take on average 10 minutes to be processed. The service counter is staffed by only one Cox representative, Mark, who works from 9AM to 5PM every day. Assume Poisson arrivals and exponential service times.

1. What are the arrival and service rates that should be used for this problem?

	A.	λ = 4 customers/hour                μ = 6 customers/hour
	B.	λ = 3 customers/hour                μ = 4 customers/hour
	C.	λ = 15 customers/hour               μ = 10 customers/hour
	D.	λ = 15 minutes/customer           μ = 10 minutes/customer

2. Assume λ = 2 customers/hour and μ = 3 customers/hour to solve problems 2-6.

What percentage of time is Mark idle?

	A.	0%
	B.	66.76%
	C.	33.33%
	D.	75%

3. Assume λ = 2 customers/hour and μ = 3 customers/hour to solve problems 2-6.

How much time, on average, does a Cox customer spend waiting in line?

	A.	0.3 hours
	B.	There will be no waiting time (0 minutes)
	C.	1.33 minutes
	D.	40 minutes

Answer 1

1. Lambda = arrival rate = 1 customer every 15 min = 60/ 15= 4 per hour

Mu = service rate = 10 min per customer = 60 / 10 = 6 per hour

Hence the correct option is a. λ = 4 customers/hour μ = 6 customers/hour

2. λ = 2 customers/hour μ = 3 customers/hour

Percentage of being busy = utilization = λ /μ * 100 = 2 / 3 * 100 = 66.66%

Percentage of busy = 1 - percentage of busy = 1 - 67.33 = 33.33%

Hence the correct option is c. 33.33%

3. Time spent waiting in line =( λ) / μ( μ - λ) = (2) / 3 (3 - 2) = 0.667 hour

Hence the correct option is d. 40 min

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