Question

Burrito King (a new fast-food franchise opening up nationwide) has successfully automated burrito production for its drive-up fast-food establishments. The Burro-Master 9000 requires a constant 50 seconds to produce a batch of burritos. It has been estimated that customers will arrive at the drive-up window according to a Poisson distribution at an average of one every 75 seconds. To help determine the amount of space needed for the line at the drive-up window

a. What is the average waiting line length (in cars)? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

b. What is the average number of cars in the system (both in line and at the window)? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

c. What is the expected average time in the system, in minutes? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

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Answer 1

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	Queuing model
	Serving time=		50.00	sec
	Lamba = arrival rate =		0.8	per min
	Mu = mean service rate = 60/serving time		1.2	per min
	Serving time= 1/Mu=		0.833	mins
	Utilization = rho = lambda / mu =		0.667	66.7%
Answer a:	Average no. in queue:
	Average no queue =Lq = (rho)2 / (1-rho)
	Average no of cars waiting in line =Lq =		1.333	cars
	Average time spent in queue:
	Wq = waiting time in the line for service = Lq / lambda =		1.6667	min
Answer c:	Average time spent in the system:
	W = average time in the system = Wq + serving time =		2.5000	min
Answer b:	Average no. of cars in the system.
	L = no. of cars in the system = W *Lambda =		2.000	cars