Question

A new fast-food franchise has successfully automated burrito production.
50 seconds are are required to produce a batch of burritos.
It is estimated that customers will arrive at the drive-up window at an average of one per 70 seconds according to poisson distribution.

(Do not round intermediate calculations, round final answers to 2 decimals)
[a] What is average line length in cars?
[b] What is the average number of cars in the system (both in line & at window)?
[c] What is average expected time in the system, in minutes?

Answer 1

	Current system
	Kendall's notation	M/M/1
					Comment
	Arrival rate	A	51.429	3600/70	per hour
	Service rate	S	72	3600/50	per hour
U	Utilization ratio	U=A/S	0.71429	<1	Length of queue diminishing
Ls	Expected number of cars in system	Ls
		A/(S-A)	2.50				Ans A,B
Ws	Avg waiting time in the system	Ws
		1/(S-A)	0.04861	hours	2.9167	mins	Ans C
Wq	Avg waiting time in the Line	Wq
		A/S(S-A)	0.03472	hous	2.0833	mins
Lq	Avg no of cars waiting in line	Lq
		A^2/S(S-A)	1.7857				Ans B