Question

As an interested student, you have volunteered to study the operation of the Sunbucks during a typical weekday. You arrive at 8 am just as Sunbucks is opening, and you diligently record information over the next hour. According to the manager, Sunbucks should be able to serve an average of 1 customer every 2 minutes and during the period you were collecting data 25 customers arrived to make a purchase. Based on your data, answer the following:

What was the average number of customers in line during the period you observed? What was the average waiting time for a customer in line during this period? What is the probability of having 2 customers in the system?

(Please list step by step so I can understand better and follow)

Answer 1

Just calculate using the formulae provided:

	Current system
	Kendall's notation	M/M/1
					Comment
	Arrival rate	A	25		per hour
	Service rate	S	30	60/2
U	Utilization ratio	U=A/S	0.83333	<1	Length of queue diminishing
Ls	Expected number of people in system	Ls
		A/(S-A)	5.00
Ws	Avg waiting time in the system	Ws
		1/(S-A)	0.20000	hours	12.0000	mins	Ans
Wq	Avg waiting time in the Line	Wq
		A/S(S-A)	0.16667	hous	10.0000	mins
Lq	Avg no of customer waiting in line	Lq
		A^2/S(S-A)	4.1667				Ans
Po	Prob of 0 units in system	Po
		1-(A/S)	0.16667
			16.67%
Pn	Prob of k units in system	(A/S)^(K+1)	0.57870				Ans
	K = 2