As an interested student, you have volunteered to study the operation of the Sun
ID: 333224 • Letter: A
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)
Explanation / Answer
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 = 2Related Questions
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