A) What service rate is needed to keep the average number of customers in the se

Question

A) What service rate is needed to keep the average number of customers in the service system (waiting line and being served) to three? B) For the service rate in part (a), What is the probability that more than three customers are in line and being served? C) For the service rate in part (a), What is the average waiting time in line for each customer?
Please show all work step-by-step. MBA 620 Spring 2018 Nicholas Muzyka &I; 43/18 4:47 PM Homework: Homework 4.4-Practice Save Score: 0 of 100 pts 1 of 1 (1 complete) HW Score: 0%, 0 of 100 pts 3 Problem 10 The daughter of the owner of a local hamburger restaurant is preparing to open a new fast-food flexible; however, the service times are expected to follow an exponential distribution. The drive-in window is a single-server operation a. What service rate is needed to keep the average number of customers in the service system (waiting line and being served) to three? ?.® customers per hour. (Enter your response as an nteger) Question Help outlets, she expects customers to arrive at the drive-up window according to a Poison distribution, with a mean of 18 customers per hour. The service rate is restaurant called Hasty Burgers. Based on the arrival rates at her Enter your answer in the answer box and then click Check Answer Clear All remaining

Explanation / Answer

We use the following formulae:

So as per the given condition

A= 18

S= ?

Ls = 3

So, Ls = A/(S-A) = 3

So 3= 18/(S-18)

S-18 = 6

S= 24

Ans A ) S = 24

Now

For B and C:

Kendall's notation M/M/1 Arrival rate A Service rate S U Utilization ratio U=A/S Ls Expected number of people in system Ls A/(S-A) Ws Avg waiting time in the system Ws 1/(S-A) Wq Avg waiting time in the Line Wq A/S(S-A) Lq Avg no of customer waiting in line Lq A^2/S(S-A) Po Prob of 0 units in system Po 1-(A/S) Pn Prob of k units in system (A/S)^(K+1)

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