Need help with this assignment. Thanks in advance!! :) Eugene is a business anal
ID: 3321221 • Letter: N
Question
Need help with this assignment.
Thanks in advance!! :)
Eugene is a business analyst at Burger King. He was assigned a task where he needs to analyze data on consumer arrivals and concluded that the arrival rate is 15 customers per hour. He also found out that the cashier can process an average of 18 customer orders per hour A. Calculate and per 10 minutes period Plug the value of and into the arrival rate and service rate cell of Case-Data-xlsm file, and calculate the value of Po, Lq, L Wq, W, Pw. And create a column (name it 'Baseline') in a nevw tab (name it 'scenario'), showing the value of Po, Lq, L, Wq, W, Pw. Interpret each value using at least 20 words. B. C. Suppose the service rate increases from its original value (value of in part A) to =4, but the arrival rate stays the same as in part a. Calculate the value of Po, Lq, L, Wq, W, Pw based on the original value of and the updated values of . Create a column (name it 'Scenario 1') in a scenario tab, showing the updated value of Po, Lq, L, Wq, W, Pw Suppose the arrival rate increases from its original value (value of in part A) to =2.8, but the service rate stays the same as in part a. Calculate the value of Po, Lq, L, Wq, W, Pw based on the updated values of and the original value of . Create a column (name it 'Scenario 2') in a scenario tab, showing the updated value of Po, Lq, L, Wq, W, Pw D. Now you have three columns in the scenario tab. Compare the values of Po, Lq, L, Wq, W, Pw across Baseline, Scenario 1('Service rate increase' option), and Scenario 2('Arrival Rate increase option), and discuss how the change in service rate or arrival rate would affect the following based on the results from part b-d using at least 200 words E. . Probability that no customers are in the system, PO Average number of customers waiting in line, Lq Average number of customers in the system, L Average time a customer spends waiting in line, Wq . Average time a customer spends in the system, W . Probability an arriving customer has to wait, Pw I NE UE NS. ANY CAN RE I AM HAVING TROUBLE UNDERSTANDIN NE NICE. AL EAS EXC MANY THANKS IN ADVANCE!!!!Explanation / Answer
This is an M/M/1 Queue System.
Back-up Theory
An M/M/1 queue system is characterized by arrivals following Poisson pattern with average rate , [this is also the same as exponential arrival with average inter-arrival time = 1/ ] service time following Exponential Distribution with average service time of (1/µ) [this is also the same as Poisson service with average service rate = 1/µ] and single service channel.
Let n = number of customers in the system and m = number of customers in the queue.
[Trivially, n = m + number of customers under service.]
Let (/µ) =
The steady-state probability of n customers in the system is given by Pn = n(1 - ) ………(1)
The steady-state probability of no customers in the system is given by P0 = (1 - ) ………(2)
Average queue length = Lq = (2)/{µ(µ - )} ……………………………………………..(3)
Average number of customers in the system = L = ()/(µ - )………………………..(4)
Average waiting time = Wq = ()/{ µ(µ - )} ……………………………………………..(5)
Average time spent in the system = W = {1/(µ - )}……………………………………..(6)
Probability of waiting = Pw = 1 - Probability of no waiting = 1 - Probability of no customer in the system = 1 – P0 = . ……………………………………………………………….(6)
Now, to work out the solution,
Given = 15 per hour and µ = 18 per hour.
Part (A)
and µ per 10 minutes:
= 2.5 per 10 min and µ = 3 per 10 min. ANSWER
Part (B)
P0 =
0.167
Lq =
4.167
L =
5
Wq =
1.667
Wq =
2
Pw =
0.833
Part (c)
= 2.5 per 10 min and µ = 4 per 10 min
P0 =
0.375
Lq =
1.042
L =
1.667
Wq =
0.417
Wq =
0.667
Pw =
0.625
Part (d)
= 2.8 per 10 min and µ = 3 per 10 min
P0 =
0.067
Lq =
13.067
L =
14
Wq =
4.667
Wq =
5
Pw =
0.933
DONE
P0 =
0.167
Lq =
4.167
L =
5
Wq =
1.667
Wq =
2
Pw =
0.833