Please read the scenario and answer the question basis on the scenario.
Scenario Four: The Main Street branch of the bank is much larger than the Elm Street location and services more customers on a daily base. Additionally it has upgraded it computer services and facilities making it quicker to service customers at its drive in window. On average each customer service representative can service 3 customers every fifteen minutes at a cost of salary and a benefit for a bank teller is $21.50 per hour. The bank is open 8 hours each day. If it has been estimated that the waiting time cost per hour is $75.00 per hour in line. The branch operates one lane for the entire 8 hours per day but opens a second lane during peak times four hours per day. Assume the arrival rate for off-peak hours is 2.5 customers every 20 minutes and the arrival rate for peak time increases to 3 customers every 15 minutes.
The table given below shows the waiting time of customers at Main street branch of the bank
|
Parameter
|
Value
|
Minutes
|
S econds
|
|
M/M/s
|
|
|
|
|
Arrival rate(lambda)
|
19.5
|
|
|
|
Service rate(mu)
|
12
|
|
|
|
Number of servers
|
2
|
|
|
|
Server cost $/time
|
21.5
|
|
|
|
Waiting cost $/time
|
75
|
|
|
|
Average server utilization
|
0.81
|
|
|
|
Average number in the queue(Lq)
|
3.16
|
|
|
|
Average number in the system(L)
|
4.78
|
|
|
|
Average time in the queue(Wq)
|
0.16
|
9.71
|
582.76
|
|
Average time in the system(W)
|
0.25
|
14.71
|
882.76
|
|
Cost (Labor + # waiting*wait cost)
|
279.75
|
|
|
|
Cost (Labor + # in system*wait cost)
|
401.62
|
|
|
The probability table is given below
|
k
|
Prob (num in sys = k)
|
Prob (num in sys <= k)
|
Prob (num in sys >k)
|
|
0
|
0.1
|
0.1
|
0.9
|
|
1
|
0.17
|
0.27
|
0.73
|
|
2
|
0.14
|
0.41
|
0.59
|
|
3
|
0.11
|
0.52
|
0.48
|
|
4
|
0.09
|
0.61
|
0.39
|
|
5
|
0.07
|
0.68
|
0.32
|
|
6
|
0.06
|
0.74
|
0.26
|
|
7
|
0.05
|
0.79
|
0.21
|
|
8
|
0.04
|
0.83
|
0.17
|
|
9
|
0.03
|
0.86
|
0.14
|
|
10
|
0.03
|
0.89
|
0.11
|
|
11
|
0.02
|
0.91
|
0.09
|
|
12
|
0.02
|
0.93
|
0.07
|
|
13
|
0.01
|
0.94
|
0.06
|
|
14
|
0.01
|
0.95
|
0.05
|
|
15
|
0.01
|
0.96
|
0.04
|
|
16
|
0.01
|
0.97
|
0.03
|
|
17
|
0.01
|
0.97
|
0.03
|
|
18
|
0
|
0.98
|
0.02
|
|
19
|
0
|
0.98
|
0.02
|
|
20
|
0
|
0.99
|
0.01
|
|
21
|
0
|
0.99
|
0.01
|
|
22
|
0
|
1
|
0.01
|
|
23
|
0
|
1
|
0.01
|
|
24
|
0
|
1
|
0.01
|
Question 1: What is the weighted average number of customers in the system?
Question 2: What is the weighted average number of customers in the queue?
Question 3: What is the weighted average time a customer spends in the system?
Question 4: What is the weighted average time a customer spends in the queue?
Question 5: What is the total (non-weighted) average wait time customers spend in the system on a typical day?
Question 6: What is the total (non-weighted) average wait time customers spend in the queue on a typical day?
Question 7: What is the total daily service cost?
Question 8: What is the total daily cost of customers waiting in the system on a typical day?
Question 9: What is the total daily cost of customers waiting in the system plus the cost of service on a typical day?