Please read the scenario and answer the question basis on the scenario.
Scenario Three: On Friday's the Elm Street branch opens a second lane (window) during its 8 hours of operation in order to accommodate employees from a local manufacturing plant who want to deposit their paychecks. When a customer in the single line reaches the front of the line, it would go to the next available lane (window) for service. On Friday's customers arrive at the rate of about 14 every hour according to a Poisson distribution and, on average, each customer service person can process a transaction every 3 minutes, following an exponential distribution. The salary and benefits for a bank teller at the Elm Street branch is $18.50 per hour. If it has been estimated that the waiting time cost per hour is $62.00 per hour in line.
The table given below shows the workings of waiting times
|
Parameter
|
Value
|
Minutes
|
Seconds
|
|
M/M/s
|
|
|
|
|
Arrival rate(lambda)
|
14
|
|
|
|
Service rate(mu)
|
20
|
|
|
|
Number of servers
|
2
|
|
|
|
Server cost $/time
|
18.5
|
|
|
|
Waiting cost $/time
|
62
|
|
|
|
Average server utilization
|
0.35
|
|
|
|
Average number in the queue(Lq)
|
0.1
|
|
|
|
Average number in the system(L)
|
0.8
|
|
|
|
Average time in the queue(Wq)
|
0.01
|
0.42
|
25.13
|
|
Average time in the system(W)
|
0.06
|
3.42
|
205.13
|
|
Cost (Labor + # waiting*wait cost)
|
43.06
|
|
|
|
Cost (Labor + # in system*wait cost)
|
86.46
|
|
|
The probability table is given below
|
k
|
Prob (num in sys = k)
|
Prob (num in sys <= k)
|
Prob (num in sys >k)
|
|
0
|
0.48
|
0.48
|
0.52
|
|
1
|
0.34
|
0.82
|
0.18
|
|
2
|
0.12
|
0.94
|
0.06
|
|
3
|
0.04
|
0.98
|
0.02
|
|
4
|
0.01
|
1
|
0.01
|
|
5
|
0.01
|
1
|
0
|
Question 1: What is the average number of customers in the system?
Question 2: What is the average number of customers in line “behind” the customer(s) receiving service?
Question 3: What is the average waiting time a customer spends in the system?
Question 4: What is the average time a customer is in the queue waiting to be serviced?
Question 5: What is the probability that there are no customers in line or being serviced?
Question 6: What percentage of the time are the customer service persons busy?
Question 7: How much total time would customers spend waiting in line to be serviced (queue) on a typical day?
Question 8: What is the total daily cost of customers waiting in line to be serviced (queue) on a typical day?
Question 9: What is the total daily cost of customers waiting in the system on a typical day?
Question 10 what is the total daily cost of customers waiting in the system plus the cost of service on a typical day?