Monte Carlo Simulation

A self-service store employs one cashier at its counter. 9 customers arrive on an average every 5 minutes while the cashier can serve 10 customers in 5 minutes. Assuming Poisson distribution for arrival rate and exponential distribution for services, find i) Average number of customers in the system, ii) Average length of the queue, iii) Average time a customer spends in the system, and iv) Average time a customer waits before being served.

A tourist car operator finds that during the past few months the car's use has varied so much that the cost of maintaining the car has varied considerably. During the past 200 days the demand for the car fluctuated as below:

Trips per week	Frequency
0	16
1	24
2	30
3	60
4	40
5	30

Using random numbers, simulate the demand for a 10-week period.

A farmer wants to decide which of the three crops he should plant on his 100-acre farm. The profit from each is dependent on the rainfall during the growing seasons. The farmer has categorized the amount of rainfall as high, medium, low. His estimated profit for each is shown in the Table below:

Rainfall	Estimated Conditional Profit (Tk.) Crop A	Crop B	Crop C
High	8000	3500	5000
Medium	4500	4500	5000
Low	2000	5000	4000

If the farmer wishes to plant only one crop, decide which will be his best crop using:
i) Maximax Criteria, ii) Maximin Criteria, iii) Hurwicz Criteria (farmer's degree of optimism being 0.6), and iv) Laplace Criteria

Customers arrive at a service facility to get the required service. The inter-arrival and service times are constant and are 1.8 minutes and 4 minutes respectively. Simulate the system for 14 minutes. Determine the average waiting time of a customer and idle time of the service facility.

The arrival rate of customers at a banking counter follows Poisson distribution with a mean of 45 per hour. The service rate of the counter person also follows Poisson distribution with a mean of 60 per hour.
What is the probability of having 0 customers in the system?
$P_5$
Find $L_s$, $L_q$, $w_s$ and $w_q$.

A tourist operator finds that during the past few month the car's uses has varied so much that the cost of maintaining the car has varied considerably. During the past 200 days the demand for the car fluctuated as below

Trips per week	Frequency
0	16
1	24
2	30
3	60
4	40
5	30