Chapter 2 – Mathematical & Statistical Models in Simulation

Computer Simulation and Modeling

Chapter 2 – Mathematical & Statistical Models in Simulation
Important Questions from Chapter 2 – Mathematical & Statistical Models in Simulation

1. The probability of a computer chip failure is 0.05. Everyday a random sample of size 14 is taken. What is the probability that 1) at most 3 will fail 2) at least 3 will fail

2. The number of accidents in a year to taxi driver follows poisson distribution with mean equal to 3. Out of 100 taxi drivers, find approximately the number of drivers with 1) no accidents in a year 2) more than 3 accidents in a year

3. Explain Poisson processes with properties.

4. Explain discrete distributions.

5. At service station an automatic carwash facility operates with only one car bay. Cars arriving according to a position distribution, with mean of 12 cars per hour. Car may wait in the facilities parking lawn if service station is busy. Service time has distribution with average 4 min with a standard deviation of 4/3 minutes. Compute the steady state parameters of the system.

6. The inter arrival time as well as service time at government hospital is known to be distributed exponentially. Currently only 1 emergency case can be handle at time .The arrival rate of patient is 4 per hour and service rate 6 per hour. Compute the steady state parameter and probability for 0, 1, 2, 3, 4 or more patients in the hospital.

7. A CNG station has 2 filling machine .The service time follows exponential distribution with the mean of 5 min and autorikshaws arrives for service in a poisson fashion at a rate of 15 per hour. Compute steady state parameters of the system.

8. A two person barber shop has five chairs to accommodate waiting customers. Potential customers are turned away when all five chairs are full. Customers arrive at the rate of 3 per hour & spend an avg. of 15 minutes in the barber chair. Compute the steadystate parameters of the system.

9. What are the characteristics queuing systems? Explain in detail.
10. Explain network of queues.
11. Give the steady state equations for M/G/1 and M/M/1 queue.
12. Give the steady state equations for finite population model M/M/c/N/K queue.
13. Suppose that the life of a lamp, in 1000 hrs, is exponentially distributed with failure rate 1/5. What is the probability that the lamp will last longer than its mean life of 5000 hrs? Also find the probability that the industrial lamp will last between 3500 and 5500 hrs.
14. At sai service station, servicing of a car is performed in three stages. Each stage has exponential distribution of service time with mean service time 20 minutes. Find the probability that the cars servicing will take 50 minutes or less. Also find the expected length of cars servicing.
15. A tool crib has exponential inter-arrival time and service time, and it serves a very large group of mechanics. The mean time between arrivals is 4 minutes. It takes 3 minutes on the average for a tool crib attendant to service a mechanic. The attendant is paid Rs. 10 per hour and the mechanic is paid Rs. 15 per hour. Would it be advisable to have a second tool crib attendant?