CSM Assignment No. 2

ASSIGNMENT NO. 2

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.

CSM Assignment No. 1

ASSIGNMENT NO. 1

1. Name Entities, Attributes, Activities, Events and State variables for the following systems.

Small appliance repair shop, Cafeteria, Grocery store, Laundromat, Fast food restaurant, Hospital emergency room, Taxicab company, Automobile assembly line.

2. Define Simulation. When Simulation is appropriate & when it is not appropriate? 
3. Explain steps involved in simulation study with diagram.
4. Grocery Store Example: Let the arrival distribution be uniformly distributed between 1 to 10 minutes and service time distribution is as follows:

Service time(min)	1	2	3	4	5	6
Probability	0.04	0.20	0.10	0.26	0.35	0.05

Develop the simulation table and analyze the system by simulating arrival and service of 10 customers. Find out Queue statistics.

Random digits for interarrival time and service time are follows:

Customer	1	2	3	4	5	6	7	8	9	10
R. D. for Interarrival Time	--	853	340	205	99	669	142	301	888	444
R. D. for Service time	71	59	12	88	97	66	81	35	29	91

5. ABLE-BAKER CARHOP PROBLEM:

TIME BETWEEN ARRIVAL (MIN)				0	1	2	3	4
PROBABILITY				0.07	0.26	0.31	0.22	0.14
ABLE’S SERVICE TIME			2	3	4	5
PROBABILITY			0.22	0.31	0.32	0.15
BAKER'S SERVICE TIME				3	4	5	6
PROBABILITY				0.34	0.28	0.16	0.22

DEVELOP THE SIMULATION TABLE AND ANALYSE THE SYSTEM BY SIMULATING ARRIVAL &SERVICE OF 10 CUSTOMERS. RANDOM DIGITS FOR INTERARRIVAL&SERVICE TIME ARE AS FOLLOWS:

CUSTOMERS		RANDOM DIGITS FOR INTER ARRIVAL				RANDOM DIGITS FOR SERVICE
1			-				15
2			5				28
3			36				62
4			41				35
5			77				7
6			52				57
7			63				82
8			38				92
9			16				19
10			32				43

CALCULATE SERVER UTILIZATION & MAXIMUM QUEUE LENGTH?

FIND OUT AVERAGE WAITING TIME, AVERAGE SERVICE TIME, AVERAGE WAITING TIME OF THOSE WHO WAIT, % BUSY TIME OF ABLE & BAKER & AVERAGE TIME CUSTOMERS SPENDS IN SYSTEM?

6. THERE IS ONLY ONE TELEPHONE IN A PUBLICBOOTH OF THE RAILWAY STATION. THE FOLLOWING TABLES INDICATE THE DISTRIBUTIONOF CALLERS ARRIVAL TIME & DURATION OF CALLS. SIMULATE FOR 20 ARRIVALS OF CURRENT SYSTEM. IT IS PROPOSED TO ADD ANOTHER TELEPHONE TO BOOTH. JUSTIFY PROPOSED BASED ON THE WAITING TIME OF CALLERS.

TIME BETWEEN ARRIVAL(MIN TIME)			2	3	4
PROBABILITY			0.2	0.7	0.1
CALL DURATION (MIN)			2	3	4	5
PROBABIITY			0.15	0.6	0.15	0.1

7. Define the terms used in simulation: Event, Event Notice, Event List, Activity, Delay, Clock.
8. Explain the Event Scheduling Algorithm in detail?
9. A small Store has only one check out counter, customers arrives at this counter at random time that are from 1 to 8 minutes apart. Check out that possible value of interarrival time that has some  probability of occurance. Service time vary from 1 to 6 minutes with the following probability .Here a stopping timeof 60 minutes is set. Simulate the system.
10. Dump Truck problem: Six drump trucks are used to haul coal from the entrance of a small mine to rail road. Fig provides a schematic of the dump truck is loaded by one of the two loaders. After a loading the dump truck immediately moves to scale to be weighted as soon as possible. Both loader and scale have a first served waiting line for trucks. Travel time from a loader to the scale is considered negligible. After being weighed, a truck begin a travel time during which time the truck unloads load then afterwords return to the loader queue. The distribution of loading time, weighting time and travel time are given together with the random digit. Simulatethe system.

Distribution of loading Time for Dump Truck :

Loading Time(min)	5	10	15
Probability	0.30	0.50	0.20

Distribution of weighting time for Dump truck:

Weighting Time (min)	12	16
Probability	0.70	0.30

Distribution of travel for Dump truck:

Travel  time(min)	40	60	80	100
probability	0.40	0.30	0.20	0.10