Jawaharlal Nehru Technological University Hyderabad 2005 B.E Computer Science Jawaharlal Nehru Technological University mathematical modelling and stimulation(MMS) - Question Paper

5. Consider a self service store with 1 cashier. presume poisson arrivals and ex-
ponential service times. Suppose that a customer arrive on the avg. every 5
minutes and the cashier can serve 10 in five minutes. obtain [16]
(a) The avg. number of customers queuing for service
(b) The probability of having more than 10 customers in the system
(c) The probability that a customer has to queue for more than two minutes
If the service can be speeded upto 12 in five minutes by using a di_erent cash register,
what will be the e_ect on the volumes (a), (b) and (c)
6. (a) discuss PERT and its importance in network analysis. elaborate the require-
ments for applications of PERT techniques. [10]
(b) List at the di_erences ranging from PERT and CPM [6]
7. (a) discuss the role of state descriptor in discrete system simulation [6]
(b) describe the terms [6]
i. Discrete event
ii. Simulation time
iii. Clock time
(c) discuss the representation of time in discrete system simulation [4]
8. Write a short notes on the subsequent [6+5+5]
(a) Output analysis of a single model
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Code No: RR410508 Set No. 3
(b) Chi-square test
(c) Kolmogorov-Smirnov test.
. . . . .
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Code No: RR410508 Set No. 4
IV B.Tech I Semester Regular Examinations, November 2005
MATHEMATICAL MODELLING & SIMULATION
( Common to Computer Science & Engineering and Electronics &
Computer Engineering)
Time: three hours Max Marks: 80
ans any 5 ques.
All ques. carry equal marks
. . . . .
1. (a) discuss the concept of degeneracy in simplex method with at lowest 1 exam-
ple? [4]
(b) Solve the subsequent L. P. issue using Big M method: [12]
Minimize z =2x1 + 5x2
subject to the constraints:
x1 + x2 = 100
x1 _ 40
x2 _ 30
and x1, x2 _ 0.
2. (a) What is a non - linear programming problem? provide 2 examples of NLPP
stating clearly why do you so classify them? [10]
(b) provide canonical form of non - linear programming issue. [6]
3. (a) Derive the E. O. Q. formula for the manufacturing model with shortages [6]
(b) A manufacturing firm has to supply 3,000 units annually to a customer who
does not have enough space for storing the material. There is a contract that
if the supplier fails to supply the material, a penalty of Rs. 40 per unit per
month will be levied. The inventory holding cost amounts to Rs. 20 per unit
per month and the setup cost is Rs. 400 per run. obtain the expected number
of shortages at the end of every scheduling period. [10]
4. (a) discuss the basis of selective inventory control [6] ?
(b) State the di_erent selection techniques adopted in inventory control system.
provide a brief note on every. [10]
5. At a railway station, only 1 train is handled at a time. The railway yard is
su_cient only for 2 trains to wait while others is provided signal to leave the station.
Trains arrive at the station at an avg. rate of six per hour and the railway station
can handle them on an avg. of 12 per hour. Assuming poisson arrivals and
exponential service distribution, obtain the steady-state probabilities for the different
number of trains in the system. Also obtain the avg. waiting time of a new train
coming into the yard. [16]
6. A PERT network has the subsequent activities with their time estimates provided below:
[16]
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Code No: RR410508 Set No. 4
Activity Optimistic (days) Most likely (days) Pessimistic (days)
0-1 two 3.5 8
0-2 three 3.75 6
0-3 one 2.5 7
1-2 three 7.5 9
1-5 four 5.5 10
2-4 two five 8
3-4 two 2.75 5
3-5 three six 9
4-5 two five 8
(a) Construct a network and obtain the expected completion time of the project.
(b) obtain the probability of completing the project three days ahead of the expected
schedule.
7. List and explain different periods in the history of simulation software [16]
8. explain the steps in the development of a useful model of input data with suitable
example. [16]
. . . . .
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Earning:   Approval pending.