Kerala University 2010-5th Sem B.Tech Computer Science and Engineering AMQM - Question Paper
Fifth Semester B.Tech. Degree Examinatior
Model Question Paper (2008 Scheme)
Computer Science / Information Techrology(RF)
AOVANCED MATHEMATICS AND QUEUING MODELS (RF)
Max.Marks; 100
Time; 3 Hours
Instructions : Answer all questions of Part - A and one full question tacb from Module I, Module II and Module III
PAATA
L Define basic feasible solution, optimal solution and degenerate solution.
2. Rewrite in standard form for the following [.PP.
Max i =2x1+J 44)t3
Subject to '2x5 ixj $ 4
Xi +2x* 5 2xi+3*s fi2
Where XX; i 0 and Kj Is unrestricted In sign.
3. What are the three main phases of a project ?
4 Distinguish between CPM and PERT.
5. Given vT and vs in a vectorspaee V, let H = Span( vx ,vj}, Show that H is a subspace of V.
6. Define linearly independent set. ff pi(t)=l, pj|t)=t and p-,{t>=4-t then prove that (pi, p* pj) is linearly dependent.
7. Find the dimension of the subspace
B. Write dawn the characteristic of waiting time distribution for the model M/M/l//ftfo.
9. Define transient and steady states.
10. At a one man barber shop, customers arrive according to Poisson distribution with a mean arrwsh rate of 5 per hour and his hair cutiing time was exponentially distributed with an average haircut taking: 10 mm. It is assumed that because of his excellent reputation customers were always willing to wait. What is the average number of customers in the shop and the average
n um ber of custo me rs waiting fo r a hair cut.
(4x10=40 Martisl
Module f
11. Solve the following LPP Min i = 4HJ+*]
Subject to 3k!+Xj = 3 4xi+3xi> 6 X)+2Xi 5 4 and xi,xj s 0
12.Construct the network fpr (he project whose activities are given below and compute the total float, free float and independent float of each activity and hence determine the critical path and the project duration.
Duration (in weeks}
then show that {u, ,Ui ,Uj} is an
12
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Module II | |||||||||||||||
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orthogonal set. | ||||||||||||
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. Construct an orthogonal basis {vi, Vi) for W. (C) find a least- squares solution of the inconsistent system Ak =bfor
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'4 |
0 |
2 | ||
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A= |
0 |
z |
b= |
0 |
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.1 |
1. |
.11. |
5 '2
-8 1
i a
-3 1
2 4
4 -5
2 '5
*6 0
1
3
14. (a)f ind an LU factorization of A =
(b)1-irtd a lingular value decomposition of A=
1 -1 -2 2 2 -2
Module III
15, in a super market the average arrival rate of customers is 5 in every 30 minutes. The arrival time it takes to list and calculate the customers purchase at the cash desk is 4,5 mrn, and this time is exponentially distributed.
(a) How long will the customer expect to wait for service at the cash desk,
(b) What ii the chance that the queue length will exceed 5.
(c) What Is the probability that the cashier is working.
16. A telephone exchange has two long distance operators. The telephone company finds that during the peak load, long distance calls arrive in a Poisson fashion at an average rate of 15 per hour. The length of service on these calls is approximately exponentially distributed with mean length 5 min.
<a| What is the probability that a subscriber will have to wait for his longdistance call during the peak hours of the day.
(b) If the subscriber will wait and are serviced in turn. What is the expected waiting time.
[3*20=60 MarksJ
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Attachment: |
| Earning: Approval pending. |
