M.Sc. DEGREE EXAMINATION, NOVEMBER/DECEMBER 2017.
Third Semester
OR SQC
QUEUING THEORY AND NETWORK ANALYSIS
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Time 3 Hours Max. Marks 70
SECTION — A
Answer any FIVE questions. 6 30 Marks)
1. Explain Queuing system and its characteristics.
2. Obtain the distribution of the number of arrivals in a time interval
3. Explain bulk queues and priority queues and give their applications two each.
4. Obtain the mean and variance of Erlangian Service time distribution with
k-phases.
5. Explain Critical path Constraints in network and rules for constructing
networks.
6. Explain the objectives of Trading-off Time and Cost.
7. Explain Travelling Salesman problem.
8. Explain maximum flow model and write the maximal flow algorithm.
SECTION — B
Answer ALL questions. 10 40 Marks)
9. Explain with infinite capacity. Obtain its steady state solution. Derive
the waiting time distribution for the system.
Or
Explain birth and death process. Obtain the steady state solution for Pn .

10. Explain M Ek 1 FIFO system. Obtain its steady state solution. Find the
average number of stages in the system.
Or
Explain M G 1 system. Derive the Pollaczek-Khinchine formula.
11. Draw the network representing the project comprising the activities given by
the accompanying tables.
Activity Immediately preceding activity Estimated duration (weeks)
Optimistic Most Likely Pessimistic
a 1 1 7
b a 1 4 7
c 2 2 8
d c 1 1 1
e c 2 5 14
f c 2 5 8
g d 3 6 15
What is the probability that the event, from which the activity g starts will be
finished within 5 weeks? Determine the critical path of the network.
Or
The following table gives the activities in a construction project and other
relevant information:
Activity Preceding
activity
Normal Crash
Time (days) Cost Time (days) Cost
1-2 20 600 17 720
1-3 25 200 25 200
2-3 1-2 10 300 8 440
2-4 1-2 12 400 6 700
3-4 2-3 5 300 2 420
4-5 3-4 10 300 5 600
Draw the network of the project Find the total and free floats for each
activity Crash the activity until the shortest duration is reached.
12. A parent has five (teenage) children and five household chores to assign to
them. Past experience has taught the parent that forcing chores on a child is
3 21231 A
counter productive. With this in mind, the children are asked to list their
preferences among the five Chores, as the following table shows:
Child A B C D E
Preferred Chores 4 or 5 1 1 or 2 2 or 5 2
The parents modest goal now is to finish as many Chores as possible while
abiding by the Children's Preferences. Determine the maximum number of
Chores that can be completed and the assignment of Chores to Children.
Or
ABC electric uses existing blurry pipes to transport coal from three mining
areas 2 and to three power plants 6). Each pipe can transport at
most 10 tons per hour. The transportation costs per ton and the capacity of
the pipes per hour are given in the following table:
4 5 6
1 5 8 4 8
2 6 9 12 10
3 3 1 5 18
16 6 14
Determine the optimum shipping schedule by the capacitated simplex
algorithm.
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