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CORK INSTITUTE OF TECHNOLOGY
INSTITIÚID TEICNEOLAÍOCHTA CHORCAÍ
Semester 1 Examinations 2009/
Module Title: Networking Embedded Systems
Module Code: CTEC 9012
School: Electronic and Electrical Engineering
Programme Title: Masters of Engineering in Embedded Systems Engineering
Programme Code: EMBED_9_Y
External Examiner(s): Mr. P. French, Dr. D. Heffernan, Mr. P. Quinlan Internal Examiner(s): Dr. Oliver Gough
Instructions: Answer four questions
Duration: 2 Hours
Sitting: Winter 2009
Requirements for this examination:
Note to Candidates: Please check the Programme Title and the Module Title to ensure that you have received the correct examination paper. If in doubt please contact an Invigilator.
Q1.
(a) Consider a LAN with a large number of PCs each running a database client application and a single database server. The server receives 1200 database queries per minute during normal operation according to a Poisson process. The database requires 20 milliseconds on average to process a query. The processing time is exponentially distributed. Assume that access and transmission delays on the LAN are negligible. (i) Calculate the total time each user has to wait until she receives a reply to her query using a suitable queuing model. (ii) By what percentage does the average query processing time need to be decreased in order to maintain the delay calculated in part (i) of the question when queries are received at a rate of 2000 per minute? [10 marks]
(b) A transmission system, is shared among 8 computer systems. Data packets of a fixed size of 256 bytes are generated by each computer system according to a Poisson process with rate λ = 0.75/sec. Due to variability in the communications environment the effective data rate has the following distribution. R 1 = 9.6kbit/s,is available 20% of the time, R 2 = 19.2kbit/s, 25% of the time, R 3 = 28.8kbit/s, 25% of the time, R 4 = 56kbit/s, 30% of the time. (i) Calculate the throughput of the system. (ii) Calculate the average delay data packets experience before transmission. [15 marks] [Total: 25 marks]
Q3.
(a) Briefly discuss the use of directed diffusion in sensor networks paying attention to the mechanisms of inhibition and activation of links. [12 Marks] (b) Consider the situation in figure Q3. Solid lines represent transmission links and dashed lines indicate tier boundaries. Here node 1 is transmitting to node 9. If a transmission takes branches in the next tier with 3 times the probability that it takes branches in the same tier with no backtracking, determine the relative probability of packets flowing through 7 and 8 to reach 9 :
5
A
Figure Q3: Data Diffusion Network
[13 Marks] [Total: 25 marks]
Q4.
(a) Using Dijkstra’s algorithm, develop the least-cost routing table for source node s = 4 for the network of 9 nodes shown in Figure Q4(a). The link costs are assumed bidirectional with equal costs in both directions. In your answer tabulate the least cost associated with each route. [10 marks]
2
2
2
6
3 3
1 1
3 3 3 2
2
1
Figure Q4 (a)
(b) Using the Ford-Fulkerson algorithm, calculate the maximum flow f between source node s = 6, and destination node d = 7 for the network of 7 nodes shown in Figure Q4(b). Link capacities and flow direction are shown with each link.
20
10 5
7
5
(^3 )
(^15 )
20
7
Figure Q4(b)
[15 marks] [Total: 25 marks]
The following formulae may be of use
Little’s theorem: A = λ T and AQ = λ W
M/M/1/∞ Queuing System: state probability of Markov chain pi = ( 1 −ρ) ρ i
A ,
M/M/m/∞ Queuing system:
Q Q 1
A P and
Q 1
A m P
Probability of queuing in M/M/m:
(^0) m! 1
m P p
m Q , where
−
1 0
m i
i m m
m i
m p
and
m
Pollazcek-Khinchine formula for an M/G/1 queuing system:
( X )
X
W
λ
λ −
2 and T = X + W , X is service time random variable
with ∑ ( )
∞
k 0
X Xk PXk and ( k)
k 0
2 k
X 2 XPX
∞
= , for discrete probability distributions
∞
−∞
X = x⋅p(x)dx, ∫
∞
−∞
X 2 = x^2 p(x)dx; for continuous probability distributions
Engset blocking probability ( )
= (^) m
k
k
m
k
s
m
s
Ems
0
ρ with
k s k
s k
s −
Jackson’s Theorem:
r p j K
K
i
j j i ij ;^1 ,^2 ,Κ
1
=
j
j
j μ
P ( ) n P ( n ) P ( n ) Λ PK ( nK )
= 1122 with n ( n 1 , n 2 ,Λ, nK )
and Pj ( n^ j )^ = ρ njj ( 1 − ρ j )^ ; nj ≥ 0
The solutions to the quadratic equation ax^2 + bx + c = 0 are a
x b b ac 2
1 , 2
=− ±^ −
Table 1. Erlang-B call attempt blocking probabilities
