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Cork Institute of Technology
Bachelor of Engineering (Honours) in Electronic Engineering
Award
National Framework of Qualifications – Level 8
January 2005
Computer Engineering
(Time: 3 Hours)
Answer any two questions from Section A [50 marks] and any two questions from Section B [50 marks]
Maximum available marks are 100.
Examiners: Mr. Fergus O’Reilly Dr. Dirk Pesch Prof. Cyril Burkley Mr. John Ryan
Section A
Q1 (a) You have been assigned the task of evaluating an interconnection network, which might extend from 100 to 1000 processing nodes. Calculate the complexity (total number of switches) of both a Cross-bar and Omega network for this task. [6 marks]
(b) Vector processors provide for high performance vector operations. What are the advantages of vector processors and explain why these are suitable for execution in array architectures? [6 marks]
(c) You have been asked to devise an algorithm to compute the following calculation across a floating point vector A with 500,000 elements. You have available a Private Memory system with 250 processor nodes. 2
500 , 000
1
y ( A [ x ])^2 ( A [ 500 , 000 x ])
x
= Develop an algorithm using pseudo code or pseudo C code which could execute on one of these processor nodes. Describe the partitioning of the problem, the data distribution over the system and provide the code to achieve the communication between the nodes to calculate the final result. [13 marks]
[Total: 25 marks]
Q2 (a) Using diagrams describe how a high-end server type machine, with 4 commodity 32 bit
processors (4GB or 32 bit of address space) (e.g. Pentium Xeon or Power PC), would typically be organised, for good flexibility and performance. It will have 4 GB RAM. State and justify the memory models used. If you wished to scale this to 64 processors with a maximum of 64 GB RAM, describe an appropriate organisation, stating why any changes you might make? [8 marks]
(b) Describe using diagrams how a paged based memory management system can translate a virtual space of 1024MB (30 bit) into a physical space of 64 MB (26 bits). Take into account that the average active code/data block is 256 KB in size for this system. [10 marks]
(c) For Massive Parallel Systems, scalability is of major importance. Using work and efficiency curves describe your understanding of it and how it relates to efficiency for Constant, Sub- Linear, Linear and Exponential work-loads. What are the boundaries on scalability and how do these affect algorithm design? [7 marks] [Total: 25 marks]
Q3 (a) A 800MHz CPU core, has a 5 stage instruction fetch/decode queue. Branches in code occurs with a 20 % frequency and impose a 4 cycle bubble. All other instructions execute with a CPI of 1. To improve performance a branch prediction unit is proposed. This will require reducing the clock rate to 600 MHz but will be able to predict 90% of branches with no-penalty, mis-prediction will impose a 7 cycle flush/re-load penalty. Calculate whether it is worthwhile adding the branch-prediction unit. [8 marks]
(b) A new machine running the SPECfp suite achieves the following execution times in seconds, in comparison with a Sun 10/40. Determine the new machine’s SPECfp figure. Program New Machine Sun 10/ hydro2d 1.6 5. su2cor 3.4 6. swim 20.1 67. tomcatv 6.3 12. wave5 6.1 20. mgrid 23.6 100. applu 5.8 12. turb3d 19.7 90. apsi 97.8 400. fpppp 45.9 98.
What is the sister benchmark to SPECfp and what does it measure, give 2 examples of its programs? [7 marks]
Section B
Q4. (a) A CRC is constructed to generate a 5-bit FCS for a 10-bit message. The generator polynomial is G(X) = X^5 + X^3 +1. (i) Generate the FCS for the data bit sequence 1010101010 (left most bit is the least significant) using the generator polynomial. (ii) Now assume that bit 9 (counting from the LSB) in the bit sequence is in error and show that the detection algorithm detects the error. [6 marks]
(b) Calculate the theoretically maximum error free data rate per user for a TDMA system with total bandwidth B = 10MHz, with average transmitter power of P = 10W, noise power density of N 0 = 10-7^ W/Hz, and K = 25 users. [8 marks]
(c) Consider a fixed wireless communication link between a subscriber device and a base station in a wireless communication network. A go-back-N ARQ technique with a window length of N = 31 is used to provide a reliable communication link. The data rate is 128kbit/s, frames are 512bits including overheads, the speed of the signal is 3⋅ 108 m/s, and the distance between subscriber device and base station is 2km. The (^) Bit Error Probability Pe (not frame error probability P) in the channel is described by a two state channel model shown in Figure 1, where G is the good channel state with no errors and B is the bad channel state where each bit transmitted during this state is in error with probability PBe = 0.001. The state transition probabilities are α = 0.45 and β = 0.25. Calculate the average throughput of the communication link. Compare the throughput of go-back-N ARQ with simple stop-and-wait ARQ. What do you observe here? NOTE: In your calculation assume that acknowledgement frames are never in error and that their transmission delay can be neglected. You may find the formulae given below useful. [11 marks]
G B
Figure 1. Two state channel model
Q5. (a) Two data packet sources generate packets into a transmission system with a single queue according to a Poisson process with rates λ 1 = 5/sec and λ 2 = 10/sec. Packets are exponentially distributed with packets of the first source having length L 1 = 8750bit and packets of the second source having length L 2 = 5250bit. The transmission system has a single output transmission line with data rate R = 256kb/s. (i) Determine the mean number of packets in the system. (ii) Determine the mean time packets are waiting in the system’s queue before transmission. [9 marks]
(b) Consider a LAN with a large number of PCs each running a database client application and a single database server. The server receives 24 database queries per minute during normal operation according to a Poisson process. The database requires 0.8 seconds 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 44 per minute? [7 marks] (c) A transmission system, comprising of a single wireless transmission link and a multiplexer, is shared among 8 computer systems. Data transmission is protected by an ARQ error correction scheme. Each computer generates fixed size data packets of size 512bytes according to a Poisson process with rate λ = 0.5/sec. Depending on the error rate on the wireless link, the transmission system provides effectively 5 different data rates, Ri, i = 1, …, 5 as follows: R 1 = 6.3kbit/s for 10% of the time, R 2 = 10.8kbit/s, 15% of the time, R 3 = 37.3kbit/s, 25% of the time, R 4 = 56.5kbit/s, 20% of the time, and rate R 5 = 71.1kbit/s, 30% of the time. (i) Calculate the throughput of the system. (ii) Calculate the average delay data packets experience in the multiplexer before transmission. (iii) What single data rate would be required for the wireless link in order to maintain the same average delay if the packet size was exponentially distributed with mean 512bytes? [9 marks]
NOTE: Some formulae you might find useful in answering questions 4, 5, and 6.
frametransmission time a =signalpropagationdelay
Stop-and-wait ARQ
Go-back-N ARQ Selective-repeat ARQ N > 2 a + 1 aP U P 1 2
1
= − U^ =^1 − P N < 2 a + 1 a U P 1 2
1
= − (^ ) ( a )( P NP ) U N P
1 ( ) 2 1
1
= − a U N P
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: (^ ) ( ρ)
ρ −
(^0) m! 1 P p m m Q , where
( ) ( ) ( )
−
1 0
m i
i m m
m i
m p ρ
ρ ρ and μ
λ ρ m
Pollazcek-Khinchine formula: ( X )
W X
λ
λ −
2 and T = X + W
with ∑ ( )
∞
k 0
X Xk PXk and ( (^) k ) k
X ∑ Xk PX
∞
0
2
The solutions of the quadratic equation ax^2 + bx + c = 0 are a
x b b ac 2
1 , 2
=− ±^ −
