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CSC 598.66: Senior Design-I course
发布时间:2023-11-06
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CSC 598.66: Senior Design-I course
Mid-term exam (take-home), 30th Oct, 2023 — answer sheets are due by 11/03
(be brief in your answers; excessive writing can result in negative scores)
(Answer all questions. The points for each question is given in brackets. Total = 90 points)
1. (10 pts) Consider a complex physical system S to be studied and a mathematical model of the system Φ(S) employed in the study1. Give the truth or otherwise of the statements given below when dealing with the model Φ(S).
A: i) Φ(S) deals with more variables than the number of variables
in an exact description of the physical system S itself;
ii) Φ(S) is easier to solve using software tools (e.g., MATLAB);
iii) It is impossible to have Φ(S) produce exactly the same behavior as S;
iv) Φ(S) can always be expressed in a closed-form (i.e., enables computationally tractable solutions).
B The piece-wise linearization in a model Φ(S) to capture an otherwise non-linear behavior of a physical system S:
i) Simplifies a computer solution of the system behavior;
ii) Improves the accuracy of modeling;
iii) Represents a behavior that holds over the entire operating region of S; iv) Simplifies the operations of the actual system S.
Give a brief explanation for your choices.
2. (10 pts) Consider a replicated web server system that maintains K functionally identical servers to process client requests for operations (say, a purchase transaction processed by Amazon.com ser- vice). The degree of server replication K impacts the overall system-level performance: namely, the client-experienced latency, the system-internal overhead incurred to service a client request , and the throughput rate (i.e., number of operations completed per sec)2. Choose the most appropriate answer in each case when the number of servers K is increased:
A: An increase of K: i) Lowers the latency; ii) increases the latency; iii) does not affect the latency;
B: An increase of K: i) Lowers the overhead; ii) increases the overhead; iii) does not affect the overhead;
C: An increase of K: i) Lowers the throughput; ii) increases the throughput; iii) does not affect the throughput.
Give reasons for your choices.
3. (15 pts) Give the truth or otherwise of the following statements (along with a brief explanation):
A: Given a server of capacity µ to process a stream of customer transactions, increasing the number of servers from 1 to 2 is equivalent to replacing the 2 servers with a single combined server with capacity µeff , where:
i) µ < µeff < 2µ;
ii) µeff = 2µ;
iii) µeff > 2µ;
iv) µeff < µ;
v) None of the above.
B: Given a FSM representation Ψ(S) and a queuing-theoretic representation Q(S) of a discrete event system S, the mapping possible between Ψ(S) and Q(S) is3 :
i) One can obtain Q(S) from Ψ(S) but not vice-versa;
ii) One can obtain Ψ(S) from Q(S) but not vice-versa;
iii) Ψ(S) and Q(S) are orthogonal to each other;
iv) Ψ(S) and Q(S) are isomorphic (i.e., one can be obtained from the other).
C: With discrete-event representations of a system S being simulated, the modeling of time-advancement depicts the following:
i) Time advances by uniform intervals;
ii) Time may advance by non-uniform intervals;
iii) Time advances continuously4 ;
iv) The number of event occurrences is directly proportional to the time elapsed.
4. (15 pts) Consider a set of k networked computers S = {s1 , s2 , ··· , sk } organized in the form of a unidirectional ring5 . The ring is defined by two variables maintained by each computer x ∈ S: succ(x) and pred(x) which denote the address of immediate successor of x in the forward direction and the address of immediate predecessor of x in the backward direction respectively. If, for instance, a computer y is the successor of computer x in the ring, then succ(x) = y and pred(y) = x. See Figure 1 for an illustration.
A: Write the axiomatic relations to prescribe the ring-structured organization of computers S. Given6 an example with 4 machines to show how the relations capture a ring structure. Be sure to give a counter-example: namely, how the relations capture a scenario of broken ring structure.
B: If S contains only one computer, can a ring structure be prescribed ? If yes, explain how. If not, explain why. Your explanation should be from a mathematical standpoint.
Figure 1: A sample ring-structure to connect computers
5. (25 pts) An AIMD-based video rate adaptation system (discussed in class) can be represented as a computational function of the form: L = net(λ), where λ > 0 and L > 0. Internal details of net( ···) to compute L for an input λ are not known to the network system programmer, i.e., net(λ) appears as a black-box taking λ as input and returning L as output. But the programmer has a high-level view how the net( ···) behaves when λ changes, as given by the relationship:
net(λ +∆) > net(λ) > net(λ − ∆)
for ∆ > 0. The main control program invokes the net(λ) function in the following ways:
Suppose λ0 is an initial input for which net(λ0 ) returns a value L0 > δh , where δh > 0. In that case, the program reduces λ in multiple steps of (β × L) decrements to a value λf such that net(λf ) < δl , where β > 0 and 0 < δl < δh. Thereupon, the program increases λ in multiple steps of α increments to a value λt such that net(λt ) > δh , where α > 0. Thereafter, the decrease procedure kicks in again. It is thus a repetitive cycle of decrease and increase of λ .
The computation steps in the program interacting with net( ···) are shown in Figure 2-(a) as a pseudo- code in a C-like language. Figure 2-(b) shows the empirical behavior of program with respect to the time-steps i = 1, 2,, 3, ··· for certain base values β = β 、and α = α、.
A: State the truth or otherwise of the following mathematical properties exhibited by the L = net(λ) function — i.e., a characterization of how L increases with respect to an increase in λ): i) Monotonically convex increase; ii) Monotonically concave increase; iii) Linear increase; iv) No changes, i.e., constant. Give reasons for your choice.
B: Show an empirical graph of how (L, λ) varies with respect to i for each of the cases: i) β >
β、,α = α、; ii) β = β、,α > α、; iii) β > β、,α > α、; and iv) β < β、,α < α、.
C: Can you reason about the convergence property of AIMD algorithm ??
Figure 2: Behavior of program that embodies a black-box view of L = net(λ) function
6. (15 pts) There are three possible functions in a networked system S — sensing, inference, and diagnosis. Sensing is about a direct measurement of the internal parameters of S; inference refers to making an intelligent guess about the parameters of S by indirect measurements from an observed behavior (when direct measurement is not possible); and diagnosis is the reasoning about the causes for an observed behavior of S. Indicate the function that the following activities pertain to (with a brief explanation to corroborate your answer):
(i) Thermometer that determines the human body temperature by observing the expansion of mercury (along a narrow tubular column) caused by body heat;
(ii) An auto salesman determining the financial affluence of potential buyers by looking at their spending patterns (e.g., what houses they live, restaurants they dine, type of dresses they wear);
(iii) A bank determining the loan worthiness of potential borrowers by examining their credit scores, job stability, monthly income, family commitments, etc;
(iv) Blood test conducted on a patient to reveal the platelet count and cholesterol level;
(v) Identifying the brake effectiveness in a car by observing the stopping distance and vehicle vibrations when applying the brake at different speeds.