## Cloud Computing, Test 2 for the courseCS 4365/CS 5354, Spring 2015

Name: _____________________________________________________

1-2. A student is taking two important classes. There is only time t left for studying for both classes, so if the student spends time t1 studying for the first class, this student will have time t2 = t − t1 left for the second class.

• The grade for the first class depends on the time t1 as f1(t1) = (t − t1)2.
• The grade for the second class depends on the time t2 as f2 = (t − t2)2, i.e., since t2 = t − t1, as
f2(t1)= (t1)2.
The student wants to maximize both grades f1(t1) and f2(t1).
• What is the solution to this multi-objective optimization problem when we select the equal weights w1 = w2 = 0.5?
• What is the solution to in the general cases, when we select an arbitrary value w1 from the interval [0, 1], and take w2 = 1 − w1?
• Why multi-objective optimization is important for cloud computing?

3. Let us now assume that every day, the company uses at least m = 100 computations, and the probabilities of different numbers of computations x is described by the power law p(x) = A * x−α, with α = 3. Assume that the cost of a unit in-house computation is c0 = 10 money units per computation unit and the cost of computing in the cloud is c1 = 20 money units per computation unit.

• How much computing power x0 should be purchased for in-house computations?
• What is the resulting expected cost?
• Compute the expected costs when we do all the computations exceeding m in the cloud, and show that the optimal arrangement indeed saves money.

In these computations, you can use the formulas that we derived in class for the power law case:

• the optimal amount of computing power to purchase is x0 = m * (c1 / c0)1 / (α − 1);
• the resulting expected cost is equal to ((α − 1) / (α − 2)) * c0(α − 2) / (α − 1) * c11 / (α − 1) * m;
• if we do all the computations exceeding m in the cloud, then the resulting cost is
m * (c0 + c1 / (α − 2)).

4. Estimate the costs and decide whether it is beneficial to sign a contract with the cloud provider for T = 2 years:

• the cost of buying a unit of computations on a year-by-year basis is c0 = 1;
• the contract offer a discount price c1 = 0.9,
• the discount rate is q = 0.8, and
• the price of computing decreases yearly by a factor of v = 0.9.

5. Neural networks:

• Why neural networks are needed for cloud computing?
• Let us assume that we have are training a neural network with K = 2 neurons to learn multiplication. This means that for inputs x1 = 2.0 and x2 = 3.0, the desired output is Y = 6.0. On a certain iteration, we have wki = 0 for all k and i, so that the outputs of the non-linear neurons are equal to 0.5: y1 = y2 = 0.5. Suppose that at this iteration, W1 = W2 = 1.0 and W0 = 0.0. Assuming that α = 0.1, describe the values of all the weights on the next iteration.

Reminder:

• In the first layer, we have K non-linear neurons. Each neuron k (k = 1, 2, ..., K) transforms the input signals x1, ..., xn into a signal
yk = s0(wk1 * x1 + ... + wkn * xn − wk0),
where s0(z) = 1 / (1 + exp(−z)).
• The last linear neuron then transform these signals yk into a single output
y = W1 * y1 + ... + WK * yK − W0.
For each pattern with the known desired output Y, once the NN computed the input y, you can find the error Δy = y − Y. Based on this error, you can compute the changes to all the weights as follows:
• ΔW0 = α * Δ y, for some small number α > 0;
• ΔWk = − yk * ΔW0;
• Δwk0 = − ΔWk * Wk * (1 − yk);
• Δwki = − xi * Δwk0.

6. Fuzzy techniques:

• Why fuzzy techniques are needed for cloud computing?
• Briefly describe the main steps of fuzzy techniques.
• Which "and"-operations are typically used in fuzzy techniques? If the expert's degree of belief in a statement A is 0.6 and the expert's degree of belief in a statement B is 0.8, what is the expert's degree of belief in the statement "A and B"?

7. What is green computing? Explain the need for saving energy in cloud computing.

8-9. Describe, in detail, the paper that you reviewed as a project for this class:

• what problem is addressed in his paper,
• what solution is proposed for this problem, and
• (if applicable) what are the remaining open problems.

10. Briefly describe someone else's project for this class.