Need the solution of Question 1 and 2 all parts.
Student ID: TELE8882 - Assignment 2, S2 2020 1 TELE8882 ASSIGNEMENT 2 Due: October 16, 2020 Name: Surname: Student ID: Q1 (35) Q2 (35) Q3 (30) Total (100) Honor Pledge: By submitting your responses to the questions in this assignment, you accept to obey to the following Honor Pledge: “I have neither given nor received aid, nor have I used unauthorized resources, on this assignment.”. Student ID: TELE8882 - Assignment 2, S2 2020 2 QUESTION 1 Consider the technique of adaptive request re-issues to reduce the latency response in datacenter networks. Assume that individual server response times are exponentially distributed. Part I: Assuming zero lead time to re-issue requests, calculate the 90th percentile latency values with 10 servers simultaneously processing the requests when i. Expected individual server response time is 0.1 [msec] ii. Expected individual server response time is 1 [msec] iii. Expected individual server response time is 5 [msec] Part II: Assuming 3 [msec] lead time to re-issue requests, calculate the 90th percentile latency values with 10 servers (including the first one to which the request was originally submitted) processing the requests when i. Expected individual server response time is 0.1 [msec] ii. Expected individual server response time is 1 [msec] iii. Expected individual server response time is 5 [msec] Student ID: TELE8882 - Assignment 2, S2 2020 3 QUESTION 2 Consider the technique of trading-off completeness for latency to reduce the latency response in datacenter networks. Part I: Assuming that the top ranked document lies in one of 1000 servers, calculate the utility loss of getting response from the fastest 990 servers. Part II: Assuming that the top ranked document lies in type A servers (300 of them) with prob- ability 0.6 and in type B servers with probability 0.4 (700 of them), calculate the utility loss of getting response from the fastest 295 type A servers and the fastest 690 type B servers. Part III: Repeat Part II by assuming that the final response is returned when we get a response from the fastest 990 servers. Assume server response times are identically distributed for all the servers. Student ID: TELE8882 - Assignment 2, S2 2020 4 QUESTION 3 In lectures, we modelled server response times using exponential distributions for the sake of an- alytical simplicity. Exponential distribution is a good model to start with to gain intuition about latency values to process requests in datacenter networks if no empirical data is available. On the other hand, some datacenter latency measurement experiments suggest that server response times exhibit statistically good fit to log-normal distributions. In this question, you will investigate the performance of adaptive request re-issues and trading-off completeness for latency techniques for log-normal server response times numerically. A random variable X is called a log-normal random variable if X can be written as X = exp (µ+ σY ) , where Y is a normal random variable (zero mean, unit variance), and µ and σ are the logarithmic mean and logarithmic standard variance of X. Part I: For µ = 1, σ = 2, lead time Ts = 3 [msec] and number of servers to process a request N = 10, simulate in MATLAB 95th and 99th percentile latency values to process a request when adaptive request re-issues technique is employed. Provide your code, simulated values and compare these values with those obtained if only one server is used to process the request, i.e., obtain percentage reduction in latency percentiles. Part II: Consider now the technique of trading-off completeness for latency to reduce the latency response times in datacenter networks with the same log-normal distribution parameters for in- dividual server response times, i.e., µ = 1 and σ = 2. Assume that the top ranked document lies in one of 103 servers equally likely. Simulate in MATLAB 95th and 99th percentile latency values obtained by using the technique of trading-off completeness for latency with utility loss 0.01 and 0.001. Repeat the same simulation for 104 servers. Provide your code, simulated values and compare these values with those obtained if responses from all servers are collected to process the request, i.e., obtain percentage reduction in latency percentiles. Hint: Some useful MATLAB functions you can use are lognrnd and prctile.