Answered step by step
Verified Expert Solution
Question
1 Approved Answer
05/7: Consider the two discrete time markov chains shown in the following figure. Assume you start at state I. You are interested in the long-term
05/7: Consider the two discrete time markov chains shown in the following figure. Assume you start at state I. You are interested in the long-term (limiting) probability of finding the chain in state 3). (a) For which of the two chains is the above probability higher? Justify your answer. (b) Which of the two chains converges to its stationary distribution fuster? Justify your answer. (C) You want to download a large file, and you are offered 4 options of servers to choose from. All servers have the same arrival rate for traffic, Poisson with rate 1 = 0.5, but differ in terms of the service times: Server 1: file download times are exponentially distributed with mean 1 (time unit). Server 2: all files take exactly 1-time unit to download. Server 3: file download times are uniformly distributed in (0,2). Server 4: file download times are either exactly 0.2 with probability 0.9 or 8.2 with probability 0.1. Which server would you prefer if you would want to minimize the (queueing) time you wait until your file starts downloading? Rank all 4 servers in terms of your preference 0.04 0.02 0.02 01 0.90 0:38 as 07 09 (a) (b) 05/7: Consider the two discrete time markov chains shown in the following figure. Assume you start at state I. You are interested in the long-term (limiting) probability of finding the chain in state 3). (a) For which of the two chains is the above probability higher? Justify your answer. (b) Which of the two chains converges to its stationary distribution fuster? Justify your answer. (C) You want to download a large file, and you are offered 4 options of servers to choose from. All servers have the same arrival rate for traffic, Poisson with rate 1 = 0.5, but differ in terms of the service times: Server 1: file download times are exponentially distributed with mean 1 (time unit). Server 2: all files take exactly 1-time unit to download. Server 3: file download times are uniformly distributed in (0,2). Server 4: file download times are either exactly 0.2 with probability 0.9 or 8.2 with probability 0.1. Which server would you prefer if you would want to minimize the (queueing) time you wait until your file starts downloading? Rank all 4 servers in terms of your preference 0.04 0.02 0.02 01 0.90 0:38 as 07 09 (a) (b)
Step by Step Solution
There are 3 Steps involved in it
Step: 1
Get Instant Access to Expert-Tailored Solutions
See step-by-step solutions with expert insights and AI powered tools for academic success
Step: 2
Step: 3
Ace Your Homework with AI
Get the answers you need in no time with our AI-driven, step-by-step assistance
Get Started