3. Jobs arrive in a computer queue in the manner of a Poisson process with intensity λ. The centralprocessor handles them one by one in the order of their arrival, and each has an exponentially distributedruntime with parameter , the runtimes of different jobs being independent of each other and of thearrival process. Let X (t) be the number of jobs in the system (either running or waiting) at time t,where X (0) = 0. Explain why X is a Markov chain, and write down its generator. Show that astationary distribution exists if and only if λ < μ, and find it in this case.

Answered: Image /qna-images/answer/d41bb54f-971d-4d5a-ac81-40084859a4fe.jpg

Answered: 3. Jobs arrive in a computer queue in…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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The functions i)= e **2f,(x) = e*-3 %3D are O A. Insufficient information to conclude None of them O B. O C. Neither linearly dependent or independent OD. Linearly independent O E. Linearly dependent
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Bioengineers construct peptides with new functions by starting with a particular peptide, and then mutating the amino acid present at different positions. They then screen the resulting mutant peptide for the desired function. Suppose the starting peptide is 10 amino acids long. Recall there are 20 amino acids. (a) How many peptides will need to be screened if the amino acids at positions three, four, and seven are all mutated?peptides(b) If we consider all possible mutants for the amino acid at one position only, but this can be at any of the 10 positions, how many new peptides will need to be screened?peptides
Q3 (4 pts): Determine whether the Mean Value Theorem applies on the given interval. If so, find the point(s) that are guaranteed to exist by the Mean Value Theorem. f(x) = 3x² + 2x+5 [−1,1]
Consider the discrete-time dynamical system bt+1 = 2.0bt for a bacterial population. Supposing each bacterium takes up 104 μm3, write the updating function for the total volume of bacteria (in μm3) as afunction of the volume the year before:vt+1 = _____ vt + ___ μm3
Let A and B represent two variants (alleles) of the DNA at a certain locus on the genome. Assume that 40% of all the alleles in a certain population are type A and 30% are type B. The locus is said to be in Hardy- Weinberg equilibrium if the proportion of organisms that are of type AB is (0.40) (0.30) = 0.12. In a sample of 300 organisms, 42 are of type AB. Can you conclude that this locus is not in Hardy-Weinberg equilibrium?
Assume a single server queueing system with exponential inter-arrival times, and service times. Assume that the expected inter-arrival time is 10 minutes, and the expected service time is 7.5 minutes. We are interested in the expected time the customers spend waiting in queue (in minutes). Develop a Monte Carlo simulation model to estimate Wg Calculate W (expected wait time in queue), and compare it with the previous result
#14).

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