Track of the proportion of the time

Reference no: EM13983582

1. Write a computer program to simulate the queue in Exercise 20. Have your program keep track of the proportion of the time that the queue length is j for j = 0, 1, . . . , n and the average queue length. Show that the behavior of the queue length is very different depending upon whether the traffic intensity s has the property s <>1, s = 1, or s > 1.

2. In the queueing problem of Exercise 20, let S be the total service time required by a customer and T the time between arrivals of the customers.

(a) Show that P (S = j) = (1 - r)j-1r and P (T = j) = (1 - p)j-1p, for j > 0.

(b) Show that E(S) = 1/r and E(T ) = 1/p.

Reference no: EM13983582

Questions Cloud

Extension to the case : The theorem that Pn → W was proved only for the case that P has no zero entries. Fill in the details of the following extension to the case that P is regular. Since P is regular, for some N, PN has no zeros.

Transition matrix of an ergodic markov chain : Let P be the transition matrix of an ergodic Markov chain. Let x be any column vector such that Px = x. Let M be the maximum value of the components of x. Assume thatxi = M . Show that if pij > 0 then xj = M . Use this to prove that x must ..

Compute the fixed vector : Form a Markov chain with states the number of sites occupied. Modify the program FixedVector to compute the fixed vector. Use this to check your conjecture by simulation.

What is the electric potential at this point : What is the electric field strength a radial distance of 4.5m from a point charge of q=1.5 x 10-8 C. What is the electric potential at this point?

Track of the proportion of the time : Write a computer program to simulate the queue in Exercise 20. Have your program keep track of the proportion of the time that the queue length is j for j = 0, 1, . . . , n and the average queue length.

Power of the transition matrix : 1. Define f (r) to be the smallest integer n such that for all regular Markov chains with r states, the nth power of the transition matrix has all entries positive. It has been shown,14 that f (r) =r2 - 2r + 2.

Draw a graph how electric field varies with radial distance : A point charge of 5 μC is then placed at its centre. Draw on, the figure below in Electrical Field Lines both inside and outside the shell and any charge that is induced on the hollow shell. Draw a graph (including values) of how the electric fiel..

Probability vector for appropriate seven state markov chain : Let Sn denote the total of the outcomes through the nth toss. Show that there is a limiting value for the proportion of the first n values of Sn that are divisible by 7, and compute the value for this limit. Hint : The desired limit is an equilibrium..

Review the income statement for the country vista company : Prepare a Statement of Cash Flows. Cite all references used and detail formulas and or calculations. Review the income statement for the Country Vista Company. You will use the income statement to help you complete Part 1 and Part 2 below.

User Account

All Pages