Answered step by step
Verified Expert Solution
Link Copied!

Question

1 Approved Answer

Consider a set ot n machines and a solitary fix office to support these machines. Assume that at the point when machine I, 1, n,

Consider a set ot n machines and a solitary fix office to support these machines. Assume that

at the point when machine I, 1,

n, tails it requires a dramatically disseminated measure of work vvith rate

Vito fix it. The maintenance office isolates its endeavors similarly among all followed machines in the sens.e

that at whatever point there are k bombed machines every one gets work at a pace of 11k per unit time. On the off chance that

there are an aggregate of r working machines, including machine I, at that point I tails at a prompt rate

(a) Define a fitting state space in order to have the option to examine the first framework as a

nonstop time Markov chain.

(b) Give the quick progress rates (that is, give the q).

(c) Write the time reversibility conditions.

(d) Find the restricting probabilities and snow that the cycle is time reversible.

Q54

('2')

curves

Think about a chart with hubs 1, 2,

, n and the

n. (See

Area 3.6.2 for proper definitions.) Suppose that a paicle moves along this chart as

follows: Events happen along the circular segments (I, D as per autonomous Poisson measures with rates

An occasion along bend (I, D makes that curve become energized. It the molecule is at hub iat the

second that (j, J) gets energized, it promptly moves to hub j, j, j-1,

, n. Let PJ

mean the extent oftime that the molecule is at hub j. Show that

1

n

Clue: use time reversibility.

Q55

A sum of N clients move about among r workers in the accompanying way. At the point when a client is

served by worker he at that point goes overto worker j, I, with likelihood 1/(r 1). Ifthe worker he

goes to is free, at that point the client enters administration; other"se he joins the line. The assistance

times are altogether autonomous, with the assistance times at worker I being dramatic with rate g, I - 1,

, r. Leave the state whenever alone the vector (171, nr), where njis the quantity of clients

by and by at worker I, I .

(a) Argue that lfX(t) is the state at time t, at that point {X t > O) is a constant time Markov

chain.

(b) Give the microscopic paces of this chain.

(c) Show that this chain is time reversible, and track down the restricting probabilities.

Q56

Four laborers share an office that contains four phones. Whenever, every laborer is all things considered

"working" or "on the telephone." Each '*vorking" time of specialist I goes on for a dramatically

circulated time with rate A1, and each "on the telephone" time frame goes on for a dramatically disseminated

time with rate 1, 2, 3, 4.

(a) What extent of time are generally laborers "working"?

Let equivalent 1 if specialist I is working at time t, and let it be 0 in any case. Let

X'(t) (NJ X2(t), X3(t), X4(t)).

(b) Argue that {X(t), t > 0} is a constant time Markov chain and give its tiny rates.

(c) Is {X(t)} time reversible? Why or why not?

Assume now that one ot the telephones has separated. Assume that a laborer who is going to

utilize a telephone however discovers them all being utilized starts another "working" period.

(d) What extent of time are on the whole laborers "working"?

Step by Step Solution

There are 3 Steps involved in it

Step: 1

blur-text-image

Get Instant Access to Expert-Tailored Solutions

See step-by-step solutions with expert insights and AI powered tools for academic success

Step: 2

blur-text-image

Step: 3

blur-text-image

Ace Your Homework with AI

Get the answers you need in no time with our AI-driven, step-by-step assistance

Get Started

Recommended Textbook for

Wavelet Based Approximation Schemes For Singular Integral Equations

Authors: Madan Mohan Panja, Birendra Nath Mandal

1st Edition

0429534280, 9780429534287

More Books

Students also viewed these Mathematics questions

Question

2. Are there more men or women? (find statistics)

Answered: 1 week ago

Question

understand how design and writing connect in mass communication.

Answered: 1 week ago

Question

Who is the audience?

Answered: 1 week ago