Answered step by step
Verified Expert Solution
Link Copied!

Question

1 Approved Answer

The ammount of waste, in tonnes, at a recycling depot can be modelled as a CTMC, where the state of the system represents the amount

image text in transcribed
The ammount of waste, in tonnes, at a recycling depot can be modelled as a CTMC, where the state of the system represents the amount of waste. Trucks arrive as a Poisson process with rate A = 3 per hour, and each truck dumps 1 tonne of waste. Each tonne of waste is processed by the facilicty in an exponentially distributed amount of time with mean = = 1 = - hours. Assume that the size of the yard is infinite and define lim P (() = *; [-+00 (a) What is the condition for an equlibrium solution to exit? OXCH OX= H (b) If the system is in equlibrium and the yard is visited at a random time, what is the probability there will be 1 tonnes of waste in the yard? (a number) (c) If the system is in equilibrium, what is the proportion of time the system will be in state k ? O TK O time is independent of k O ATE (d) Calculate the expected amount of waste in the yard at equilibrium. [a number)

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_2

Step: 3

blur-text-image_3

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

Discrete Mathematics, Edition

Authors: Seymour Lipschutz, Marc Lipson

4th Edition

126425881X, 9781264258819

More Books

Students also viewed these Mathematics questions

Question

2. The purpose of the acquisition of the information.

Answered: 1 week ago

Question

1. What is the meaning of the information we are collecting?

Answered: 1 week ago