Homework Help is Here – Start Your Trial Now!
Engineering
Computer Science
Continous Time Markov Chain: A roadside Dhaba has 4 chairs. Customers come

Continous Time Markov Chain: A roadside Dhaba has 4 chairs. Customers come

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
See similar textbooks
icon
Related questions
Question
6. Continous Time Markov Chain: A roadside Dhaba has 4 chairs. Customers come according to a Poisson process with a rate of 1 customer per 10 minute and take an empty chair and eats, occupying the chair with an exponential distribution with mean of 10 minutes. If all chairs are filled, the customer just leaves. The rate diagram is shown in figure 2 below where each state is the number of occupied chairs. 3 FIG. 2. (a) Explain the rates in the diagram. Why there are different numbers in the arrows going backwards. (b) Find the generator G for this process. (e) If 3 chairs are occupied, what is the expected time untill it changes. (d) Find the stationary distribution and hence the probability that 3 chairs will be ocupied at any given time.
Transcribed Image Text:6. Continous Time Markov Chain: A roadside Dhaba has 4 chairs. Customers come according to a Poisson process with a rate of 1 customer per 10 minute and take an empty chair and eats, occupying the chair with an exponential distribution with mean of 10 minutes. If all chairs are filled, the customer just leaves. The rate diagram is shown in figure 2 below where each state is the number of occupied chairs. 3 FIG. 2. (a) Explain the rates in the diagram. Why there are different numbers in the arrows going backwards. (b) Find the generator G for this process. (e) If 3 chairs are occupied, what is the expected time untill it changes. (d) Find the stationary distribution and hence the probability that 3 chairs will be ocupied at any given time.
Expert Solution
steps

Step by step

Solved in 3 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Uncertainty Problems
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, computer-science and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Database System Concepts
Database System Concepts
Computer Science
ISBN:
9780078022159
Author:
Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:
McGraw-Hill Education
Starting Out with Python (4th Edition)
Starting Out with Python (4th Edition)
Computer Science
ISBN:
9780134444321
Author:
Tony Gaddis
Publisher:
PEARSON
Digital Fundamentals (11th Edition)
Digital Fundamentals (11th Edition)
Computer Science
ISBN:
9780132737968
Author:
Thomas L. Floyd
Publisher:
PEARSON
C How to Program (8th Edition)
C How to Program (8th Edition)
Computer Science
ISBN:
9780133976892
Author:
Paul J. Deitel, Harvey Deitel
Publisher:
PEARSON
Database Systems: Design, Implementation, & Manag…
Database Systems: Design, Implementation, & Manag…
Computer Science
ISBN:
9781337627900
Author:
Carlos Coronel, Steven Morris
Publisher:
Cengage Learning
Programmable Logic Controllers
Programmable Logic Controllers
Computer Science
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education
SEE MORE TEXTBOOKS