6. Continous Time Markov Chain: A roadside Dhaba has 4 chairs. Customers comeaccording to a Poisson process with a rate of 1 customer per 10 minute and take anempty chair and eats, occupying the chair with an exponential distribution with meanof 10 minutes. If all chairs are filled, the customer just leaves. The rate diagram isshown in figure 2 below where each state is the number of occupied chairs.3FIG. 2.(a) Explain the rates in the diagram. Why there are different numbers in the arrowsgoing 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 beocupied at any given time.

This is very simple. Solution 1) The rates in the diagram is explained below. If 1st person finds…

Answered: Continous Time Markov Chain: A roadside…

Engineering

Computer Science

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

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

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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.

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