SuggestFinalsolution

# SuggestFinalsolution - 1 Customers arrive at a 2-server...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 1. Customers arrive at a 2-server station in accordance with a Poisson process having rate 1. Upon arriving, a customer joins the queue when both servers are busy. The service times of servers A and B are exponential with respective rates 2 and 1. Whenever a server completes a service, the person first in line enters service. An arrival finding both servers free goes to server A. (a) (20 marks) Define an appropriate continuous-time Markov Chain for this model and find the limiting probabilities. (b) (5 marks) Is this a time reversible continuous-time Markov Chain? Why? (c) (Bonus 5 marks) Modify the system as follows: When server A is idle and server B is busy, the customer will immediately shift to A. Does this modified system make a time reversible continuous-time Markov Chain? Why? Suggested solution: (a) Let the state be the number of customers in the system. We have the following transition rate diagram. Let μ 1 = 2, μ 2 = 1, λ = 1. Forming the flow balance equations, we have P = 2P 1A + P 1B // at state 0 3P 1A = P + P 2 // at state 1 A 2P 1B = 2P 2 // at state 1 B P k = (1/3) k-2 P 2 . // at state k for k ≥ 2 We can solve from the first three equations and obtain P 1A...
View Full Document

{[ snackBarMessage ]}

### Page1 / 3

SuggestFinalsolution - 1 Customers arrive at a 2-server...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online