1. CSE 221: Probabilistic Analysis of Computer Systems Topics covered: Simple queuing models (Sec. 8.2.1-8.2.2)

2. M/M/1 queue  Web server example:

3. M/M/1 queue (contd..)  State transition diagram:  What is M/M/1?

4. M/M/1 queue (contd..)  Balance equations:  Steady state or limiting probabilities:

5. M/M/1 queue (contd..)  Traffic intensity:

6. M/M/1 queue (contd..)  Steady state probabilities in terms of traffic intensity:  Server utilization:  Average number of customers in the queue:

7. M/M/1 queue (contd..)  Response time:  Little’s law:

8. M/M/1 queue (contd..)  Numerical example:

9. M/M/m queue (contd..)  What is M/M/m?  State transition diagram:

10. M/M/m queue (contd..)  Balance equations:

11. M/M/m queue (contd..)  Steady state probabilities: