CSE 221: Probabilistic Analysis of Computer Systems Topics covered: Simple queuing models (Sec )

M/M/1 queue  Web server example:

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

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

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

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

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

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

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

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

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