Most of the reading on queueing theory I've done focuses on when the arrival rate is less than the service rate so that the queue doesn't explode. However, if I have a queueing system (either M/M/1 or M/M/c) where the arrival rate is greater than the service rate, how can I find properties such as the following:
- How large will the queueing system grow after a certain amount of time?
- What is the probability that the expected wait time upon arrival will be greater than a certain amount of time at time t?
- How many servers should the system have so that the queue never grows beyond a certain size in a fixed amount of time?