# Thread: Probability in an "on-off" cycle

1. ## Probability in an "on-off" cycle

A process runs in a cycle and has a wait time prior to and then after a period of activity. So say at time = 0 the process is "off" for a count of 10, then "on" for a count of 4, then "off" for a count of 10. That would be one cycle. The cycle may or may not restart right away. If I have some number - say 20 for instance - of these processes starting randomly, how do I compute the probability that a chosen number of them - 5 for instance - are in the "on" state?

2. ## Re: Probability in an "on-off" cycle

What are the distributions of those waiting times staying on/off state respectively? Please provide more information / assumptions for these.

E.g. this maybe modeled by a continuous Markov chain if exponential distribution is chosen.

3. ## Re: Probability in an "on-off" cycle

Originally Posted by BGM
What are the distributions of those waiting times staying on/off state respectively? Please provide more information / assumptions for these.

E.g. this maybe modeled by a continuous Markov chain if exponential distribution is chosen.
There is no additional information. Beyond that I don't understand your question.

4. ## Re: Probability in an "on-off" cycle

Is this for homework?

5. ## Re: Probability in an "on-off" cycle

Originally Posted by Dason
Is this for homework?
Is this strictly a homework forum?

6. ## Re: Probability in an "on-off" cycle

No - of course not. But we do treat homework a little differently and if it was homework then I would tell you to ask your instructor for some additional info because the problem isn't completely well defined at the moment.

7. ## Re: Probability in an "on-off" cycle

Originally Posted by Dason
the problem isn't completely well defined at the moment.
Why is that?

8. ## Re: Probability in an "on-off" cycle

Is the "process" always exactly as you described? (off for 10, on for 4, off for 10) and then there isn't enough information describing what is actually going on and with what probabilities these actions happen in this:
The cycle may or may not restart right away. If I have some number - say 20 for instance - of these processes starting randomly
So what happens after the "process" ends - is it still considered off? If so then I don't really get what is happening or what the difference is between the process being 'in cycle' but off and the process not being in cycle and off.

If there are differences then without knowing something about the probability distribution of how long it takes the cycle to start up again we really can't say anything.

9. ## Re: Probability in an "on-off" cycle

Originally Posted by Dason

If there are differences then without knowing something about the probability distribution of how long it takes the cycle to start up again we really can't say anything.
OK. So the idea would be "off" vs "in-cycle but waiting". So a computer program for example may be "off" in which case it can start at any random time (maybe it waits for a keypress or some other random event), but once it starts it has to wait X counts before actually consuming CPU for some fixed time - then waits X and goes "off". So we might say we want to know the probability that for some number of these programs that CPU is being consumed. The random event - keypress or whatever - I guess would be Gaussian.

How would the approach to this differ if there were no difference between "on" and "waiting"?

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