Essentially you need to compute the difference between two timestamps. To make it easier, you may need to add a custom attribute to hold the value of this "period", and update the attribute programmatically using attribute customization scripts or precondition/follow-up actions. For example, when a work item transitions into the "waiting state", you set the value of "period" attribute to 0. Oh, you may need another attribute to hold the transition timestamp. Then when the work item transitions out of the "waiting state", you compute the difference between "now" and the recorded timestamp, and get the "period" value and set it accordingly. The same goes to other "period" that you may consider.
Note that if you want to show the "period" when the work item is still in the "waiting state", you will need to do dynamic calculation (between "now" and the last transition timestamp"). I think this can be done only with reports, not queries.