Second, if you find yourself in this type of situation, put the problem on the table the very first time a production support event occurs that drags resources off your project. Complain openly about the problems this causes. Use the large body of evidence about the impact of task switching, interruptions, etc. on productivity to make your case. Make it clear that project dates are dependent on resource availability and be clear about the slippage that is occurring.
Some project managers will try to forecast project plans using lower allocations, like putting a body on their project at 30% or 50% or some other fraction of a person. I don't recommend that. All it does is hide the problem behind a plan, and it voids any recognition you might get from delivering early, since others will attribute it to higher availability than expected even if it is due to your brilliant project management or the spectacular efforts of the project team.
You should insist on dedicated resources, at least to the limit of your organizations tolerance for complaining. Don't take this one lying down. Take care of it right away or you will watch your project fail.