Well,

historically, just as in Medieval and Early Modern history it depended a lot on the circumstances... often a besieging army could be as devastated by (food) shortages and disease as the besieged were. Similarly many societies lacked the capabilities to support a strong siege, or storm a fortification in a state of readiness...

And then it became a quick calculation of potential rewards vs risks. The Romans were one of the most effective (at both) because they possessed the resources, the capabilities and will to do both.
But even (at least in the later Roman era) when going up against more spohisticated, prepared enemies with strong resolve and no major defections and betrayals, they could usually only mount a single major siege a season.

Similarly, assuming their defences were in order, most Roman cities were fairly safe from incursions from the Germanic peoples.