The random mass combat method of the minute that I thought of is similar to the Battlefield series of computer games, if anyone here is familiar with the concept. Making modifications to adapt it to D&D, the battleground can have several pivotal points that either belong to a particular faction or lie contested between the sides in the conflict. Both sides have many troops, but only some of them are actually present in the battle (how many should be adjusted per different battles). New troops will constantly be entering the battle to replace that fallen, entering at friendly control points.
Control points that have friendly and enemy units are contested, and no one can enter the battle there until the fight for that point is resolved. In a head-on battle, if one side controls a majority of the control points, the other side will take casualties, depleting their reserve of troops (again, how many should be based on the size of the armies, among other factors, at the DM's discretion). Optionally, both sides can have a base, a control point that cannot be captured by the other side. Assaults and sieges should start with all control points controlled by the defender, causing the defender to take casualties at a slow rate. If the attacker takes every control point, the defender takes casualties at a rapid rate.