[RPG] the actual casting time of Summon Monster

No attack of opportunity is granted.

According to the Pathfinder's RSD attacks of opportunity are triggered only by:

• moving out of a square in the threatened area of a hostile creature. Exceptions are: the 5-ft. step, the withdraw action, and teleportation (but not necessarily casting a teleport spell).
• performing a distracting act while in a square in the threatened area of a hostile creature. This usually include:
  • attacking with a ranged weapon,
  • attacking unarmed,
  • delivering a coup de grace,
  • performing a combat maneuver,
  • casting a spell,
  • using a touch spell (if the spell is harmful you are considered armed; you don't draw AoO from the target, but sill draw from other enemies)
  • activating a spell-like ability,
  • activating a spell-completion magic item,
  • drinking a potion or applying an oil,
  • loading a crossbow,
  • moving heavy objects around,
  • picking up objects,
  • sheathing a weapon,
  • retrieving a stored item,
  • standing up from prone,
  • escaping from a net,
  • locking or unlocking a weapon to a gauntlet,
  • preparing to throw a splash weapon,
  • running,
  • using many skills.

Appearing into a square because of a summoning spell seems to not fall in these two categories.

However, appearing in the middle of a fight may or may not be considered a distracting act, according to how your group interpret Summoning effects.

Probably so by RAW and yes in practice.

The reason a summoned creature takes until the beginning of your next turn to act is because that's when a one-round spell comes into effect: the creature is not present before then.

A spell that takes 1 round to cast is a full-round action. It comes into effect just before the beginning of your turn in the round after you began casting the spell. You then act normally after the spell is completed.

Therefore, using the Sp as a standard action allows the usual rules of spell effect timing to control: the creature arrives as you finish casting, on your turn, and acts immediately, potentially before the remainder of your actions on that turn.

It's less clear whether the summoned creature acts on a potentially independent initiative count in later rounds (since it says that it "acts on your turn", but not that it always does), but one could argue that the ability to instruct the summon to take various actions, including delaying or readying, would imply that.

In any case, though, even if the creature acts on your turn, simply readying an action to summon a new one once it has finished its next attack sequence will do the job in essentially all cases. A readied action takes place outside your regular turn, so there is no problem there.