Vayigash starts with Yehuda's plea to Yoseph to take Binyamin's place as a slave. At the conclusion of his declamation, the Torah records that Yoseph 'could not hold back', and that he then revealed his true identity to his brothers. The fact that he 'held back' implies that , had he been able, he would have kept stringing them along. Why to what end? What was his original plan?
There are a number of different theories about what Yoseph was trying to accomplish with the whole charade: bring about the fruition of his dreams, make his brothers repent, etc. Part of the drama of these parshiyot, which indeed provide some of the best drama in all of TaNach, is in trying to figure out who knows what, when.
It seems to me that Yoseph never intended to reveal himself to his brothers. As far as he was concerned, they were strangers ('va-yitnaker Yosef le-echav') and he wanted nothing to do with them. He felt that their betrayal of him had severed familial ties; he could not have known what Yaakov's role in the sale was: he may have missed his father, or he may have thought that his father was somehow party to his disenfranchisement (Menashe = 'for God has made me forget my father's house'). Either way, the only family member about whom he was concerned was Binyamin, his full brother who was very young at the time of Yoseph's departure.
The entire charade was to get Binyamin down to Egypt and keep him there. He designed the frame-up job to give a pretense for keeping Binyamin there while turning the rest of them loose. He even provoked their jealousy to make them less willing to go to bat for their pampered brother. Had all gone well, he would have been free to start his own, Rachelide family together with his brother.
He did not count on the brothers going to bat for Binyamin. He did not count on the fact that Yaakov never got over Yoseph's disappearance, as Yehuda described in his speech. Thus, Yehuda's speech causes Yoseph to change his plan and leads to the dramatic resolution of the fraternal conflict.