The wikipedia page of Battle of Yarmouk you cite, had impressions on this.
Vahan was instructed by Heraclius not to engage in battle until all avenues of diplomacy had been explored. This was probably because Yazdegerd III's forces were not yet ready for the offensive in Iraq. Accordingly, Vahan sent Gregory and then Jabalah to negotiate, though their efforts proved futile. Before the battle, on Vahan's invitation, Khalid came to negotiate peace, to a similar end. These negotiations delayed the battles for a month. On the other hand, Caliph Umar, whose forces at Qadisiyah were threatened with confronting the Sassanid armies, ordered Sa`d ibn Abi Waqqas to enter into negotiations with the Persians and send emissaries to Yazdegerd III and his commander Rostam Farrokhzād, apparently inviting them to Islam. This was most probably the delaying tactic employed by Umar on the Persian front. Meanwhile, he sent reinforcements of 6,000 troops, mostly from Yemen, to Khalid. This force included 1,000 Sahaba (companions of Muhammad), among whom were 100 veterans of the Battle of Badr, the first battle in Islamic history, and included citizens of the highest rank, such as Zubayr ibn al-Awwam, Abu Sufyan, and his wife Hind bint Utbah.
It is said( by I do not remember who), the byzantines were supposed to wait for the arrival and uniting with the sassanids. On the battlefield of Yarmouk, they waited for a month. Umar sent a constant stream of reinforcements, which gave Vahan the impression that the muslim armies were really large, and that waiting for battle anymore would turn the odds against them.
On the front with the persians, there were the stalling moves, of negotiating and inviting to islam , which kept them occupied and unable to co-ordinate.
Pardon the vagueness.