What if Alexander invades Arabia

Alexander had already send expeditions to cruise around the Arabian peninsula and the first trustworthy maps of the region were made back then.

He intended to capture costal cities that would act as commercial stations. They would support commerce between Egypt, Persia and India and would help him consolidate his empire. After his death, with the Diadochi in constant war between them, there was no point for commerce between them and therefore no reason for the conquest of Arabia. (no need for oil back then, as Evildoer has noticed!)

You mean Saudi Arabia?

I don't know much of this... but I don't think Saudi Arabia would have had much attraction for Alexander because there was virtually no useful resource there that could be exploited. Alexander did not need oil after all...

I think Alexander would have most likely attacked India first. The sub-continent was rich, although not easy to conquer.

That could have been possible. Contrary to popular knowledge, in classical times Arabia was home to a series of affluent kingdoms, especially along the western coast and the southwestern tip of the peninsula where rainfall was relatively high and stable. The Yemeni kingdom that built the famous Ma'rib dam was one of them--and it was also famous for being the principal supplier of frankincense. So, overall, Arabia was not probably a crucial spot by then, but a well-managed invasion followed by the establishment of a capable government could have actually ended up as a profitable enterprise.