The Persian Empire extended much further east beyond the boundaries of this map.  The Persians controlled territory across Parthia and into the edge of India.  They also had control of areas along the eastern side of the Caspian Sea northward toward the Aral Sea.  Also note that during the time of Xerxes when he lead the great invasion of Greece, the Persians controlled parts of Thrace and Macedonia, not indicated on this map.  The area shown is sufficient to give a general idea of the extent of the Persian Empire.