Considering the fact that the disciples' boat was filled with water, it is amazing that the they had to awaken Jesus. This was not a large ship with cabins below deck but rather a small, open boat and Jesus was, no doubt, "soaked to the bone."  This shows Jesus' humanity and how tired He must have been. It also shows that Jesus must have been in a very deep sleep. Medical science has discovered that the deeper we sleep, the more rest our bodies get. This is a clue as to how Jesus could maintain the grueling pace He kept, along with an occasional all-night prayer time. He was receiving the maximum benefit from His sleep.

Jesus did not say "Let us go out into the midst of the sea and drown in a storm." He was going to the other side. This shows that the disciples still didn't understand Jesus' authority. They were committed to Him as their Messiah, but they hadn't yet realized that Jesus was Lord even over the physical elements. Many Christians still do this. They receive the spiritual benefits of salvation but have not reaped the physical benefits of health and prosperity, which are also part of our salvation.

Whichever we focus upon ( the storm, or the Lord in the midst of our storm ) will determine how we manage the storms we face in life. He is not asleep concerning the things we face, He's right there in our "ship," resting, because He knows we'll both get to the "other side." His peace is ours, if we believe His Word and rest in His love.