Following are examples that, to me, represent Jesus managing his accessibility.  These are taken straight out of my journaling and simply reflect my thoughts in response to reading the scripture passages: 

Mark 1:32-38. I’m reading this story of Jesus like this: One evening He healed the sick and demon-possessed that had been brought to him – “the whole town gathered at the door.” Then, very early in the morning Jesus found a place to pray alone. Simon and company went looking for him and when they found him they said “everyone is looking for you!” Jesus said, “Let’s go somewhere else…so I can preach there also…that is why I have come.” To me this story represents Jesus, aware of his purpose (“that is why I have come”), choosing to walk away from “everyone” who wanted him and going to fulfill that purpose.

How about the story of Lazarus’ death? (John 11) Or the story of raising the dead girl? (Luke 8:40-56) In both of these stories, people were actually dying.  In fact, they died!   Even though he eventually raised Lazarus and the girl from death, Jesus did not abruptly interrupt what he was doing to rush and address these situations. I don’t think he was being lazy or insensitive or rudely inappropriate; however sometimes I feel that I will be these things if I don’t voluntarily become immediately consumed by pressing drama that is truly insignificant compared to these situations.

So, he wasn’t available to everyone, right when they wanted him. Consider the story of him sleeping in the boat when there was a storm and his disciples were panicking. (Luke 8:22-25) I’m going to believe that was self-care and not laziness, and a great example of not losing sleep because “everyone needs me.” Ironically everyone needs Jesus and his story, but he could still sleep.  He was able to sleep because He knew that the Father had His eye on everything and would alert him at the right moment to what was necessary for him to do.  That is the mindset I aspire to.