When are people most alone?

Since I am a single child, I felt lonely at home during the summer, when both of my parents went to work and when all my friends in the community have other activities and cannot play with me. I also feel alone when I sit in the cafeteria, when all of my friends did not come, and other tables around me are full of people. These are situations when I feel lonely.

I also enjoy being all alone.
I like to be all alone when I am studying. I don't want my parents or my nephews walking all around when I am writing my homework or preparing for tests.
I also like to be all alone when I am reading. I like to sit in my room, open the air conditioner (if it is summer), turn on the music, and relax myself.

However, I feel most alone when I entered a new school. I still remember my first day to Pacific American School, I still remember my first day to my middle school, I still remember my first day to my cram school, and I still remember my first day when I go to my summer camps.
I really believe that people are most alone when they entered a new condition. They don't know any people, not familiar with the environment, and not sure what to do.