  This paper mainly focuses on the utilization frequency in receiving end of
communication systems, which shows the inclination of the user about different
symbols. When the average number of use is limited, a specific utility
distribution is proposed on the best effort in term of fairness, which is also
the closest one to occurring probability in the relative entropy. Similar to a
switch, its parameter can be selected to make it satisfy different users'
requirements: negative parameter means the user focus on high-probability
events and positive parameter means the user is interested in small-probability
events. In fact, the utility distribution is a measure of message importance in
essence. It illustrates the meaning of message importance measure (MIM), and
extend it to the general case by selecting the parameter. Numerical results
show that this utility distribution characterizes the message importance like
MIM and its parameter determines the concern of users.
