Utilization
Utilization is the proportion of the system's resources which is used by the traffic which arrives at it. It should be strictly less than one for the system to function well. It is usually represented by the symbol . If then the queue will continue to grow as time goes on. In the simplest case of an M/M/1 queue (Poisson arrivals and a single Poisson server) then it is given by the mean arrival rate over the mean service rate, that is,
where is the mean arrival rate and is the mean service rate. More generally:
where is the mean arrival rate, is the mean service rate, and M is the number of servers.
In general, a lower utilization corresponds to less queueing for customers but means that the system is more idle, which may be considered inefficient.
Read more about this topic: Queueing Theory