Utilization

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Utilization, in queueing theory, 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 ρ. 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 λ is the mean arrival rate and μ is the mean service rate.

In most cases a lower utilization will mean less queuing for customers but will mean that the system is idle more (which could be considered inefficient).