Certain relationships exist among specific operating characteristics for any queuing system in a steady state. A steady state condition exists when a queuing system is in its normal stabilized operating condition, usually after an initial or transient state that may occur (e.g., having customers waiting at the door when a business opens in the morning). Both the arrival rate and the service rate should be stable in steady state. John D. C. Little is credited with the first two of these relationships, and hence they are called Little’s Flow Equations:

A third condition that must always be met is

Average time in $\text{system}=\text{Average}$ time waiting in $\text{queue}+\text{Average}$ time receiving service

The advantage of these formulas is that once one of these four characteristics is known, the other characteristics can easily be found. This is important because for certain queuing models, one of these may be much easier to determine than the others. These are applicable to all of the queuing systems discussed in this chapter except the finite population model.