In waiting line systems where the length of the waiting line is limited,the mean number of units entering the system might be less than the arrival rate.

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If the length of the waiting line is limited, then the maximum number of units that can be in the system at any given time is also limited. Therefore, if the arrival rate is greater than the mean number of units entering the system, the waiting line will eventually exceed its limit, causing the system to fail. Thus it is necessary for the mean number of units entering the system to be less than or equal to the arrival rate in order to prevent overloading of the waiting line system.

In Waiting Line Systems Where the Length of the Waiting