A novel policer mechanism that incorporates randomization of the rate threshold which prevents “lockup” and “synchronization” problems associated with prior art policers that employ fixed rate thresholds. In one embodiment, a policer machine utilizes the well known sliding window technique to implement traffic control. In a second embodiment, a policer machine utilizes the well known token bucket technique to implement traffic control. In both embodiments, a random dimension is added to the rate threshold used by each policer algorithm. For the sliding window embodiment, the effect of randomization of the rate threshold is that the policer machine applies a scattering of rate values centered around the desired rate to the incoming traffic. For the token bucket embodiment, a random dimension is added to the empty bucket (i.e. zero tokens) threshold. The effect of randomization of the empty bucket threshold is that the policer machine applies a scattering of token values above the empty bucket threshold value of zero.