We present an approach to derive performance bounds of a queue under histogram-based input traffics. The results are obtained through strong stochastic bounds on the queue length and on the output traffic. The bounds provide probability inequalities on transient behaviors and on steady-state when it exists. We consider both stationary and non-stationary traffics and provide some numerical techniques in both cases. Unlike approximate methods, these bounds can be used to check if the Quality of Service constraints are satisfied or not. Our approach provides a trade-off between the accuracy of results and the computational complexity and it is much faster than the histogram-based simulation