We generalise to non stationary traffics an approach that we have previously proposed to derive performance bounds of a queue under histogram-based input traffics. We use strong stochastic ordering to derive stochastic bounds on the queue length and the output traffic. These bounds are valid for transient distributions of these measures and also for the steady-state distributions when they exist. We provide some numerical techniques under arrivals modelled by a Switched Batch Bernoulli Process (SBBP). Unlike approximate methods, these bounds can be used to check if the Quality of Service constraints are satisfied or not. Our approach provides a tradeoff between the accuracy of results and the computational complexity and it is much faster than the histogram-based simulation proposed in the literature