On the interaction between stratification and control variates, with illustrations in a call centre simulation

Variance reduction techniques (VRTs) are often essential to make simulation quick and accurate enough to be useful. A case in point is simulation-based optimization of complex systems. An obvious idea to push the improvement one step further is to combine several VRTs for a given simulation, But such combinations often give rise to new issues. This paper studies the combination of stratification with control variates. We detail and compare several ways of doing the combination. Nontrivial synergies between the two methods are exhibited. We illustrate this with a telephone call centre simulation, where we combine a control variate with stratification with respect to one of the uniform random variates that drive the simulation. It turns out that using more information in the control variate degrades the performance (significantly) in our example. This seemingly paradoxical behaviour is not rare and our theoretical analysis explains why.