In this paper we empirically evaluate the workload process of a single-server queue with service times having heavy-tailed distribution, in an effort to investigate the applicability of statistical detection methods for long memory (long range dependence). While it is known that theoretically (under specific moment conditions) such a workload process has long memory, it is not easy to evidence this property in simulation or within real data. Using numerical experiments, we compare two known statistical testing methods, and demonstrate moderate optimism regarding their applicability.