A Note on the Accuracy of Several Existing Approximations for M/Ph/m Queues

High variability of system parameters is a complicating factor in the modeling of the performance of big data systems. In this paper, we assess the potential inaccuracy of several existing approximations for evaluating the mean number of jobs queued in a parallelized device that can be represented as an M/Ph/m queue. Unlike existing studies, we consider the effect of the third moment of the service time, or equivalently, its skewness. We show that the approximations accuracy can be poor even for "easy" examples with a low coefficient of variation of the service time. Our examples demonstrate the important influence of the skewness of the service time distribution on the accuracy of the approximations. None of the approximations accounts for this property. We provide recommendations for the choice of the approximation that allow the user to choose the best suited approximation based on the actual queue parameters.