A Note on the Effects of Service Time Distribution in the M/G/1 Queue

The M/G/1 queue is a classical model used to represent a large number of real-life computer and networking applications. In this note, we show that, for coefficients of variation of the service time in excess of one, higherorder properties of the service time distribution may have an important effect on the steady-state probability distribution for the number of customers in the M/G/1 queue. As a result, markedly different state probabilities can be observed even though the mean numbers of customers remain the same. This should be kept in mind when sizing buffers based on the mean number of customers in the queue. Influence of higher-order distributional properties can also be important in the M/G/1/K queue where it extends to the mean number of customers itself. Our results have potential implications for the design of benchmarks, as well as the interpretation of their results.