Symbolic higher-order moments of the waiting time in an M/G/1 queue with random order of service

The explicit expressions for the mean and the second moment of the waiting time distribution for an M/G/l queue with random order of service can be found in the literature. However, higher-order moments have been unavailable, because their calculation is extremely laborious, albeit straightforward in principle. This paper presents the third through sixth order moments of the waiting time in symbolic form, which is obtained by a Mathematica program developed for formula manipulation. The results provide more information about the characteristic of the waiting time distribution. In particular, they are used to compare the skewness and kurtosis of the waiting time with those for the first-come first-served and last-come first-served systems