Using discrete distributions to approximate general service time distributions in queueing models

In solving discrete time queueing models by numerical techniques, the computational requirements (computer memory and time) are a practical limitation and are particularly dependent on the number of discrete time intervals required in the discrete distribution chosen to match the general service distribution. This paper shows that the minimum number of points required for matching to the first two moments depends on the size of the discrete interval relative to the mean and also on the coefficient of variation. Equations and graphs are provided that will enable the Operational Research OR practitioner to select the discrete distribution to be used as an approximation. Additionally, it is concluded that discrete time modelling, using these approximations to model service time, now provides a practical means to model both steady-state measures and transient behaviour of M/G/c, M(t)/G/c and M(t)/G/c(t) queueing systems on a personal computer.