USING DISCRETE-DISTRIBUTIONS TO APPROXIMATE GENERAL SERVICE TIME DISTRIBUTION IN QUEUING 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 ti me intervals required in the discrete distribution chosen to match the general service distribution. This paper shows that the minimum numbe r 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 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 tra nsient behaviour of M/G/c, M(t)/G/c and M(t)/G/c(t) queueing systems o n a personal computer.