A Note On Approximations Of Discrete-Time Queueing Systems With Their Continuous-Time Counterparts

In this paper, we discuss the performances of approximations of discrete-time queues with their continuous-time counterparts. Taking the discrete-time single-arrival Geo/G/1, batch-arrival Geo(X)/G/1, and tandem queues for examples, we present the absolute and relative errors resulting from such approximations and demonstrate that they can be quite vulnerable for a considerable range of parameter values. Therefore, special attention has to be paid to such approximations, and further sophisticated analysis needs to be carried out for more accurate evaluation of discrete-time queueing systems, taking their discrete-time characteristics into account.