Analysis of the transient delay in a discrete-time buffer with batch arrivals

We perform a discrete-time analysis of the delay of customers in a FIFO buffer with batch arrivals. The numbers of arrivals per slot are independent and identically distributed variables. Since the arrivals come in batches, the delays of the subsequent customers do not constitute a Markov chain, which complicates the analysis. By using generating functions and the supplementary variable technique, moments of the delay of the k-th customer are calculated

USING SINGULARITY ANALYSIS TO APPROXIMATE TRANSIENT CHARACTERISTICS IN QUEUEING SYSTEMS

In this article, we develop a simple method to approximate the transient behavior of queueing systems. In particular, it is shown how singularity analysis of a known generating function of a transient sequence of some performance measure leads to an approximation of this sequence. To illustrate our approach, several specific transient sequences are investigated in detail. By means of some numerical examples, we validate our approximations and demonstrate the usefulness of the technique