On analytic modeling of multimedia batching schemes

In modern multimedia-on-demand systems, user requests for video programs can be serviced in batches. An important aspect in this type of service is providing access to the users upon request, either instantaneously or within a small latency. We develop an approximate model for evaluating the performance of multimedia batching schemes with respect to system latency. Our mathematical model provides a method for analyzing the performance of the first come first served (FCFS) and the round robin (RR) scheme. We also study the maximal queue length (MQL) scheme and derive a bound on the ratio of its expected latency to optimal. Finally, we give a simple algorithm called the rounded ratio. We show that its expected latency is at most twice optimal.