Dispersed messages in discrete-time queues: delay, jitter and threshold crossing

The authors study discrete-time, single server queueing systems, with messages that consist of blocks of consecutive cells. They focus on the model of dispersed cell generation processes which naturally arises in packet switched networks such as ATM. Several important performance measures are considered. These are the message delay process, the maximum delay of a cell in a message and the number of cells in a message whose delays exceed a pre-specified time threshold. The latter two quantities are important for proper design of playback algorithms and time-out mechanisms. They present a new analytical approach that yields efficient recursions for the computation of the probability distribution of each quantity. Numerical examples are provided to compare this distribution with the distribution obtained by using an independence assumption on the cell delays. These examples show that the correlation between cell delays of the same message has a strong effect on each of these quantities