DELAY, JITTER AND THRESHOLD CROSSING IN ATM SYSTEMS WITH DISPERSED MESSAGES

We consider networking systems with messages that consist of blocks of consecutive (fixed length) cells. A message can be generated at a sin gle instant of time as a batch or it can be dispersed over time. In th is paper we focus on the model of dispersed generation processes which naturally arises in packet switched networks such as ATM. The main di fficulty in the analysis of message related quantities is due to the c orrelation between the system states observed by different cells of th e same message. The following important quantities are analyzed in thi s paper: (1) The message delay process, defined as the time elapsing b etween the arrival epoch of the first cell of the message to the syste m until after the transmission of the last cell of that message is com pleted. In many systems the message delay, and not the individual cell delay, is the measure of interest for the network designer. (2) The m aximum delay of a cell in a message. (3) Number of cells in a message whose delays exceed a pre-specified time threshold. The latter two qua ntities are important for the proper design of playback algorithms and time-out mechanisms for retransmissions. We analyze the probability d istribution of these quantities. In particular, we present a new analy tical 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. A simulation of an 8-nod e tandem queueing model of a virtual connection is provided to show th at the general phenomena observed for the single node system hold for a network environment as well.