Delay, jitter and threshold crossing in ATM systems with dispersed messages

Abstract

We consider networking systems with messages that consist of blocks of consecutive (fixed length) cells. A message can be generated at a single instant of time as a batch or it can be dispersed over time. In this paper we focus on the model of dispersed generation processes which naturally arises in packet switched networks such as ATM. The main difficulty in the analysis of message related quantities is due to the correlation between the system states observed by different cells of the same message. The following important quantities are analyzed in this paper: (1) The message delay process, defined as the time elapsing between the arrival epoch of the first cell of the message to the system until after the transmission of the last cell of that message is completed. In many systems the message delay, and not the individual cell delay, is the measure of interest for the network designer. (2) The maximum 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 quantities are important for the proper design of playback algorithms and time-out mechanisms for retransmissions. We analyze the probability distribution of these quantities. In particular, we 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. A simulation of an 8-node tandem queueing model of a virtual connection is provided to show that the general phenomena observed for the single node system hold for a network environment as well.