Analysis of message delay processes

The authors study the message queuing delays in a node of a communication system, where a message consists of a block of consecutive packets. Two types of message generation process are distinguished. The message can be generated as a batch or it can be dispersed over time. The authors focus on the dispersed generation model. The main difficulty in the analysis is due to the correlation between the system states observed by different packets of the same message. A technique for analyzing the message delay in such systems for different arrival models is introduced, and it is shown that the correlation has a strong effect on the performance of the system. For an M/M/1 system with variable size messages, an explicit expression for the Laplace-Stieltjes transform (LST) of the message delay is obtained. It is shown that the commonly used independence assumption can lead to wrong conclusions