On queueing delays of dispersed messages

On queueing delays of dispersed messages

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Article ID: iaor19942496
Country: United States
Volume: 15
Start Page Number: 325
End Page Number: 345
Publication Date: Jun 1994
Journal: Queueing Systems
Authors: , ,
Keywords: queueing networks
Abstract:

The authors study the message queueing delays in a node of a communication system, where a message consists of a block of consecutive packets. The message delay is defined as the time elapsing between the arrival epoch of the first packet of the message to the system until after the transmission of the last packet of that message is completed. The authors distinguish between two types of message generation processes. The message can be generated as a batch or it can be dispersed over time. In this paper 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. This paper introduces a new technique to analyze the message delay in such systems for different arrival models and different number of sessions. For an M/M/1 system with variable size messages and for the bursty traffic model, the authors obtain an explicit expression for the Laplace-Stieltjes transform of the message delay. Derivations are also provided for an M/G/1 system, for multiple session systems and for fixed message sizes. The authors show that the correlation has a strong effect on the performance of the system, and that the commonly used independence assumption, i.e., the assumption that the delays of packets are independent from packet to packet, can lead to wrong conclusions.

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