A study of the accuracy of the Bernoulli approximation of the slot occupancy process in high-speed unidirectional-bus networks

Abstract

Analytical models for unidirectional-bus protocols often employ a Bernoulli process to approximate the occupancy process of the slots on the bus. This approximation, which assumes independence among the statuses of consecutive slots on the bus facilitates analysis; however, it is known to provide inaccurate results, especially for stations located at the downstream end of the bus. In this paper, we quantify this inaccuracy by comparing results from the Bernoulli-based analytical model with results from a simulation model of two different access protocols. We study the Bernoulli-based model as compared to simulation in its ability both to predict network delay behavior and to describe the actual slot occupancy process as characterized by various statistical characteristics. We reveal the inaccuracy of the model as a function of station index and network load, and we identify a characteristic of the slot occupancy pattern not captured by the Bernoulli-based model, that is crucial to more accurately modeling the process for the sake of delay analysis.<>