# Algebraic tools for the performance evaluation of discrete event systems

Article Abstract:

The number of events that will occur in a certain time interval in discrete event dynamic systems (DEDS) and the time at which the 'n'th occurrence of an event of a certain type will happen are considered. The two combined constitute what is usually referred to as performance evaluation, which is also the scope of queueing theory and timed Petri nets. The approach taken here is deterministic, the same as that of time Petri nets, which can deal with transient behavior. It is shown that linearity seems to be an integral property of the specific class of DEDSs that are modeled by event graphs, which are a special class of Petri nets, although it is necessary to become acquainted with new algebraic tools called dioids.

Publication Name: Proceedings of the IEEE

Subject: Electronics

ISSN: 0018-9219

Year: 1989

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# Relationship Between Volterra Series and Generalized Power Series

Article Abstract:

Weakly nonlinear systems with single-valued and frequency-dependent input-output characteristics can be analyzed using the Volterra series expansion. A formula is developed which enables the Volterra nonlinear transfer functions to be obtained from the power series expansion of the characters of a system. The relationship is established by comparing two formulas for the phasor of an output component of a system.

Publication Name: Proceedings of the IEEE

Subject: Electronics

ISSN: 0018-9219

Year: 1983

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# An Algebraic Formula for the Output of a System with Large- Signal Multifrequency Excitation

Article Abstract:

A formula for output components of a nonlinearity which can be described by a power series with frequency- and order-dependent time delays is defined. The input is multifrequency sinusoids. Other work is related to this new formula.

Publication Name: Proceedings of the IEEE

Subject: Electronics

ISSN: 0018-9219

Year: 1983

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