The ASTA property

Benjamin Melamed; David D. Yao

doi:https://doi.org/10.1201/9781003418283-8

The ASTA property

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Abstract

ASTA (Arrivals See Time Averages) is concerned with properties of stochastic systems where “event” averages sampled over certain sequences of time epochs are equal to time averages. We present a detailed review of three approaches to ASTA: (i) the elementary approach that treats event averages as stochastic Riemann-Stieltjes integrals; (ii) the martingale approach, which exploits properties of the compensators and intensities of point processes, the Doob-Meyer decomposition, and the martingale strong law of large numbers; and (Hi) the Palm calculus approach that focuses on the stationary setting. We also illustrate the applications of ASTA in queueing networks. In particular, we demonstrate that for Markovian queues, a key ASTA condition, the lack of bias assumption (LBA), is in fact equivalent to quasi-reversibility, and that LBA is preserved when quasi-reversible queues are connected into a network.

Original language	English (US)
Title of host publication	Advances in Queueing Theory, Methods, and Open Problems
Publisher	CRC Press
Pages	195-224
Number of pages	30
ISBN (Electronic)	9781000943290
ISBN (Print)	9780367448912
DOIs	https://doi.org/10.1201/9781003418283-8
State	Published - Jan 1 2023
Externally published	Yes

ASJC Scopus subject areas

Economics, Econometrics and Finance(all)
Business, Management and Accounting(all)
Mathematics(all)
Engineering(all)

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Cite this

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AB - ASTA (Arrivals See Time Averages) is concerned with properties of stochastic systems where “event” averages sampled over certain sequences of time epochs are equal to time averages. We present a detailed review of three approaches to ASTA: (i) the elementary approach that treats event averages as stochastic Riemann-Stieltjes integrals; (ii) the martingale approach, which exploits properties of the compensators and intensities of point processes, the Doob-Meyer decomposition, and the martingale strong law of large numbers; and (Hi) the Palm calculus approach that focuses on the stationary setting. We also illustrate the applications of ASTA in queueing networks. In particular, we demonstrate that for Markovian queues, a key ASTA condition, the lack of bias assumption (LBA), is in fact equivalent to quasi-reversibility, and that LBA is preserved when quasi-reversible queues are connected into a network.

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The ASTA property

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