The ASTA property

Benjamin Melamed, David D. Yao

Research output: Chapter in Book/Report/Conference proceedingChapter


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 languageEnglish (US)
Title of host publicationAdvances in Queueing Theory, Methods, and Open Problems
PublisherCRC Press
Number of pages30
ISBN (Electronic)9781000943290
ISBN (Print)9780367448912
StatePublished - Jan 1 2023
Externally publishedYes

ASJC Scopus subject areas

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


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