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|
|Number of pages||30|
|State||Published - Jan 1 2023|
ASJC Scopus subject areas
- Economics, Econometrics and Finance(all)
- Business, Management and Accounting(all)