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. The authors 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 (iii) the Palm calculus approach that focuses on the stationary setting. They also illustrate the applications of ASTA in queueing networks. In particular, the authors 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.
