PASTA (Poisson Arrivals See Time Averages) is a term coined by R. Wolff in his well known 1982 paper. In keeping with Wolff's terminology, we use the term anti-PASTA to refer to the following converse of PASTA. Given that arrivals do indeed see time averages, when must the arrival process necessarily be Poisson? We show that anti-PASTA is satisfied in a pure-jump Markov process, provided that the arrival process corresponds to a subset of the Markov process jumps.
Green, Linda, and Benjamin Melamed. "An anti-PASTA result for Markovian systems." Operations Research 38, no. 1 (1990): 173-175.
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