A Note on PASTA and Anti-PASTA for Continuous-Time Markov Chains

The result Poisson Arrivals See Time Averages (PASTA) is well established in the queueing literature. Although there are some well known examples where non-Poisson arrivals see time averages, arrival and time averages usually are different when arrivals are not Poisson. There are also situations where it has been shown that arrivals see time averages only if arrivals are Poisson, a property called Anti-PASTA. We present a simple and direct proof of Anti-PASTA for continuous-time Markov chains.