Motivated by interest in making delay announcements in service systems, we study real-time delay estimators in manyserver service systems, both with and without customer abandonment. Our main contribution here is to consider the realistic feature of time-varying arrival rates. We focus especially on delay estimators exploiting recent customer delay history. We show that time-varying arrival rates can introduce significant estimation bias in delay-history-based delay estimators when the system experiences alternating periods of overload and underload. We then introduce refined delayhistory estimators that effectively cope with time-varying arrival rates together with non-exponential service-time and abandonment-time distributions, which are often observed in practice. We use computer simulation to verify that our proposed estimators outperform several natural alternatives. Key words: delay estimation; delay announcements; time-varying arrival rates; simulatio
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