Real-Time Delay Estimation Based on Delay History in Many-Server Service Systems with Time-Varying Arrivals

Motivated by interest in making delay announcements in service systems, we study real-time delay estimators in many-server 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 delay-history 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.