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

Abstract

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.