Delay predictors for customer service systems with time-varying parameters

Motivated by interest in making delay announcements in service systems, we develop new real-time delay predictors that effectively cope with customer abandonment and time-varying parameters. First, we focus on delay predictors exploiting recent customer delay history. We show that time-varying arrival rates can introduce significant prediction bias in delay-history-based predictors when the system experiences alternating periods of overload and underload. We then introduce a new delay-history-based predictor that effectively copes with time-varying arrival rates. Second, we consider a time-varying number of servers. We develop two new predictors which exploit an established deterministic fluid approximation for a many-server queueing model with time-varying demand and capacity. The new predictors effectively cope with those features, often observed in practice. Throughout, we use computer simulation to quantify the performance of the alternative delay predictors.