Finding the Knee of a Waiting Line “Hockey Stick” Curve

Researchers: John Maleyeff, Canan Gunes Corlu, and Danqi Lu

The project concerns determining the mathematical approach that most closely resembles a human’s innate ability to make decisions associated with queuing system optimization.  The relationship between planned server utilization and customer waiting times follows a “hockey stick” function.  Here, the waiting time increases linearly in proportion to the server utilization until a certain threshold is reached, where the waiting times begin to increase at a higher rate until the server utilization reaches 100%.  This threshold (called the knee or elbow of the hockey stick curve) differs depending on many factors, most importantly the number of servers, the coefficient of variation in service times, and the arrival pattern (e.g., scheduled or random).   In almost all cases server costs are known.  When customer’s waiting time aversion costs are also known, the system can easily be optimized.  However, in most cases, waiting time costs are impossible to quantify.

The project will present a series of “hockey stick” patterns that show the relationship between server utilization and customer waiting times without context (i.e., a generic scenario).  Their decisions will be compared with a variety of mathematical approaches that have been published or will be created.