Service Systems with Slowdowns: Potential Failures and Proposed Solutions

Many service systems exhibit service slowdowns when the system is congested. Our goal in this paper is to investigate this phenomenon and its effect on system performance. We modify the Erlang-A model to account for service slowdowns and carry out the performance analysis in the Quality-and-Efficiency Driven (QED) regime. We find that when the load sensitivity is low, the system can achieve QED performance, but the square-root staffing parameter requires an adjustment to achieve the same performance as an ordinary Erlang-A queue. When the load sensitivity is high, the system alternates randomly between a QED and an Efficiency Driven (ED) regime performance levels, a phenomenon which we refer to as bi-stability. We analyze how the system scale and the model parameters affect the bi-stability phenomenon and propose an admission control policy to avoid ED performance.