Delay-Based Service Differentiation with Many Servers and Time-Varying Arrival Rates

We study the problem of staffing (specifying a time-varying number of servers) and scheduling (assigning newly idle servers to a waiting customer from one of $K$ classes) in the many-server V model with class-dependent time-varying arrival rates. In order to stabilize performance at class-dependent delay targets, we propose the blind (model-free) head-of-line delay-ratio (HLDR) scheduling rule, which extends an earlier dynamic-priority rule that exploits the head-of-line delay information. We study the HLDR rule in the quality-and-efficiency-driven many-server heavy-traffic (MSHT) regime. We staff to the MSHT fluid limit plus a control function in the diffusion scale. We establish a MSHT limit for the Markov model, which has dramatic state-space collapse, showing that the targeted ratios are attained asymptotically. In the MSHT limit, meeting staffing goals reduces to a one-dimensional control problem for the aggregate queue content, which may be approximated by recently developed staffing algorithms for time-varying single-class models. Simulation experiments confirm that the overall procedure can be effective, even for non-Markov models.

The online appendix is available at https://doi.org/10.1287/stsy.2018.0015.