Abstract
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 [Formula: see text] 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 .
Highlights
Introduction and SummaryIn this paper, we study delay-based service differentiation via ratio controls in a multiclass many-server service system with time-varying arrival rates
As part of our proof of the many-server heavy-traffic (MSHT) functional central limit theorem (FCLT), we show that the impact of this high-priority queue is asymptotically negligible; see Step 2 of the proof of Theorem 1
We show that the scaling in (4) puts the model into the quality-and-efficiency-driven (QED) MSHT regime; that is, we establish a nondegenerate joint MSHT FCLT for the number of class-i customers in the system at time t for all i, together with associated delay processes, where the target HoL delay ratios hold almost surely for all t in the limit process; see Theorem 1
Summary
We study delay-based service differentiation via ratio controls in a multiclass many-server service system with time-varying arrival rates. We show that the scaling in (4) puts the model into the quality-and-efficiency-driven (QED) MSHT regime; that is, we establish a nondegenerate joint MSHT FCLT for the (appropriately scaled) number of class-i customers in the system at time t for all i, together with associated delay processes, where the target HoL delay ratios hold almost surely for all t in the limit process; see Theorem 1. The papers Gurvich and Whitt (2009a, b; 2010) establish MSHT limits for these ratio controls, showing that they induce a simplifying state-space collapse, that permit achieving performance goals asymptotically We extend those results (for a single service pool) to a TV setting.
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