Staffing Large Service Systems Under Arrival-rate Uncertainty

TL;DR

This paper develops asymptotically optimal staffing strategies for large service systems with multiple customer classes and uncertain arrival rates, ensuring quality-of-service constraints are met.

Contribution

It extends deterministic staffing solutions to stochastic arrival scenarios using bounds and asymptotic analysis, addressing uncertainty in large-scale systems.

Findings

Asymptotically optimal staffing levels derived for deterministic arrivals.

Extension of solutions to stochastic arrival rate models.

Effective bounds used to approximate optimal staffing in large systems.

Abstract

We consider the problem of staffing large-scale service systems with multiple customer classes and multiple dedicated server pools under joint quality-of-service (QoS) constraints. We first analyze the case in which arrival rates are deterministic and the QoS metric is the probability a customer is queued, given by the Erlang-C formula. We use the Janssen-Van Leeuwaarden-Zwart bounds to obtain asymptotically optimal solutions to this problem. The second model considered is one in which the arrival rates are not completely known in advance (before the server staffing levels are chosen), but rather are known via a probability distribution. In this case, we provide asymptotically optimal solutions to the resulting stochastic integer program, leveraging results obtained for the deterministic arrivals case.