# Asymptotic optimality of the generalized cμ rule under model uncertainty

*Asaf Cohen* and
*Subhamay Saha*

*Stochastic Processes and their Applications*, 2021, vol. 136, issue C, 206-236

**Abstract:**
We consider a critically-loaded multiclass queueing control problem with model uncertainty. The model consists of I types of customers and a single server. At any time instant, a decision-maker (DM) allocates the server’s effort to the customers. The DM’s goal is to minimize a convex holding cost that accounts for the ambiguity with respect to the model, i.e., the arrival and service rates. For this, we consider an adversary player whose role is to choose the worst-case scenario. Specifically, we assume that the DM has a reference probability model in mind and that the cost function is formulated by the supremum over equivalent admissible probability measures to the reference measure with two components, the first is the expected holding cost, and the second one is a penalty for the adversary player for deviating from the reference model. The penalty term is formulated by a general divergence measure.

**Keywords:** Diffusion scaling; Heavy-traffic; Model uncertainty; General divergence; Generalized cμ rule (search for similar items in EconPapers)

**Date:** 2021

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**Persistent link:** https://EconPapers.repec.org/RePEc:eee:spapps:v:136:y:2021:i:c:p:206-236

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**DOI:** 10.1016/j.spa.2021.03.004

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