Asymptotic analysis of a multiclass queueing control problem under heavy-traffic with model uncertainty

TL;DR

This paper analyzes a multiclass queueing control problem under heavy-traffic with model uncertainty, establishing the asymptotic optimality of a $c$-type policy that balances rejection and scheduling decisions based on workload and ambiguity levels.

Contribution

It introduces the first asymptotic analysis of a heavy-traffic queueing control problem considering model uncertainty, deriving a $c$-type policy with proven optimality.

Findings

Rejections are avoided below a workload cutoff with high probability.

Rejections occur only from the buffer with the lowest rejection cost when workload exceeds the cutoff.

The scheduling policy remains consistent across different ambiguity levels.

Abstract

We study a multiclass M/M/1 queueing control problem with finite buffers under heavy-traffic where the decision maker is uncertain about the rates of arrivals and service of the system and by scheduling and admission/rejection decisions acts to minimize a discounted cost that accounts for the uncertainty. The main result is the asymptotic optimality of a $c\mu$-type of policy derived via underlying stochastic differential games studied in [16]. Under this policy, with high probability, rejections are not performed when the workload lies below some cut-off that depends on the ambiguity level. When the workload exceeds this cut-off, rejections are carried out and only from the buffer with the cheapest rejection cost weighted with the mean service rate in some reference model. The allocation part of the policy is the same for all the ambiguity levels. This is the first work to address a heavy-traffic queueing control problem with model uncertainty.