Asymptotic Analysis of a Multiclass Queueing Control Problem Under Heavy Traffic with Model Uncertainty

Abstract

We study a multiclass M/M/1 queueing control problem with finite buffers under heavy traffic in which 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 cμ type of policy derived via underlying stochastic differential games studied in Cohen [Cohen A (2018) Brownian control problems for a multiclass M/M/1 queueing problem with model uncertainty. Math. Oper. Res. 44(2):739–766.]. Under this policy, with high probability, rejections are not performed when the workload lies below some cutoff that depends on the ambiguity level. When the workload exceeds this cutoff, rejections are carried out and only from the buffer with the cheapest rejection cost weighted with the mean service rate. The allocation part of the policy is the same for all the ambiguity levels. To our knowledge, this is the first work to address a heavy-traffic queueing control problem with model uncertainty.