Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Learning the $c\mu$ Rule in Single and Parallel Server Networks   We consider learning-based variants of the $c \mu$ rule for scheduling in
single and parallel server settings of multi-class queueing systems.
  In the single server setting, the $c \mu$ rule is known to minimize the
expected holding-cost (weighted queue-lengths summed over classes and a fixed
time horizon). We focus on the problem where the service rates $\mu$ are
unknown with the holding-cost regret (regret against the $c \mu$ rule with
known $\mu$) as our objective. We show that the greedy algorithm that uses
empirically learned service rates results in a constant holding-cost regret
(the regret is independent of the time horizon). This free exploration can be
explained in the single server setting by the fact that any work-conserving
policy obtains the same number of samples in a busy cycle.
  In the parallel server setting, we show that the $c \mu$ rule may result in
unstable queues, even for arrival rates within the capacity region. We then
present sufficient conditions for geometric ergodicity under the $c \mu$ rule.
Using these results, we propose an almost greedy algorithm that explores only
when the number of samples falls below a threshold. We show that this algorithm
delivers constant holding-cost regret because a free exploration condition is
eventually satisfied.

19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph