13 research outputs found
Optimal heavy-traffic queue length scaling in an incompletely saturated switch
We consider an input queued switch operating under the MaxWeight scheduling algorithm. This system is interesting to study because it is a model for Internet routers and data center networks. Recently, it was shown that the MaxWeight algorithm has optimal heavy-traffic queue length scaling when all ports are uniformly saturated. Here we consider the case when an arbitrary number of ports are saturated (which we call the incompletely saturated case), and each port is allowed to saturate at a different rate. We use a recently developed drift technique to show that the heavy-traffic queue length under the MaxWeight scheduling algorithm has optimal scaling with respect to the switch size even in these cases
On Optimal Weighted-Delay Scheduling in Input-Queued Switches
Motivated by relatively few delay-optimal scheduling results, in comparison
to results on throughput optimality, we investigate an input-queued switch
scheduling problem in which the objective is to minimize a linear function of
the queue-length vector. Theoretical properties of variants of the well-known
MaxWeight scheduling algorithm are established within this context, which
includes showing that these algorithms exhibit optimal heavy-traffic
queue-length scaling. For the case of input-queued switches, we
derive an optimal scheduling policy and establish its theoretical properties,
demonstrating fundamental differences with the variants of MaxWeight
scheduling. Our theoretical results are expected to be of interest more broadly
than input-queued switches. Computational experiments demonstrate and quantify
the benefits of our optimal scheduling policy
Adaptive Matching for Expert Systems with Uncertain Task Types
A matching in a two-sided market often incurs an externality: a matched
resource may become unavailable to the other side of the market, at least for a
while. This is especially an issue in online platforms involving human experts
as the expert resources are often scarce. The efficient utilization of experts
in these platforms is made challenging by the fact that the information
available about the parties involved is usually limited.
To address this challenge, we develop a model of a task-expert matching
system where a task is matched to an expert using not only the prior
information about the task but also the feedback obtained from the past
matches. In our model the tasks arrive online while the experts are fixed and
constrained by a finite service capacity. For this model, we characterize the
maximum task resolution throughput a platform can achieve. We show that the
natural greedy approaches where each expert is assigned a task most suitable to
her skill is suboptimal, as it does not internalize the above externality. We
develop a throughput optimal backpressure algorithm which does so by accounting
for the `congestion' among different task types. Finally, we validate our model
and confirm our theoretical findings with data-driven simulations via logs of
Math.StackExchange, a StackOverflow forum dedicated to mathematics.Comment: A part of it presented at Allerton Conference 2017, 18 page