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Tonghoon Suk

Publications and source records attributed to Tonghoon Suk.

6 recordsLinked to original sources
arXiv2019

Optimal Scheduling Control in Fluid Models of General $n\times n$ Input-Queued Switches

Most of the early input-queued switch research focused on establishing throughput optimality of the max-weight scheduling policy, with some recent research showing that max-weight scheduling is optimal with respect to total expected delay asymptotically in the heavy-traffic regime. However, the question of delay-optimal scheduling in input-queued switches remains open in general, as does the question of delay-optimal scheduling under more general objective functions. To gain fundamental insights into these very difficult problems, we consider a fluid model of $n \times n$ input-queued switches with associated fluid-flow costs, and we derive an optimal scheduling control policy to an infinite horizon discounted control problem with a general linear objective function of fluid cost. Our optimal policy coincides with the $c\mu$-rule in certain parameter domains. More generally, due to the input-queued switch constraints, the optimal policy takes the form of the solution to a flow maximization problem, after we identify the Lagrangian multipliers of some key constraints through carefully designed algorithms. Computational experiments demonstrate the benefits of our optimal scheduling policy over variants of max-weight scheduling within fluid models of input-queued switches.

math.OC↗
arXiv2017

Optimal Pricing for Tandem Queues: Does It Have to Be Dynamic Pricing to Earn the Most?

Tandem queueing systems are widely-used stochastic models that arise from many real-life service operations systems. Motivated by the desire to understand the trade-off between the performance and complexity of policies for capacity-constrained tandem queueing systems, we investigate the long-run expected time-average revenue, the gain, of the service provider for various pricing policies. The gain-maximization problem is formulated as a Markov decision process model but the optimal policy, which dynamically adjusts service prices, is hard to obtain due to the curse of dimensionality. For general tandem queueing systems, rather than identifying an optimal dynamic policy, we show that the best possible static policy that quotes the same price to all customers is asymptotically optimal when the buffer size at the first station is sufficiently large. A noteworthy feature of our analysis is that we identify an easy-to-obtain but asymptotic optimal static policy associated with a simple optimization problem. We validate our analytic results through numerical experiments and learn that, surprisingly, the gain under the simple static policy is close to the optimal gain even when the buffer size at the first station is moderate.

math.OC↗
arXiv2017

Optimal Weighted-Delay Scheduling in $2\times 2$ Input-Queued Switches

Motivated by few delay-optimal scheduling results, in comparison to results on throughput optimality, we investigate a canonical input-queued switch scheduling problem in which the objective is to minimize the discounted delay cost over an infinite time horizon. We derive an optimal scheduling policy and establish corresponding theoretical properties, which are expected to be of interest more broadly than input-queued switches. Computational experiments demonstrate and quantify the benefits of our optimal scheduling policy over alternative policies such as variants of MaxWeight scheduling, well-known to be throughput optimal and more recently shown to be delay optimal in the heavy-traffic regime limit.

math.OC↗
arXiv2016

Scheduling using Interactive Optimization Oracles for Constrained Queueing Networks

Ever since Tassiulas and Ephremides (1992) proposed the maximum weight scheduling algorithm of throughput-optimality for constrained queueing networks that arise in the context of communication networks, extensive efforts have been devoted to resolving its most important drawback: high complexity. This paper proposes a generic framework for designing throughput- optimal and low-complexity scheduling algorithms for constrained queueing networks. Under our framework, a scheduling algorithm updates current schedules by interacting with a given oracle system that generates an approximate solution to a related optimization task. One can utilize our framework to design a variety of scheduling algorithms by choosing an oracle system such as random search, Markov chain, belief propagation, and primal-dual methods. The complexity of the resulting scheduling algorithm is determined by the number of operations required for an oracle to process a single query, which is typically small. We provide sufficient conditions for throughput-optimality of the scheduling algorithm in general constrained queueing network models. The linear-time algorithm of Tassiulas (1998) and the random access algorithm of Shah and Shin (2012) correspond to special cases of our framework using random search and Markov chain oracles, respectively. Our generic framework, however, provides a unified proof with milder assumptions.

math.PR↗
arXiv2014

Randomized longest-queue-first scheduling for large-scale buffered systems

We develop diffusion approximations for parallel-queueing systems with the randomized longest-queue-first scheduling algorithm by establishing new mean-field limit theorems as the number of buffers $n\to\infty$. We achieve this by allowing the number of sampled buffers $d=d(n)$ to depend on the number of buffers $n$, which yields an asymptotic `decoupling' of the queue length processes. We show through simulation experiments that the resulting approximation is accurate even for moderate values of $n$ and $d(n)$. To our knowledge, we are the first to derive diffusion approximations for a queueing system in the large-buffer mean-field regime. Another noteworthy feature of our scaling idea is that the randomized longest-queue-first algorithm emulates the longest-queue-first algorithm, yet is computationally more attractive. The analysis of the system performance as a function of $d(n)$ is facilitated by the multi-scale nature in our limit theorems: the various processes we study have different space scalings. This allows us to show the trade-off between performance and complexity of the randomized longest-queue-first scheduling algorithm.

math.PR↗