arXiv subjects

Kuang Xu

Publications and source records attributed to Kuang Xu.

21 records · Page 2Linked to original sources

arXiv2014

Queuing with future information

We study an admissions control problem, where a queue with service rate $1-p$ receives incoming jobs at rate $λ\in(1-p,1)$, and the decision maker is allowed to redirect away jobs up to a rate of $p$, with the objective of minimizing the time-average queue length. We show that the amount of information about the future has a significant impact on system performance, in the heavy-traffic regime. When the future is unknown, the optimal average queue length diverges at rate $\sim\log_{1/(1-p)}\frac{1}{1-λ}$, as $λ\to 1$. In sharp contrast, when all future arrival and service times are revealed beforehand, the optimal average queue length converges to a finite constant, $(1-p)/p$, as $λ\to1$. We further show that the finite limit of $(1-p)/p$ can be achieved using only a finite lookahead window starting from the current time frame, whose length scales as $\mathcal{O}(\log\frac{1}{1-λ})$, as $λ\to1$. This leads to the conjecture of an interesting duality between queuing delay and the amount of information about the future.

math.PR↗

arXiv2013

Go Viral, or Not: Rate-Optimal Control for Resource-Constrained Branching Processes

We propose and analyze a new class of controlled multi-type branching processes with a per-step linear resource constraint, motivated by potential applications in viral marketing and cancer treatment. We show that the optimal exponential growth rate of the population can be achieved by maintaining a fixed proportion among the species, for both deterministic and stochastic branching processes. In the special case of a two-type population and with a symmetric reward structure, the optimal proportion is obtained in closed-form. In addition to revealing structural properties of controlled branching processes, our results are intended to provide the practitioners with an easy-to-interpret benchmark for best practices, if not exact policies. As a proof of concept, the methodology is applied to the linkage structure of the 2004 US Presidential Election blogosphere, where the optimal growth rate demonstrates sizable gains over a uniform selection strategy, and to a two-compartment cell-cycle kinetics model for cancer growth, with realistic parameters, where the robust estimate for minimal treatment intensity under a worst-case growth rate is noticeably more conservative compared to that obtained using more optimistic assumptions.

math.OC↗

arXiv2012

On the Power of Centralization in Distributed Processing

In this thesis, we propose and analyze a multi-server model that captures a performance trade-off between centralized and distributed processing. In our model, a fraction $p$ of an available resource is deployed in a centralized manner (e.g., to serve a most-loaded station) while the remaining fraction $1-p$ is allocated to local servers that can only serve requests addressed specifically to their respective stations. Using a fluid model approach, we demonstrate a surprising phase transition in the steady-state delay, as $p$ changes: in the limit of a large number of stations, and when any amount of centralization is available ($p>0$), the average queue length in steady state scales as $\log_{1/(1-p)} 1/(1-λ)$ when the traffic intensity $λ$ goes to 1. This is exponentially smaller than the usual M/M/1-queue delay scaling of $1/(1-λ)$, obtained when all resources are fully allocated to local stations ($p=0$). This indicates a strong qualitative impact of even a small degree of centralization. We prove convergence to a fluid limit, and characterize both the transient and steady-state behavior of the finite system, in the limit as the number of stations $N$ goes to infinity. We show that the sequence of queue-length processes converges to a unique fluid trajectory (over any finite time interval, as $N$ approaches infinity, and that this fluid trajectory converges to a unique invariant state $v^I$, for which a simple closed-form expression is obtained. We also show that the steady-state distribution of the $N$-server system concentrates on $v^I$ as $N$ goes to infinity.

cs.DC↗