Network Utility Maximization under Maximum Delay Constraints and Throughput Requirements

We consider the problem of maximizing aggregate user utilities over a multi-hop network, subject to link capacity constraints, maximum end-to-end delay constraints, and user throughput requirements. A user's utility is a concave function of the achieved throughput or the experienced maximum delay. The problem is important for supporting real-time multimedia traffic, and is uniquely challenging due to the need of simultaneously considering maximum delay constraints and throughput requirements. We first show that it is NP-complete either (i) to construct a feasible solution strictly meeting all constraints, or (ii) to obtain an optimal solution after we relax maximum delay constraints or throughput requirements up to constant ratios. We then develop a polynomial-time approximation algorithm named PASS. The design of PASS leverages a novel understanding between non-convex maximum-delay-aware problems and their convex average-delay-aware counterparts, which can be of independent interest and suggest a new avenue for solving maximum-delay-aware network optimization problems. Under realistic conditions, PASS achieves constant or problem-dependent approximation ratios, at the cost of violating maximum delay constraints or throughput requirements by up to constant or problem-dependent ratios. PASS is practically useful since the conditions for PASS are satisfied in many popular application scenarios. We empirically evaluate PASS using extensive simulations of supporting video-conferencing traffic across Amazon EC2 datacenters. Compared to existing algorithms and a conceivable baseline, PASS obtains up to $100\%$ improvement of utilities, by meeting the throughput requirements but relaxing the maximum delay constraints that are acceptable for practical video conferencing applications

On the Min-Max-Delay Problem: NP-completeness, Algorithm, and Integrality Gap

We study a delay-sensitive information flow problem where a source streams information to a sink over a directed graph G(V,E) at a fixed rate R possibly using multiple paths to minimize the maximum end-to-end delay, denoted as the Min-Max-Delay problem. Transmission over an edge incurs a constant delay within the capacity. We prove that Min-Max-Delay is weakly NP-complete, and demonstrate that it becomes strongly NP-complete if we require integer flow solution. We propose an optimal pseudo-polynomial time algorithm for Min-Max-Delay, with time complexity O(\log (Nd_{\max}) (N^5d_{\max}^{2.5})(\log R+N^2d_{\max}\log(N^2d_{\max}))), where N = \max\{|V|,|E|\} and d_{\max} is the maximum edge delay. Besides, we show that the integrality gap, which is defined as the ratio of the maximum delay of an optimal integer flow to the maximum delay of an optimal fractional flow, could be arbitrarily large

When Backpressure Meets Predictive Scheduling

Motivated by the increasing popularity of learning and predicting human user behavior in communication and computing systems, in this paper, we investigate the fundamental benefit of predictive scheduling, i.e., predicting and pre-serving arrivals, in controlled queueing systems. Based on a lookahead window prediction model, we first establish a novel equivalence between the predictive queueing system with a \emph{fully-efficient} scheduling scheme and an equivalent queueing system without prediction. This connection allows us to analytically demonstrate that predictive scheduling necessarily improves system delay performance and can drive it to zero with increasing prediction power. We then propose the \textsf{Predictive Backpressure (PBP)} algorithm for achieving optimal utility performance in such predictive systems. \textsf{PBP} efficiently incorporates prediction into stochastic system control and avoids the great complication due to the exponential state space growth in the prediction window size. We show that \textsf{PBP} can achieve a utility performance that is within $O(\epsilon)$ of the optimal, for any $\epsilon>0$, while guaranteeing that the system delay distribution is a \emph{shifted-to-the-left} version of that under the original Backpressure algorithm. Hence, the average packet delay under \textsf{PBP} is strictly better than that under Backpressure, and vanishes with increasing prediction window size. This implies that the resulting utility-delay tradeoff with predictive scheduling beats the known optimal $[O(\epsilon), O(\log(1/\epsilon))]$ tradeoff for systems without prediction

Pituitary Morphology and Function in 43 Children with Central Diabetes Insipidus

Objective. In pediatric central diabetes insipidus (CDI), etiology diagnosis and pituitary function monitoring are usually delayed. This study aimed to illustrate the importance of regular follow-up and pituitary function monitoring in pediatric CDI. Methods. The clinical, hormonal, and neuroradiological characteristics of children with CDI at diagnosis and during 1.5–2-year follow-up were collected and analyzed. Results. The study included 43 CDI patients. The mean interval between initial manifestation and diagnosis was 22.29 ± 3.67 months (range: 2–108 months). The most common complaint was polyuria/polydipsia. Causes included Langerhans cell histiocytosis, germinoma, and craniopharyngioma in 2, 5, and 4 patients; the remaining were idiopathic. No significant changes were found during the 1.5–2 years after CDI diagnosis. Twenty-three of the 43 cases (53.5%) had ≥1 anterior pituitary hormone deficiency. Isolated growth hormone deficiency was the most frequent abnormality (37.5%) and was not associated with pituitary stalk diameter. Multiple pituitary hormone deficiencies were found in 8 cases with pituitary stalk diameter > 4.5 mm. Conclusion. Diagnosis of CDI is usually delayed. CDI with a pituitary stalk diameter > 4.5 mm carries a higher risk of multiple pituitary hormone deficiencies. Long-term MRI and pituitary function follow-ups are necessary for children with idiopathic CDI

Minimizing Age-of-Information with Throughput Requirements in Multi-Path Network Communication

We consider the scenario where a sender periodically sends a batch of data to a receiver over a multi-hop network, possibly using multiple paths. Our objective is to minimize peak/average Age-of-Information (AoI) subject to throughput requirements. The consideration of batch generation and multi-path communication differentiates our AoI study from existing ones. We first show that our AoI minimization problems are NP-hard, but only in the weak sense, as we develop an optimal algorithm with a pseudo-polynomial time complexity. We then prove that minimizing AoI and minimizing maximum delay are "roughly" equivalent, in the sense that any optimal solution of the latter is an approximate solution of the former with bounded optimality loss. We leverage this understanding to design a general approximation framework for our problems. It can build upon any $\alpha$-approximation algorithm of the maximum delay minimization problem, to construct an $(\alpha+c)$-approximate solution for minimizing AoI. Here $c$ is a constant depending on the throughput requirements. Simulations over various network topologies validate the effectiveness of our approach.Comment: Accepted by the ACM Twentieth International Symposium on Mobile Ad Hoc Networking and Computing (ACM MobiHoc 2019

Shuttle-like supramolecular nanostructures formed by self-assembly of a porphyrin via an oil/water system

In this paper, in terms of the concentration of an aqueous solution of a surfactant, we investigate the self-assembly behavior of a porphyrin, 5, 10, 15, 20-tetra(4-pyridyl)-21H, 23H-porphine [H2TPyP], by using an oil/water system as the medium. We find that when a chloroform solution of H2TPyP is dropwise added into an aqueous solution of cetyltrimethylammonium bromide [CTAB] with a lower concentration, a large amount of irregular nanoarchitectures, together with a small amount of well-defined shuttle-like nanostructures, hollow nanospheres, and nanotubes, could be produced. While a moderate amount of shuttle-like nanostructures accompanied by a few irregular nanoarchitectures, solid nanospheres, and nanorods are produced when a CTAB aqueous solution in moderate concentration is employed, in contrast, a great quantity of shuttle-like nanostructures together with a negligible amount of solid nanospheres, nanofibers, and irregular nanostructures are manufactured when a high-concentration CTAB aqueous solution is involved. An explanation on the basis of the molecular geometry of H2TPyP and in terms of the intermolecular π-π interactions between H2TPyP units, and hydrophobic interactions between CTAB and H2TPyP has been proposed. The investigation gives deep insights into the self-assembly behavior of porphyrins in an oil/water system and provides important clues concerning the design of appropriate porphyrins when related subjects are addressed. Our investigation suggests that an oil/aqueous system might be an efficient medium for producing unique organic-based nanostructures

A Novel Multi-Charged Draw Solute That Removes Organic Arsenicals from Water in a Hybrid Membrane Process

The potential of forward osmosis for water treatment can only be maximized with suitable draw solutes. Here a three-dimensional, multicharge draw solute of decasodium phytate (Na₁₀-phytate) is designed and synthesized for removing organic arsenicals from water using a hybrid forward osmosis (FO) – membrane distillation (MD) process. Efficient water recovery is achieved using Na₁₀-phytate as a draw solute with a water flux of 20.0 LMH and negligible reverse solute diffusion when 1000 ppm organic arsenicals as the feed and operated under ambient conditions with FO mode. At 50 °C, the novel draw solute increases water flux by more than 30% with water fluxes higher than 26.0 LMH on the FO side, drastically enhancing water recovery efficiency. By combining the FO and MD processes into a single hybrid process, a 100% recovery of Na₁₀-phytate draw solute was achieved. Crucially, organic arsenicals or Na₁₀-phytate draw solutes are both rejected 100% and not detected in the permeate of the hybrid process. The complete rejection of both organic arsenicals and draw solutes using hybrid membrane processes is unprecedented; creating a new application for membrane separations