arXiv subjects

Eytan Modiano

Publications and source records attributed to Eytan Modiano.

At least 55 records · Page 3Linked to original sources

arXiv2020

Learning-NUM: Network Utility Maximization with Unknown Utility Functions and Queueing Delay

Network Utility Maximization (NUM) studies the problems of allocating traffic rates to network users in order to maximize the users' total utility subject to network resource constraints. In this paper, we propose a new NUM framework, Learning-NUM, where the users' utility functions are unknown apriori and the utility function values of the traffic rates can be observed only after the corresponding traffic is delivered to the destination, which means that the utility feedback experiences \textit{queueing delay}. The goal is to design a policy that gradually learns the utility functions and makes rate allocation and network scheduling/routing decisions so as to maximize the total utility obtained over a finite time horizon $T$. In addition to unknown utility functions and stochastic constraints, a central challenge of our problem lies in the queueing delay of the observations, which may be unbounded and depends on the decisions of the policy. We first show that the expected total utility obtained by the best dynamic policy is upper bounded by the solution to a static optimization problem. Without the presence of feedback delay, we design an algorithm based on the ideas of gradient estimation and Max-Weight scheduling. To handle the feedback delay, we embed the algorithm in a parallel-instance paradigm to form a policy that achieves $\tilde{O}(T^{3/4})$-regret, i.e., the difference between the expected utility obtained by the best dynamic policy and our policy is in $\tilde{O}(T^{3/4})$. Finally, to demonstrate the practical applicability of the Learning-NUM framework, we apply it to three application scenarios including database query, job scheduling and video streaming. We further conduct simulations on the job scheduling application to evaluate the empirical performance of our policy.

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arXiv2020

Throughput Maximization in Uncooperative Spectrum Sharing Networks

Throughput-optimal transmission scheduling in wireless networks has been a well considered problem in the literature, and the method for achieving optimality, MaxWeight scheduling, has been known for several decades. This algorithm achieves optimality by adaptively scheduling transmissions relative to each user's stochastic traffic demands. To implement the method, users must report their queue backlogs to the network controller and must rapidly respond to the resulting resource allocations. However, many currently-deployed wireless systems are not able to perform these tasks and instead expect to occupy a fixed assignment of resources. To accommodate these limitations, adaptive scheduling algorithms need to interactively estimate these uncooperative users' queue backlogs and make scheduling decisions to account for their predicted behavior. In this work, we address the problem of scheduling with uncooperative legacy systems by developing algorithms to accomplish these tasks. We begin by formulating the problem of inferring the uncooperative systems' queue backlogs as a partially observable Markov decision process and proceed to show how our resulting learning algorithms can be successfully used in a queue-length-based scheduling policy. Our theoretical analysis characterizes the throughput-stability region of the network and is verified using simulation results.

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arXiv2020

Age of Information: An Introduction and Survey

We summarize recent contributions in the broad area of age of information (AoI). In particular, we describe the current state of the art in the design and optimization of low-latency cyberphysical systems and applications in which sources send time-stamped status updates to interested recipients. These applications desire status updates at the recipients to be as timely as possible; however, this is typically constrained by limited system resources. We describe AoI timeliness metrics and present general methods of AoI evaluation analysis that are applicable to a wide variety of sources and systems. Starting from elementary single-server queues, we apply these AoI methods to a range of increasingly complex systems, including energy harvesting sensors transmitting over noisy channels, parallel server systems, queueing networks, and various single-hop and multi-hop wireless networks. We also explore how update age is related to MMSE methods of sampling, estimation and control of stochastic processes. The paper concludes with a review of efforts to employ age optimization in cyberphysical applications.

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arXiv2020

Learning Algorithms for Minimizing Queue Length Regret

We consider a system consisting of a single transmitter/receiver pair and $N$ channels over which they may communicate. Packets randomly arrive to the transmitter's queue and wait to be successfully sent to the receiver. The transmitter may attempt a frame transmission on one channel at a time, where each frame includes a packet if one is in the queue. For each channel, an attempted transmission is successful with an unknown probability. The transmitter's objective is to quickly identify the best channel to minimize the number of packets in the queue over $T$ time slots. To analyze system performance, we introduce queue length regret, which is the expected difference between the total queue length of a learning policy and a controller that knows the rates, a priori. One approach to designing a transmission policy would be to apply algorithms from the literature that solve the closely-related stochastic multi-armed bandit problem. These policies would focus on maximizing the number of successful frame transmissions over time. However, we show that these methods have $Ω(\log{T})$ queue length regret. On the other hand, we show that there exists a set of queue-length based policies that can obtain order optimal $O(1)$ queue length regret. We use our theoretical analysis to devise heuristic methods that are shown to perform well in simulation.

cs.PF↗

arXiv2019

Optimizing Information Freshness in Wireless Networks under General Interference Constraints

Age of information (AoI) is a recently proposed metric for measuring information freshness. AoI measures the time that elapsed since the last received update was generated. We consider the problem of minimizing average and peak AoI in a wireless networks, consisting of a set of source-destination links, under general interference constraints. When fresh information is always available for transmission, we show that a stationary scheduling policy is peak age optimal. We also prove that this policy achieves average age that is within a factor of two of the optimal average age. In the case where fresh information is not always available, and packet/information generation rate has to be controlled along with scheduling links for transmission, we prove an important separation principle: the optimal scheduling policy can be designed assuming fresh information, and independently, the packet generation rate control can be done by ignoring interference. Peak and average AoI for discrete time G/Ber/1 queue is analyzed for the first time, which may be of independent interest.

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arXiv2019

A Theory of Uncertainty Variables for State Estimation and Inference

We develop a new framework of uncertainty variables to model uncertainty. An uncertainty variable is characterized by an uncertainty set, in which its realization is bound to lie, while the conditional uncertainty is characterized by a set map, from a given realization of a variable to a set of possible realizations of another variable. We prove Bayes' law and the law of total probability equivalents for uncertainty variables. We define a notion of independence, conditional independence, and pairwise independence for a collection of uncertainty variables, and show that this new notion of independence preserves the properties of independence defined over random variables. We then develop a graphical model, namely Bayesian uncertainty network, a Bayesian network equivalent defined over a collection of uncertainty variables, and show that all the natural conditional independence properties, expected out of a Bayesian network, hold for the Bayesian uncertainty network. We also define the notion of point estimate, and show its relation with the maximum a posteriori estimate. Probability theory starts with a distribution function (equivalently a probability measure) as a primitive and builds all other useful concepts, such as law of total probability, Bayes' law, independence, graphical models, point estimate, on it. Our work shows that it is perfectly possible to start with a set, instead of a distribution function, and retain all the useful ideas needed for state estimation and inference.

stat.ML↗

arXiv2019

Age-Delay Tradeoffs in Queueing Systems

We consider an M server system in which each server can service at most one update packet at a time. The system designer controls (1) scheduling - the order in which the packets get serviced, (2) routing - the server that an arriving update packet joins for service, and (3) the service time distribution with fixed service rate. Given a fixed update generation process, we prove a strong age-delay and age-delay variance tradeoff, wherein, as the average AoI approaches its minimum, the packet delay and its variance approach infinity. In order to prove this result, we consider two special cases of the M server system, namely, a single server system with last come first server with preemptive service and an infinite server system. In both these cases, we derive sufficient conditions to show that three heavy tailed service time distributions, namely Pareto, log-normal, and Weibull, asymptotically minimize the average AoI as their tail gets heavier, and establish the age-delay tradeoff results. We provide an intuitive explanation as to why such a seemingly counter intuitive age-delay tradeoff is natural, and that it should exist in many systems.

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arXiv2019

Optimal Control of Distributed Computing Networks with Mixed-Cast Traffic Flows

Distributed computing networks, tasked with both packet transmission and processing, require the joint optimization of communication and computation resources. We develop a dynamic control policy that determines both routes and processing locations for packets upon their arrival at a distributed computing network. The proposed policy, referred to as Universal Computing Network Control (UCNC), guarantees that packets i) are processed by a specified chain of service functions, ii) follow cycle-free routes between consecutive functions, and iii) are delivered to their corresponding set of destinations via proper packet duplications. UCNC is shown to be throughput-optimal for any mix of unicast and multicast traffic, and is the first throughput-optimal policy for non-unicast traffic in distributed computing networks with both communication and computation constraints. Moreover, simulation results suggest that UCNC yields substantially lower average packet delay compared with existing control policies for unicast traffic.

cs.NI↗

arXiv2019

Minimizing the Age of Information in Wireless Networks with Stochastic Arrivals

We consider a wireless network with a base station serving multiple traffic streams to different destinations. Packets from each stream arrive to the base station according to a stochastic process and are enqueued in a separate (per stream) queue. The queueing discipline controls which packet within each queue is available for transmission. The base station decides, at every time t, which stream to serve to the corresponding destination. The goal of scheduling decisions is to keep the information at the destinations fresh. Information freshness is captured by the Age of Information (AoI) metric. In this paper, we derive a lower bound on the AoI performance achievable by any given network operating under any queueing discipline. Then, we consider three common queueing disciplines and develop both an Optimal Stationary Randomized policy and a Max-Weight policy under each discipline. Our approach allows us to evaluate the combined impact of the stochastic arrivals, queueing discipline and scheduling policy on AoI. We evaluate the AoI performance both analytically and using simulations. Numerical results show that the performance of the Max-Weight policy is close to the analytical lower bound.

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arXiv2019

Optimal Routing for Delay-Sensitive Traffic in Overlay Networks

We design dynamic routing policies for an overlay network which meet delay requirements of real-time traffic being served on top of an underlying legacy network, where the overlay nodes do not know the underlay characteristics. We pose the problem as a constrained MDP, and show that when the underlay implements static policies such as FIFO with randomized routing, then a decentralized policy, that can be computed efficiently in a distributed fashion, is optimal. Our algorithm utilizes multi-timescale stochastic approximation techniques, and its convergence relies on the fact that the recursions asymptotically track a nonlinear differential equation, namely the replicator equation. Extensive simulations show that the proposed policy indeed outperforms the existing policies.

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arXiv2019

Topology Discovery Using Path Interference

We consider the problem of inferring the topology of a network using the measurements available at the end nodes, without cooperation from the internal nodes. To this end, we provide a simple method to obtain path interference which identifies whether two paths in the network intersect with each other. Using this information, we formulate the topology inference problem as an integer program and develop polynomial time algorithms to solve it optimally for networks with tree and ring topologies. Finally, we use the insight developed from these algorithms to develop a heuristic for identifying general topologies. Simulation results show that our heuristic outperforms a recently proposed algorithm that uses distance measurements for topology discovery.

cs.NI↗

arXiv2019

Age of Information for Discrete Time Queues

Age of information (AoI) is a time-evolving measure of information freshness, that tracks the time since the last received fresh update was generated. Analyzing peak and average AoI, two time average metrics of AoI, for various continuous time queueing systems has received considerable attention. We analyze peak and average age for various discrete time queueing systems. We first consider first come first serve (FCFS) Ber/G/1 and Ber/G/1 queue with vacations, and derive explicit expressions for peak and average age. We also obtain age expressions for the last come first serve (LCFS) queue and the $G/G/\infty$ queue. We build upon proof techniques from earlier results, and also present new techniques that might be of independent interest in analyzing age in discrete time queuing systems.

cs.IT↗

arXiv2019

A Hierarchical WDM-based Scalable Data Center Network Architecture

Massive data centers are at the heart of the Internet. The rapid growth of Internet traffic and the abundance of rich data-driven applications have raised the need for enormous network bandwidth. Towards meeting this growing traffic demand, optical interconnects have gained significant attention, as they can provide high throughput, low latency, and scalability. In particular, optical Wavelength Division Multiplexing (WDM) provides the possibility to build data centers comprising of millions of servers, while providing hundreds of terabits per second bandwidth. In this paper, we propose a WDM-based Reconfigurable Hierarchical Optical Data Center Architecture (RHODA) that can satisfy future Internet traffic demands. To improve scalability, our DCN architecture is hierarchical, as it groups server racks into clusters. Cluster membership is reconfigurable through the use of optical switches. Each cluster enables heavy-traffic communication among the racks within. To support varying traffic patterns, the inter-cluster network topology and link capacities are also reconfigurable, which is achieved through the use of optical space switches and Wavelength Selective Switches (WSSs). Our simulation results demonstrate that in terms of average hop distance, RHODA outperforms OSA, FatTree and WaveCube by up to 81%, 66% and 60%, respectively.

cs.NI↗

arXiv2019

Can Determinacy Minimize Age of Information?

Age-of-information (AoI) is a newly proposed performance metric of information freshness. It differs from the traditional delay metric, because it is destination centric and measures the time that elapsed since the last received fresh information update was generated at the source. AoI has been analyzed for several queueing models, and the problem of optimizing AoI over arrival and service rates has been studied in the literature. We consider the problem of minimizing AoI over the space of update generation and service time distributions. In particular, we ask whether determinacy, i.e. periodic generation of update packets and/or deterministic service, optimizes AoI. By considering several queueing systems, we show that in certain settings, deterministic service can in fact result in the worst case AoI, while a heavy-tailed distributed service can yield the minimum AoI. This leads to an interesting conclusion that, in some queueing systems, the service time distribution that minimizes expected packet delay, or variance in packet delay can, in fact, result in the worst case AoI. This exposes a fundamental difference between AoI metrics and packet delay.

cs.NI↗

arXiv2019

Age-Delay Tradeoffs in Single Server Systems

Information freshness and low latency communication is important to many emerging applications. While Age of Information (AoI) serves as a metric of information freshness, packet delay is a traditional metric of communication latency. We prove that there is a natural tradeoff between the AoI and packet delay. We consider a single server system, in which at most one update packet can be serviced at a time. The system designer controls the order in which the packets get serviced and the service time distribution, with a given service rate. We analyze two tradeoff problems that minimize packet delay and the variance in packet delay, respectively, subject to an average age constraint. We prove a strong age-delay and age-delay variance tradeoff, wherein, as the average age approaches its minimum, the delay and its variance approach infinity. We show that the service time distribution that mininizes average age, must necessarily have an unbounded-second moment.

cs.IT↗

arXiv2019

Network Interdiction Using Adversarial Traffic Flows

Traditional network interdiction refers to the problem of an interdictor trying to reduce the throughput of network users by removing network edges. In this paper, we propose a new paradigm for network interdiction that models scenarios, such as stealth DoS attack, where the interdiction is performed through injecting adversarial traffic flows. Under this paradigm, we first study the deterministic flow interdiction problem, where the interdictor has perfect knowledge of the operation of network users. We show that the problem is highly inapproximable on general networks and is NP-hard even when the network is acyclic. We then propose an algorithm that achieves a logarithmic approximation ratio and quasi-polynomial time complexity for acyclic networks through harnessing the submodularity of the problem. Next, we investigate the robust flow interdiction problem, which adopts the robust optimization framework to capture the case where definitive knowledge of the operation of network users is not available. We design an approximation framework that integrates the aforementioned algorithm, yielding a quasi-polynomial time procedure with poly-logarithmic approximation ratio for the more challenging robust flow interdiction. Finally, we evaluate the performance of the proposed algorithms through simulations, showing that they can be efficiently implemented and yield near-optimal solutions.

cs.NI↗

arXiv2019

Age Optimal Information Gathering and Dissemination on Graphs

We consider the problem of timely exchange of updates between a central station and a set of ground terminals $V$, via a mobile agent that traverses across the ground terminals along a mobility graph $G = (V, E)$. We design the trajectory of the mobile agent to minimize peak and average age of information (AoI), two newly proposed metrics for measuring timeliness of information. We consider randomized trajectories, in which the mobile agent travels from terminal $i$ to terminal $j$ with probability $P_{i,j}$. For the information gathering problem, we show that a randomized trajectory is peak age optimal and factor-$8\mathcal{H}$ average age optimal, where $\mathcal{H}$ is the mixing time of the randomized trajectory on the mobility graph $G$. We also show that the average age minimization problem is NP-hard. For the information dissemination problem, we prove that the same randomized trajectory is factor-$O(\mathcal{H})$ peak and average age optimal. Moreover, we propose an age-based trajectory, which utilizes information about current age at terminals, and show that it is factor-$2$ average age optimal in a symmetric setting.

cs.IT↗

arXiv2019

Optimal Network Control in Partially-Controllable Networks

The effectiveness of many optimal network control algorithms (e.g., BackPressure) relies on the premise that all of the nodes are fully controllable. However, these algorithms may yield poor performance in a partially-controllable network where a subset of nodes are uncontrollable and use some unknown policy. Such a partially-controllable model is of increasing importance in real-world networked systems such as overlay-underlay networks. In this paper, we design optimal network control algorithms that can stabilize a partially-controllable network. We first study the scenario where uncontrollable nodes use a queue-agnostic policy, and propose a low-complexity throughput-optimal algorithm, called Tracking-MaxWeight (TMW), which enhances the original MaxWeight algorithm with an explicit learning of the policy used by uncontrollable nodes. Next, we investigate the scenario where uncontrollable nodes use a queue-dependent policy and the problem is formulated as an MDP with unknown queueing dynamics. We propose a new reinforcement learning algorithm, called Truncated Upper Confidence Reinforcement Learning (TUCRL), and prove that TUCRL achieves tunable three-way tradeoffs between throughput, delay and convergence rate.

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