arXiv subjects

Rajat Talak

Publications and source records attributed to Rajat Talak.

32 records · Page 2Linked to original sources

arXiv2021

Information Freshness in Multi-Hop Wireless Networks

We consider the problem of minimizing age of information in multihop wireless networks and propose three classes of policies to solve the problem - stationary randomized, age difference, and age debt. For the unicast setting with fixed routes between each source-destination pair, we first develop a procedure to find age optimal Stationary Randomized policies. These policies are easy to implement and allow us to derive closed-form expression for average AoI. Next, for the same unicast setting, we develop a class of heuristic policies, called Age Difference, based on the idea that if neighboring nodes try to reduce their age differential then all nodes will have fresher updates. This approach is useful in practice since it relies only on the local age differential between nodes to make scheduling decisions. Finally, we propose the class of policies called Age Debt, which can handle 1) non-linear AoI cost functions; 2) unicast, multicast and broadcast flows; and 3) no fixed routes specified per flow beforehand. Here, we convert AoI optimization problems into equivalent network stability problems and use Lyapunov drift to find scheduling and routing schemes that stabilize the network. We also provide numerical results comparing our proposed classes of policies with the best known scheduling and routing schemes available in the literature for a wide variety of network settings.

cs.NI↗

arXiv2021

Neural Trees for Learning on Graphs

Graph Neural Networks (GNNs) have emerged as a flexible and powerful approach for learning over graphs. Despite this success, existing GNNs are constrained by their local message-passing architecture and are provably limited in their expressive power. In this work, we propose a new GNN architecture -- the Neural Tree. The neural tree architecture does not perform message passing on the input graph, but on a tree-structured graph, called the H-tree, that is constructed from the input graph. Nodes in the H-tree correspond to subgraphs in the input graph, and they are reorganized in a hierarchical manner such that the parent of a node in the H-tree always corresponds to a larger subgraph in the input graph. We show that the neural tree architecture can approximate any smooth probability distribution function over an undirected graph. We also prove that the number of parameters needed to achieve an $ε$-approximation of the distribution function is exponential in the treewidth of the input graph, but linear in its size. We prove that any continuous $\mathcal{G}$-invariant/equivariant function can be approximated by a nonlinear combination of such probability distribution functions over $\mathcal{G}$. We apply the neural tree to semi-supervised node classification in 3D scene graphs, and show that these theoretical properties translate into significant gains in prediction accuracy, over the more traditional GNN architectures. We also show the applicability of the neural tree architecture to citation networks with large treewidth, by using a graph sub-sampling technique.

cs.LG↗

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.

cs.IT↗

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.

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

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

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↗

arXiv2018

Capacity and Delay Scaling for Broadcast Transmission in Highly Mobile Wireless Networks

We study broadcast capacity and minimum delay scaling laws for highly mobile wireless networks, in which each node has to disseminate or broadcast packets to all other nodes in the network. In particular, we consider a cell partitioned network under the simplified independent and identically distributed (IID) mobility model, in which each node chooses a new cell at random every time slot. We derive scaling laws for broadcast capacity and minimum delay as a function of the cell size. We propose a simple first-come-first-serve (FCFS) flooding scheme that nearly achieves both capacity and minimum delay scaling. Our results show that high mobility does not improve broadcast capacity, and that both capacity and delay improve with increasing cell sizes. In contrast to what has been speculated in the literature we show that there is (nearly) no tradeoff between capacity and delay. Our analysis makes use of the theory of Markov Evolving Graphs (MEGs) and develops two new bounds on flooding time in MEGs by relaxing the previously required expander property assumption.

cs.IT↗

arXiv2018

Strategic Arrivals to Queues Offering Priority Service

We consider strategic arrivals to a FCFS service system that starts service at a fixed time and has to serve a fixed number of customers, e.g., an airplane boarding system. Arriving early induces a higher waiting cost (waiting before service begins) while arriving late induces a cost because earlier arrivals take the better seats. We first consider arrivals of heterogeneous customers that choose arrival times to minimize the weighted sum of waiting cost and and cost due to expected number of predecessors. We characterize the unique Nash equilibria for this system. Next, we consider a system offering L levels of priority service with a FCFS queue for each priority level. Higher priorities are charged higher admission prices. Customers make two choices - time of arrival and priority of service. We show that the Nash equilibrium corresponds to the customer types being divided into L intervals and customers belonging to each interval choosing the same priority level. We further analyze the net revenue to the server and consider revenue maximizing strategies - number of priority levels and pricing. Numerical results show that with only three queues the server can attain near maximum revenue.

cs.GT↗

arXiv2018

Scheduling Policies for Age Minimization in Wireless Networks with Unknown Channel State

Age of information (AoI) is a recently proposed metric that measures the time elapsed since the generation of the last received information update. We consider the problem of AoI minimization for a network under general interference constraints, and time varying channel. We study the case where the channel statistics are known, but the current channel state is unknown. We propose two scheduling policies, namely, the virtual queue based policy and age-based policy. In the virtual queue based policy, the scheduler schedules links with maximum weighted sum of the virtual queue lengths, while in the age-based policy, the scheduler schedules links with maximum weighted sum of a function of link AoI. We prove that the virtual queue based policy is peak age optimal, up to an additive constant, while the age-based policy is at most factor 4 away from the optimal age. Numerical results suggest that both the proposed policies are, in fact, very close to the optimal.

cs.NI↗

arXiv2018

Distributed Scheduling Algorithms for Optimizing Information Freshness in Wireless Networks

Age of Information (AoI), measures the time elapsed since the last received information packet was generated at the source. We consider the problem of AoI minimization for single-hop flows in a wireless network, under pairwise interference constraints and time varying channel. We consider simple, yet broad, class of distributed scheduling policies, in which a transmission is attempted over each link with a certain attempt probability. We obtain an interesting relation between the optimal attempt probability and the optimal AoI of the link, and its neighboring links. We then show that the optimal attempt probabilities can be computed by solving a convex optimization problem, which can be done distributively.

cs.IT↗

arXiv2018

Optimizing Age of Information in Wireless Networks with Perfect Channel State Information

Age of information (AoI), defined as the time elapsed since the last received update was generated, is a newly proposed metric to measure the timeliness of information updates in a network. We consider AoI minimization problem for a network with general interference constraints, and time varying channels. We propose two policies, namely, virtual-queue based policy and age-based policy when the channel state is available to the network scheduler at each time step. We prove that the virtual-queue based policy is nearly optimal, up to a constant additive factor, and the age-based policy is at-most factor 4 away from optimality. Comparing with our previous work, which derived age optimal policies when channel state information is not available to the scheduler, we demonstrate a 4 fold improvement in age due to the availability of channel state information.

cs.IT↗