We study the sample complexity of learning in average-reward weakly-coupled Markov decision processes (WCMDPs) and Restless Bandits (RBs) under a generative model. Naive reduction to a tabular MDP leads to high complexity bounds as the state-action space is exponentially large in the number of arms $N$. By exploiting the weakly coupled structure, we show that near-optimal policies can be learned with sample and computational complexities that are polynomial in $N$. Specifically, we analyze the plug-in approach, which applies an efficient planning algorithm to an empirical model estimated from data. For fully heterogeneous WCMDPs, we establish the first finite-sample PAC guarantee with polynomial complexity and an $O(1/\sqrt{N})$ optimality gap. For homogeneous RBs, we further prove that a smaller optimality gap is achievable under mild structural assumptions. A primary technical contribution of our work is a novel Lyapunov-based analysis framework. Unlike classical approaches that rely on the difficult-to-control bias function, our framework uses an explicitly constructed Lyapunov function along with a drift transfer technique between the true and empirical models. A key step of independent interest in our framework is a fine-grained perturbation analysis for the underlying linear programming (LP) relaxation, which provides a general tool for analyzing LP-based policies and weakly-coupled systems.

Heterogeneity poses a fundamental challenge for many real-world large-scale decision-making problems but remains largely understudied. In this paper, we study the _fully heterogeneous_ setting of a prominent class of such problems, known as weakly-coupled Markov decision processes (WCMDPs). Each WCMDP consists of $N$ arms (or subproblems), which have distinct model parameters in the fully heterogeneous setting, leading to the curse of dimensionality when $N$ is large. We show that, under mild assumptions, an efficiently computable policy achieves an $O(1/\sqrt{N})$ optimality gap in the long-run average reward per arm for fully heterogeneous WCMDPs as $N$ becomes large. This is the _first asymptotic optimality result_ for fully heterogeneous average-reward WCMDPs. Our main technical innovation is the construction of projection-based Lyapunov functions that certify the convergence of rewards and costs to an optimal region, even under full heterogeneity.

Graph alignment refers to the task of finding the vertex correspondence between two correlated graphs ofnvertices. Extensive study has been done on polynomial-time algorithms for the graph alignment problem under the Erdős–Rényi graph pair model, where the two graphs are Erdős–Rényi graphs with edge probability$q_{\mathrm {u}}$, correlated under certain vertex correspondence. To achieve exact recovery of the correspondence, all existing algorithms at least require the edge correlation coefficient$\rho _{\mathrm {u}}$between the two graphs to benon-vanishingas$n\rightarrow \infty $. Moreover, it is conjectured that no polynomial-time algorithm can achieve exact recovery under vanishing edge correlation${\rho _{\mathrm {u}}}\lt 1/\mathrm {polylog}(n)$. In this paper, we show that with a vanishing amount of additionalattribute information, exact recovery is polynomial-time feasible undervanishingedge correlation${\rho _{\mathrm {u}}}\ge n^{-\Theta (1)}$. We identify alocaltree structure, which incorporates one layer of user information and one layer of attribute information, and apply the subgraph counting technique to such structures. A polynomial-time algorithm is proposed that recovers the vertex correspondence for most of the vertices, and then refines the output to achieve exact recovery. The consideration of attribute information is motivated by real-world applications like LinkedIn and Twitter, where user attributes like birthplace and education background can aid alignment.

We consider the problem of efficiently routing jobs that arrive into a central queue to a system of heterogeneous servers. Unlike homogeneous systems, a threshold policy, that routes jobs to the slow server(s) when the queue length exceeds a certain threshold, is known to be optimal for the one-fast-one-slow two-server system. But an optimal policy for the multi-server system is unknown and non-trivial to find. While Reinforcement Learning (RL) has been recognized to have great potential for learning policies in such cases, our problem has an exponentially large state space size, rendering standard RL inefficient. In this work, we propose ACHQ, an efficient policy gradient based algorithm with a low dimensional soft threshold policy parameterization that leverages the underlying queueing structure. We provide stationary-point convergence guarantees for the general case and despite the low-dimensional parameterization prove that ACHQ converges to an approximate global optimum for the special case of two servers. Simulations demonstrate an improvement in expected response time of up to ${\sim}30%$ over the greedy policy that routes to the fastest available server.

Graph alignment refers to the task of finding the vertex correspondence between two correlated graphs of $n$ vertices. Extensive study has been done on polynomial-time algorithms for the graph alignment problem under the Erdős–Rényi graph pair model, where the two graphs are Erdős–Rényi graphs with edge probability $q_\mathrm{u}$, correlated under certain vertex correspondence. To achieve exact recovery of the correspondence, all existing algorithms at least require the edge correlation coefficient $\rho_\mathrm{u}$ between the two graphs to be \emph{non-vanishing} as $n\rightarrow\infty$. Moreover, it is conjectured that no polynomial-time algorithm can achieve exact recovery under vanishing edge correlation $\rho_\mathrm{u}<1/\mathrm{polylog}(n)$. In this paper, we show that with a vanishing amount of additional \emph{attribute information}, exact recovery is polynomial-time feasible under \emph{vanishing} edge correlation $\rho_\mathrm{u} \ge n^{-\Theta(1)}$. We identify a \emph{local} tree structure, which incorporates one layer of user information and one layer of attribute information, and apply the subgraph counting technique to such structures. A polynomial-time algorithm is proposed that recovers the vertex correspondence for most of the vertices, and then refines the output to achieve exact recovery. The consideration of attribute information is motivated by real-world applications like LinkedIn and Twitter, where user attributes like birthplace and education background can aid alignment.

Graph alignment aims at finding the vertex correspondence between two correlated graphs, a task that frequently occurs in graph mining applications such as social network analysis. Attributed graph alignment is a variant of graph alignment, in which publicly available side information or attributes are exploited to assist graph alignment. Existing studies on attributed graph alignment focus on either theoretical performance without computational constraints or empirical performance of efficient algorithms. This motivates us to investigate efficient algorithms with theoretical performance guarantee. In this paper, we propose two polynomial-time algorithms that exactly recover the vertex correspondence with high probability. The feasible region of the proposed algorithms is near optimal compared to the information-theoretic limits. When specialized to the seeded graph alignment problem under the seeded Erdős-Rényi graph pair model, the proposed algorithms extends the best known feasible region for exact alignment by polynomial-time algorithms.

Motivated by various data science applications including de-anonymizing user identities in social networks, we consider the graph alignment problem, where the goal is to identify the vertex/user correspondence between two correlated graphs. Existing work mostly recovers the correspondence by exploiting the user-user connections. However, in many real-world applications, additional information about the users, such as user profiles, might be publicly available. In this paper, we introduce the attributed graph alignment problem, where additional user information, referred to as attributes, is incorporated to assist graph alignment. We establish both the achievability and converse results on recovering vertex correspondence exactly, where the conditions match for certain parameter regimes. Our results span the full spectrum between models that only consider user-user connections and models where only attribute information is available.

We study the infinite-horizon restless bandit problem with the average reward criterion, in both discrete-time and continuous-time settings. A fundamental goal is to efficiently compute policies that achieve a diminishing optimality gap as the number of arms, $N$, grows large. Existing results on asymptotic optimality all rely on the uniform global attractor property (UGAP), a complex and challenging-to-verify assumption. In this paper, we propose a general, simulation-based framework, Follow-the-Virtual-Advice, that converts any single-armed policy into a policy for the original $N$-armed problem. This is done by simulating the single-armed policy on each arm and carefully steering the real state towards the simulated state. Our framework can be instantiated to produce a policy with an $O(1/\sqrt{N})$ optimality gap. In the discrete-time setting, our result holds under a simpler synchronization assumption, which covers some problem instances that violate UGAP. More notably, in the continuous-time setting, we do not require \emph{any} additional assumptions beyond the standard unichain condition. In both settings, our work is the first asymptotic optimality result that does not require UGAP.

This paper considers a class of reinforcement learning problems, which involve systems with two types of states: stochastic and pseudo-stochastic. In such systems, stochastic states follow a stochastic transition kernel while the transitions of pseudo-stochastic states are deterministic {\em given} the stochastic states/transitions. We refer to such systems as mixed systems, which are widely used in various applications, including Manufacturing systems, communication networks, and queueing networks. We propose a sample-efficient RL method that accelerates learning by generating augmented data samples. The proposed algorithm is data-driven (model-free), but it learns the policy from data samples from both real and augmented samples. This method significantly improves learning by reducing the sample complexity such that the dataset only needs to have sufficient coverage of the stochastic states. We analyze the sample complexity of the proposed method under Fitted Q Iteration (FQI) and demonstrate that the optimality gap decreases as $O\left(\sqrt{\frac{1}{n}}+\sqrt{\frac{1}{m}}\right),$ where $n$ represents the number of real samples, and $m$ is the number of augmented samples per real sample. It is important to note that without augmented samples, the optimality gap is $O(1)$ due to the insufficient data coverage of the pseudo-stochastic states. Our experimental results on multiple queueing network applications confirm that the proposed method indeed significantly accelerates both deep Q-learning and deep policy gradient.

We develop approximation algorithms for set-selection problems with deterministic constraints, but random objective values, i.e., stochastic probing problems. When the goal is to maximize the objective, approximation algorithms for probing problems are well-studied. On the other hand, few techniques are known for minimizing the objective, especially in the adaptive setting, where information about the random objective is revealed during the set-selection process and allowed to influence it. For minimization problems in particular, incorporating adaptivity can have a considerable effect on performance. In this work, we seek approximation algorithms that compare well to the optimal adaptive policy. We develop new techniques for adaptive minimization, applying them to a few problems of interest. The core technique we develop here is an approximate reduction from an adaptive expectation minimization problem to a set of adaptive probability minimization problems which we call threshold problems. By providing near-optimal solutions to these threshold problems, we obtain bicriteria adaptive policies. We apply this method to obtain an adaptive approximation algorithm for the Min-Element problem, where the goal is to adaptively pick random variables to minimize the expected minimum value seen among them, subject to a knapsack constraint. This partially resolves an open problem raised in [Goel et al., 2010]. We further consider three extensions on the Min-Element problem, where our objective is the sum of the smallest k element-weights, or the weight of the min-weight basis of a given matroid, or where the constraint is not given by a knapsack but by a matroid constraint. For all three of the variations we explore, we develop adaptive approximation algorithms for their corresponding threshold problems, and prove their near-optimality via coupling arguments.

This paper is eligible for the Jack Keil Wolf ISIT Student Paper Award. Reviewers in peer review are often miscalibrated: they may be strict, lenient, extreme, moderate, etc. A number of algorithms have previously been proposed to calibrate reviews. Such attempts of calibration can however leak sensitive information about which reviewer reviewed which paper. In this paper, we identify this problem of calibration with privacy, and provide a foundational building block to address it. Specifically, we present a theoretical study of this problem under a simplified-yet-challenging model involving two reviewers, two papers, and an MAP-computing adversary. Our main results establish the Pareto frontier of the tradeoff between privacy (preventing the adversary from inferring reviewer identity) and utility (accepting better papers), and design explicit computationally-efficient algorithms that we prove are Pareto optimal.

Graph alignment aims at finding the vertex correspondence between two correlated graphs, a task that frequently occurs in graph mining applications such as social network analysis. Attributed graph alignment is a variant of graph alignment, in which publicly available side information or attributes are exploited to assist graph alignment. Existing studies on attributed graph alignment focus on either theoretical performance without computational constraints or empirical performance of efficient algorithms. This motivates us to investigate efficient algorithms with theoretical performance guarantee. In this paper, we propose two polynomial-time algorithms that exactly recover the vertex correspondence with high probability. The feasible region of the proposed algorithms is near optimal compared to the information-theoretic limits. When specialized to the seeded graph alignment problem, the proposed algorithms strictly improve the best known feasible region for exact alignment by polynomial-time algorithms.

Most data generated by modern applications is stored in the cloud, and there is an exponential growth in the volume of jobs to access these data and perform computations using them. The volume of data access or computing jobs can be heterogeneous across different job types and can unpredictably change over time. Cloud service providers cope with this demand heterogeneity and unpredictability by over-provisioning the number of servers hosting each job type. In this paper, we propose the addition of erasure-coded servers that can flexibly serve multiple job types without additional storage cost. We analyze the service capacity region and the response time of such erasure-coded systems and compare them with standard uncoded replication-based systems currently used in the cloud. We show that coding expands the service capacity region, thus enabling the system to handle variability in demand for different data types. Moreover, we characterize the response time of the coded system in various arrival rate regimes. This analysis reveals that adding even a small number of coded servers can significantly reduce the mean response time, with a drastic reduction in regimes where the demand is skewed across different job types.

Multiserver jobs, which are jobs that occupy multiple servers simultaneously during service, are prevalent in today's computing clusters. But little is known about the delay performance of systems with multiserver jobs. We consider queueing models for multiserver jobs in a scaling regime where the system load becomes heavy and meanwhile the total number of servers in the system and the number of servers that a job needs become large. Prior work has derived upper bounds on the queueing probability in this scaling regime. However, without proper lower bounds, the existing results cannot be used to differentiate between policies. In this paper, we study the delay performance by establishing sharp bounds on the mean waiting time of multiserver jobs, where the waiting time of a job is the time spent in queueing rather than in service. We first consider the commonly used First-Come-First-Serve (FCFS) policy and characterize the exact order of its mean waiting time. We then prove a lower bound on the mean waiting time of all policies, and demonstrate that there is an order gap between this lower bound and the mean waiting time under FCFS. We finally complement the lower bound with an achievability result: we show that under a priority policy that we call P-Priority, the mean waiting time achieves the order of the lower bound. This achievability result implies the tightness of the lower bound, the asymptotic optimality of P-Priority, and the strict suboptimality of FCFS.

We consider the problem of controlling a mutated diffusion process with an unknown mutation time. The problem is formulated as the quickest intervention problem with the mutation modeled by a change-point, which is a generalization of the quickest change-point detection (QCD). Our goal is to intervene in the mutated process as soon as possible while maintaining a low intervention cost with optimally chosen intervention actions. This model and the proposed algorithms can be applied to pandemic prevention (such as Covid-19) or misinformation containment. We formulate the problem as a partially observed Markov decision process (POMDP) and convert it to an MDP through the belief state of the change-point. We first propose a grid-approximation approach to calculate the optimal intervention policy, whose computational complexity could be very high when the number of grids is large. In order to reduce the computational complexity, we further propose a low-complexity threshold-based policy through the analysis of the first-order approximation of the value functions in the "local intervention" regime. Simulation results show the low-complexity algorithm has a similar performance as the grid-approximation approach and both perform much better than the QCD-based algorithms.

Denial-of-Service (DoS) attacks are the bane of public-facing network deployments. Algorithmic complexity attacks (ACAs) are a class of DoS attacks where an attacker uses a small amount of adversarial traffic to induce a large amount of work in the target system, pushing the system into overload and causing it to drop packets from innocent users. ACAs are particularly dangerous because, unlike volumetric DoS attacks, ACAs don't require a significant network bandwidth investment from the attacker Today, network functions (NFs) on the Internet must be designed and engineered on a case-by-case basis to mitigate the debilitating impact of ACAs. Further, the resulting designs tend to be overly conservative in their attack mitigation strategy, limiting the innocent traffic that the NF can serve under common-case operation.

Parallelizable jobs typically consist of multiple phases of computation, where the job is more parallelizable in some phases and less parallelizable in others. For example, in a database, a query may consist of a highly parallelizable table scan, followed by a less parallelizable table join. In the past, this phase-varying parallelizability was summarized by a single sub-linear speedup curve that measures a job’s average parallelizability over its entire lifetime. Today, however, modern systems have fine-grained knowledge of the exact phase each job is in at every moment in time. Unfortunately, these systems do not fully leverage this real-time feedback when scheduling parallelizable jobs. Theory has failed to produce practical phase-aware scheduling policies, and thus scheduling in current systems is largely heuristic. A phase-aware scheduling policy must decide, given its knowledge of each job’s current phase, how many servers or cores to allocate to each job in the system at every moment in time. This paper provides the first stochastic model of a system processing parallelizable jobs composed of phases. Using our model, we derive an optimal phase-aware scheduling policy that minimizes the mean response time across jobs. Our provably optimal policy, Inelastic-First (IF), gives strict priority to jobs that are currently in less parallelizable phases. We validate our theoretical results using a simulation of a database running queries from the Star Schema Benchmark. We compare IF to a range of policies from both systems and theory, and show that IF reduces mean response time by up to a factor of 3.

Motivated by various data science applications including de-anonymizing user identities in social networks, we consider the graph alignment problem, where the goal is to identify the vertex/user correspondence between two correlated graphs. Existing work mostly recovers the correspondence by exploiting the user-user connections. However, in many real-world applications, additional information about the users, such as user profiles, might be publicly available. In this paper, we introduce the attributed graph alignment problem, where additional user information, referred to as attributes, is incorporated to assist graph alignment. We establish sufficient and necessary conditions for recovering vertex correspondence exactly, where the conditions match for a wide range of practical regimes. Our results recover existing tight information-theoretic limits for models where only the user-user connections are available, and further span the full spectrum between these models and models where only attribute information is available.

In multi-server queueing systems where there is no central queue holding all incoming jobs, job dispatching policies are used to assign incoming jobs to the queue at one of the servers. Classic job dispatching policies such as join-the-shortest-queue and shortest expected delay assume that the service rates and queue lengths of the servers are known to the dispatcher. In this work, we tackle the problem of job dispatching without the knowledge of service rates and queue lengths, where the dispatcher can only obtain noisy estimates of the service rates by observing job departures. This problem presents a novel exploration-exploitation trade-off between sending jobs to all the servers to estimate their service rates, and exploiting the currently known fastest servers to minimize the expected queueing delay. We propose a bandit-based exploration policy that learns the service rates from observed job departures. Unlike the standard multi-armed bandit problem where only one out of a finite set of actions is optimal, here the optimal policy requires identifying the optimal fraction of incoming jobs to be sent to each server. We present a regret analysis and simulations to demonstrate the effectiveness of the proposed bandit-based exploration policy.

Caches are at the heart of latency-sensitive systems. In this paper, we identify a growing challenge for the design of latency-minimizing caches called delayed hits. Delayed hits occur at high throughput, when multiple requests to the same object queue up before an outstanding cache miss is resolved. This effect increases latencies beyond the predictions of traditional caching models and simulations; in fact, caching algorithms are designed as if delayed hits simply didn't exist. We show that traditional caching strategies -- even so called 'optimal' algorithms -- can fail to minimize latency in the presence of delayed hits. We design a new, latency-optimal offline caching algorithm called belatedly which reduces average latencies by up to 45% compared to the traditional, hit-rate optimal Belady's algorithm. Using belatedly as our guide, we show that incorporating an object's 'aggregate delay' into online caching heuristics can improve latencies for practical caching systems by up to 40%. We implement a prototype, Minimum-AggregateDelay (mad), within a CDN caching node. Using a CDN production trace and backends deployed in different geographic locations, we show that mad can reduce latencies by 12-18% depending on the backend RTTs.

Modern data centers are tasked with processing heterogeneous workloads consisting of various classes of jobs. These classes differ in their arrival rates, size distributions, and job parallelizability. With respect to parallelizability, some jobs are elastic, meaning they can parallelize linearly across any number of servers. Other jobs are inelastic, meaning they can only run on a single server. Although job classes can differ drastically, they are typically forced to share a single cluster. When sharing a cluster among heterogeneous jobs, one must decide how to allocate servers to each job at every moment in time. In this paper, we design and analyze allocation policies which aim to minimize the mean response time across jobs, where a job's response time is the time from when it arrives until it completes.

We study the value of data privacy in a game-theoretic model of trading private data, where a data collector purchases private data from strategic data subjects (individuals) through an incentive mechanism. The private data of each individual represents her knowledge about an underlying state, which is the information that the data collector desires to learn. Different from most of the existing work on privacy-aware surveys, our model does not assume the data collector to be trustworthy. Then, an individual takes full control of its own data privacy and reports only a privacy-preserving version of her data. In this paper, the value of ε units of privacy is measured by the minimum payment of all nonnegative payment mechanisms, under which an individual's best response at a Nash equilibrium is to report the data with a privacy level of ε. The higher ε is, the less private the reported data is. We derive lower and upper bounds on the value of privacy which are asymptotically tight as the number of data subjects becomes large. Specifically, the lower bound assures that it is impossible to use less amount of payment to buy ε units of privacy, and the upper bound is given by an achievable payment mechanism that we designed. Based on these fundamental limits, we further derive lower and upper bounds on the minimum total payment for the data collector to achieve a given learning accuracy target, and show that the total payment of the designed mechanism is at most one individual's payment away from the minimum.

This paper investigates the relation between three different notions of privacy: identifiability, differential privacy, and mutual-information privacy. Under a unified privacydistortion framework, where the distortion is defined to be the expected Hamming distance between the input and output databases, we establish some fundamental connections between these three privacy notions. Given a maximum allowable distortion D, we define the privacy-distortion functions ∈i* (D), ∈d*(D), and ∈m*(D) to be the smallest (most private/best) identifiability level, differential privacy level, and mutual information between the input and the output, respectively. We characterize ∈i* (D) and ∈d*(D), and prove that ∈i* (D) - ∈X≤ ∈d*(D) ≤ ∈i* (D) for D within certain range, where ∈Xis a constant determined by the prior distribution of the original database X, and diminishes to zero when X is uniformly distributed. Furthermore, we show that ∈i* (D) and ∈m*(D) can be achieved by the same mechanism for D within certain range, i.e., there is a mechanism that simultaneously minimizes the identifiability level and achieves the best mutual-information privacy. Based on these two connections, we prove that this mutual-information optimal mechanism satisfies ∈-differential privacy with ∈d*(D) ≤ ∈ ≤ ∈d*(D)+2∈X. The results in this paper reveal some consistency between two worst case notions of privacy, namely, identifiability and differential privacy, and an average notion of privacy, mutual-information privacy.

This paper considers the problem of scheduling real-time traffic in wireless networks. We consider ad hoc wireless networks with general conflict graph-based interference model and single-hop traffic. Each packet is associated with a deadline and will be dropped if it is not transmitted before the deadline. The number of packet arrivals in each time-slot and the maximum delay before the deadline are independent and identically distributed across time. We require a minimum fraction of packets to be delivered. At each link, we assume the link keeps track of the difference between the minimum number of packets that need to be delivered so far and the number of packets that are actually delivered, which we call the deficit. The largest-deficit-first (LDF) policy schedules links in descending order according to their deficit values, which is a variation of the longest-queue-first (LQF) policy for non-real-time traffic. We prove that the efficiency ratio of LDF, which is the fraction of the throughput region that LDF can achieve for given traffic distributions, can be lower-bounded by a quantity that we call the real-time local-pooling factor (R-LPF). We further prove that a lower bound on the R-LPF can be related to the weighted sum of the service rates, with a special case of 1/(β+1) by considering the uniform weight, where β is the interference degree of the conflict graph. We also propose a heuristic consensus algorithm that can be used to obtain a good weight vector for such lower bounds for given network topology.

MapReduce/Hadoop framework has been widely used to process large-scale datasets on computing clusters. Scheduling map tasks with data locality consideration is crucial to the performance of MapReduce. Many works have been devoted to increasing data locality for better efficiency. However, to the best of our knowledge, fundamental limits of MapReduce computing clusters with data locality, including the capacity region and theoretical bounds on the delay performance, have not been well studied. In this paper, we address these problems from a stochastic network perspective. Our focus is to strike the right balance between data locality and load balancing to simultaneously maximize throughput and minimize delay. We present a new queueing architecture and propose a map task scheduling algorithm constituted by the Join the Shortest Queue policy together with the MaxWeight policy. We identify an outer bound on the capacity region, and then prove that the proposed algorithm can stabilize any arrival rate vector strictly within this outer bound. It shows that the outer bound coincides with the actual capacity region, and the proposed algorithm is throughput-optimal. Furthermore, we study the number of backlogged tasks under the proposed algorithm, which is directly related to the delay performance based on Little's law. We prove that the proposed algorithm is heavy-traffic optimal, i.e., it asymptotically minimizes the number of backlogged tasks as the arrival rate vector approaches the boundary of the capacity region. Therefore, the proposed algorithm is also delay-optimal in the heavy-traffic regime. The proofs in this paper deal with random processing times with heterogeneous parameters and nonpreemptive task execution, which differentiate our work from many existing works on MaxWeight-type algorithms, so the proof techniques themselves for the stability analysis and the heavy-traffic analysis are also novel contributions.

Scheduling map tasks to improve data locality is crucial to the performance of MapReduce. Many works have been devoted to increasing data locality for better efficiency. However, to the best of our knowledge, fundamental limits of MapReduce computing clusters with data locality, including the capacity region and theoretical bounds on the delay performance, have not been studied. In this paper, we address these problems from a stochastic network perspective. Our focus is to strike the right balance between data-locality and load-balancing to simultaneously maximize throughput and minimize delay. We present a new queueing architecture and propose a map task scheduling algorithm constituted by the Join the Shortest Queue policy together with the MaxWeight policy. We identify an outer bound on the capacity region, and then prove that the proposed algorithm stabilizes any arrival rate vector strictly within this outer bound. It shows that the algorithm is throughput optimal and the outer bound coincides with the actual capacity region. Further, we study the number of backlogged tasks under the proposed algorithm, which is directly related to the delay performance based on Little's law. We prove that the proposed algorithm is heavy-traffic optimal, i.e., it asymptotically minimizes the number of backlogged tasks as the arrival rate vector approaches the boundary of the capacity region. Therefore, the proposed algorithm is also delay optimal in the heavy-traffic regime.

This paper considers the problem of scheduling real-time traffic in wireless networks. We consider an ad hoc wireless network with general interference and general one-hop traffic. Each packet is associated with a deadline and will be dropped if it is not transmitted before the deadline expires. The number of packet arrivals in each time slot and the length of a deadline are both stochastic and follow certain distributions. We only allow a fraction of packets to be dropped. At each link, we assume the link keeps track of the difference between the minimum number of packets that need to be delivered and the number of packets that are actually delivered, which we call deficit. The largest-deficit-first (LDF) policy schedules links in descending order according to their deficit values, which is a variation of the largest-queue-first (LQF) policy for non-real-time traffic. We prove that the efficiency ratio of LDF can be lower bounded by a quantity that we call the real-time local-pooling factor (R-LPF). We further prove that given a network with interference degree β, the R-LPF is at least 1/(β+1), which in the case of the one-hop interference model translates into an R-LPF of at least 1/3.