Abhishek Sinha

Optimal caching of files in a content distribution network (CDN) is a problem of fundamental and growing commercial interest. Although many different caching algorithms are in use today, the fundamental performance limits of the network caching algorithms from an online learning point-of-view remain poorly understood to date. In this paper, we resolve this question in the following two settings: (1) a single user connected to a single cache, and (2) a set of users and a set of caches interconnected through a bipartite network. Recently, an online gradient-based coded caching policy was shown to enjoy sub-linear regret. However, due to the lack of known regret lower bounds, the question of the optimality of the proposed policy was left open. In this paper, we settle this question by deriving tight non-asymptotic regret lower bounds in the above settings. In addition to that, we propose a new Follow-the-Perturbed-Leader-based uncoded caching policy with near-optimal regret. Technically, the lower-bounds are obtained by relating the online caching problem to the classic probabilistic paradigm of balls-into-bins. Our proofs make extensive use of a new result on the expected load in the most populated half of the bins, which might also be of independent interest. We evaluate the performance of the caching policies by experimenting with the popular MovieLens dataset and conclude the paper with design recommendations and a list of open problems.

We consider a virtualized RAN architecture for 5G networks where the Remote Units are connected to a central unit via a mid-haul. To support high data rates, the mid-haul is realized with a Passive Optical Network (PON). In this architecture, the data are stored at the central unit until the scheduler decides to transmit it through the mid-haul to an appropriate remote unit, and then over the air at the same slot. We study an optimal scheduling problem that arises in this context. This problem has two key features. First, multiple cells must be scheduled simultaneously for efficient operation. Second, the interplay between the time-varying wireless interface rates and the fixed capacity PON needs to be handled efficiently. In this paper, we take a comprehensive look at this resource allocation problem by formulating it as a utility-maximization problem. Using combinatorial techniques, we derive useful structural properties of the optimal allocation and utilize these results to design polynomial-time approximation algorithms and a pseudo- polynomial-time optimal algorithm. Finally, we numerically compare the performance of the proposed algorithms to heuristics which are natural generalizations of the ubiquitous Proportional Fair algorithm.

Age of Information AoI is a performance metric that captures the freshness of the information from the perspective of the destination. The AoI measures the time that elapsed since the generation of the packet that was most recently delivered to the destination. In this paper, we consider a single-hop wireless network with a number of nodes transmitting time-sensitive information to a base station and address the problem of minimizing the expected weighted sum AoI of the network while simultaneously satisfying timely-throughput constraints from the nodes. We develop four low-complexity transmission scheduling policies that attempt to minimize AoI subject to minimum throughput requirements and evaluate their performance against the optimal policy. In particular, we develop a randomized policy, a Max-Weight policy, a Drift-Plus-Penalty policy, and a Whittle's Index policy, and show that they are guaranteed to be within a factor of two, four, two, and eight, respectively, away from the minimum AoI possible. The simulation results show that Max-Weight and Drift-Plus-Penalty outperform the other policies, both in terms of AoI and throughput, in every network configuration simulated, and achieve near-optimal performance.

This paper considers a multi-user downlink scheduling problem with access to the channel state information at the transmitter (CSIT) to minimize the Age-of-Information (AoI) in a non-stationary environment. The non-stationary environment is modelled using a novel adversarial framework. In this setting, we propose a greedy scheduling policy, called MA-CSIT, that takes into account the current channel state information. We establish a finite upper bound on the competitive ratio achieved by the MA-CSIT policy for a small number of users and show that the proposed policy has a better performance guarantee than a recently proposed greedy scheduler that operates without CSIT. In particular, we show that access to the additional channel state information improves the competitive ratio from 8 to 2 in the two-user case and from 18 to 8/3 in the three-user case. Finally, we carry out extensive numerical simulations to quantify the advantage of knowing CSIT in order to minimize the Age-of-Information for an arbitrary number of users.

We consider the classical uncoded caching problem from an online learning point-of-view. A cache of limited storage capacity can hold C files at a time from a large catalog. A user requests an arbitrary file from the catalog at each time slot. The request sequence could be adversarial. Before the file request from the user arrives, a caching policy populates the cache with any C files of its choice. In the case of a cache-hit, the policy receives a unit reward and zero rewards otherwise. In addition to that, there is a cost associated with fetching files to the cache, which we refer to as the switching cost. The objective is to design a caching policy that incurs minimal regret while considering both the rewards due to cache-hits and the switching cost due to the file fetches. The main contribution of this paper is the switching regret analysis of a Follow The Perturbed LEADER-based anytime caching policy, which is shown to have an order optimal switching regret. In this pursuit, we improve the best-known switching regret bound for this problem by a factor of Θ(√C). We conclude the paper by comparing the performance of different popular caching policies using a publicly available trace from a commercial CDN server.

We consider the problem of efficient packet dissemination in wireless networks with point-to-multipoint wireless broadcast channels. We propose a dynamic policy, which achieves the broadcast capacity of the network. This policy is obtained by first transforming the original multi-hop network into a precedence-relaxed virtual single-hop network and then finding an optimal broadcasting policy for the relaxed network. The resulting policy is shown to be throughput-optimal for the original wireless network using a sample-path argument. We also prove the NP-completeness of the finite-horizon broadcasting problem, which is in contrast with the polynomial-time solvability of the problem with point-to-point channels. Illustrative simulation results demonstrate the efficacy of the proposed broadcast policy in achieving the full broadcast capacity with low delay.

We design efficient online scheduling policies to maximize the freshness of information delivered to the users in a cellular network under both adversarial and stochastic channel and mobility assumptions. The information freshness achieved by a policy is investigated through the lens of a recently proposed metric - Age-of-Information (AoI). We show that a natural greedy scheduling policy is competitive against any optimal offline policy in minimizing the AoI in the adversarial setting. We also derive universal lower bounds to the competitive ratio achievable by any online policy in the adversarial framework. In the stochastic setting, we show that a simple index policy is near-optimal for minimizing the average AoI in two different mobility scenarios. Further, we prove that the greedy scheduling policy minimizes the peak AoI for static users in the stochastic setting. Simulation results show that the proposed policies perform well under realistic conditions.

We investigate the problem of fast and secure packet routing in multi-hop Quantum Key Distribution (QKD) networks. We consider a practical trusted-node setup where a QKD protocol randomly generates symmetric private key pairs over each QKD-enabled link in a network. Packets are first encrypted with the available quantum keys and then transmitted on a point-to-point basis. A fundamental problem in this setting is the design of a secure and capacity-achieving routing policy that takes into account the time-varying availability of the encryption keys and diverse physical-layer link capacities. To address this problem, we propose a new secure throughput-optimal policy called Tandem Queue Decomposition (TQD). The TQD policy is designed by incorporating the QKD process into the Universal Max Weight (UMW) routing policy. We show that the TQD policy achieves the entire secure capacity region for a broad class of traffic, including unicast, broadcast, multicast, and anycast. The TQD policy operates by reducing the problem to the generalized network flow problem without the key availability constraints over a transformed network. The throughput-optimality of the TQD policy is established using the Lyapunov stability theory by carefully analyzing the interdependent queueing process and the key-storage dynamics. Finally, we demonstrate the practical efficiency of the TQD policy over the existing routing algorithms by numerically comparing their performance on a realistic simulator built on top of the state-of-the-art OMNeT++ network simulator platform.

In this short paper, we consider the problem of designing a near-optimal competitive scheduling policy to maximize the freshness of available information uniformly across N mobile users. Motivated by the unreliability and non-stationarity of the emerging 5G-mmWave channels for high-speed users, we forego of any statistical modeling assumptions of the wireless channels and user-mobility. Instead, we allow the channel states and the mobility patterns to be dictated by an omniscient adversary. It is not difficult to see that no competitive scheduling policy can exist for the corresponding throughput-maximization problem in this adversarial model. Surprisingly, we show that there exists a simple online distributed scheduling policy with a finite competitive ratio for maximizing the freshness of information in this model. We also prove that the proposed policy is competitively optimal up to an O(logN) factor.

This paper considers the problem of secure packet routing at the maximum achievable rate in a Quantum key distribution (QKD) network. Assume that a QKD protocol generates symmetric private keys for secure communication over each link in a multi-hop network. The quantum key generation process, which is affected by noise, is assumed to be modeled by a stochastic counting process. Packets are first encrypted with the available quantum keys for each hop and then transmitted on a point-to-point basis over the communication links. A fundamental problem that arises in this setting is to design a secure and capacity-achieving routing policy that accounts for the time-varying availability of the quantum keys for encryption and finite link capacities for transmission. In this paper, by combining the QKD protocol with the Universal Max Weight (UMW) routing policy [1] - [3], we design a new secure throughput-optimal routing policy, called Tandem Queue Decomposition (TQD). TQD solves the problem of secure routing efficiently for a wide class of traffic, including unicast, broadcast, and multicast. One of our main contributions in this paper is to show that the problem can be reduced to the usual generalized network flow problem on a transformed network without the key availability constraints. Simulation results show that the proposed policy incurs a substantially smaller delay as compared to the state-of-the-art routing and key management policies. The proof of throughput-optimality of the proposed policy makes use of the Lyapunov stability theory along with a careful treatment of the key-storage dynamics.