Arpan Chattopadhyay

Gibbsian On-Line Distributed Content Caching Strategy for Cellular Networks

In this paper, we develop Gibbs sampling-based techniques for learning the optimal placement of contents in a cellular network. We consider the situation where a finite collection of base stations are scattered on the plane, each covering a cell (possibly overlapping with other cells). Mobile users request downloads from a finite set of contents according to some popularity distribution which may be known or unknown to the base stations. Each base station has a fixed memory space that can store only a strict subset of the contents at a time; hence, if a user requests content that is not stored at any of its serving base stations, the content has to be downloaded from the backhaul. Hence, we consider the problem of optimal content placement which minimizes the rate of download from the backhaul, or equivalently maximize the cache hit rate. It is known that, when multiple cells can overlap with one another (e.g., under dense deployment of base stations in small cell networks), it is not optimal to place the most popular contents in each base station. However, the optimal content placement problem is NP-complete. Using the ideas of Gibbs sampling, we propose simple sequential content update rules that decide whether to store content at a base station (if required from the base station) and which content has to be removed from the corresponding cache, based on the knowledge of contents stored in its neighboring base stations. The update rule is shown to be asymptotically converging to the optimal content placement for all nodes under the knowledge of content popularity. Next, we extend the algorithm to address the situation where content popularities and cell topology are initially unknown, but are estimated as new requests arrive to the base stations; we show that our algorithm working with the running estimates of content popularities and cell topology also converges asymptotically to the optimal content placement. Finally, we demonstrate the improvement in cache hit rate compared with the most popular content placement and independent content placement strategies via numerical exploration.

Impromptu Deployment of Wireless Relay Networks: Experiences Along a Forest Trail

We are motivated by the problem of impromptu or as-you-go deployment of wireless sensor networks. As an application example, a person, starting from a sink node, walks along a forest trail, makes link quality measurements (with the previously placed nodes) at equally spaced locations, and deploys relays at some of these locations, so as to connect a sensor placed at some a priori unknown point on the trail with the sink node. In this paper, we report our experimental experiences with some as-you-go deployment algorithms. Two algorithms are based on Markov decision process (MDP) formulations, these require a radio propagation model. We also study purely measurement based strategies: one heuristic that is motivated by our MDP formulations, one asymptotically optimal learning algorithm, and one inspired by a popular heuristic. We extract a statistical model of the propagation along a forest trail from raw measurement data, implement the algorithms experimentally in the forest, and compare them. The results provide useful insights regarding the choice of the deployment algorithm and its parameters, and also demonstrate the necessity of a proper theoretical formulation.

As-you-go deployment of a 2-connected wireless relay network for sensor-sink interconnection

A person walks along a line (which could be an idealisation of a forest trail, for example), placing relays as he walks, in order to create a multihop network for connecting a sensor at a point along the line to a sink at the start of the line. The potential placement points are equally spaced along the line, and at each such location the decision to place or not to place a relay is based on link quality measurements to the previously placed relays. The location of the sensor is unknown apriori, and is discovered as the deployment agent walks. In this paper, we extend our earlier work on this class of problems to include the objective of achieving a 2-connected multihop network. We propose a network cost objective that is additive over the deployed relays, and accounts for possible alternate routing over the multiple available paths. As in our earlier work, the problem is formulated as a Markov decision process. Placement algorithms are obtained for two source location models, which yield a discounted cost MDP and an average cost MDP. In each case we obtain structural results for an optimal policy, and perform a numerical study that provides insights into the advantages and disadvantages of multi-connectivity. We validate the results obtained from numerical study experimentally in a forest-like environment.

Deploy-As-You-Go Wireless Relay Placement: An Optimal Sequential Decision Approach Using the Multi-Relay Channel Model

We use information theoretic achievable rate formulas for the multi-relay channel to study the problem of as-you-go deployment of relay nodes. The achievable rate formulas are for full-duplex radios at the relays and for decode-and-forward relaying. Deployment is done along the straight line joining a source node and a sink node at an unknown distance from the source. The problem is for a deployment agent to walk from the source to the sink, deploying relays as he walks, given the knowledge of the wireless path-loss model, and given that the distance to the sink node is exponentially distributed with known mean. As a precursor to the formulation of the deploy-as-you-go problem, we apply the multi-relay channel achievable rate formula to obtain the optimal power allocation to relays placed along a line, at fixed locations. This permits us to obtain the optimal placement of a given number of nodes when the distance between the source and sink is given. Numerical work for the fixed source-sink distance case suggests that, at low attenuation, the relays are mostly clustered close to the source in order to be able to cooperate among themselves, whereas at high attenuation they are uniformly placed and work as repeaters. We also prove that the effect of path-loss can be entirely mitigated if a large enough number of relays are placed uniformly between the source and the sink. The structure of the optimal power allocation for a given placement of the nodes, then motivates us to formulate the problem of as-you-go placement of relays along a line of exponentially distributed length, and with the exponential path-loss model, so as to minimize a cost function that is additive over hops. The hop cost trades off a capacity limiting term, motivated from the optimal power allocation solution, against the cost of adding a relay node. We formulate the problem as a total cost Markov decision process, establish results for the value function, and provide insights into the placement policy and the performance of the deployed network via numerical exploration.

Sequential Decision Algorithms for Measurement-Based Impromptu Deployment of a Wireless Relay Network Along a Line

We are motivated by the need, in some applications, for impromptu or as-you-go deployment of wireless sensor networks. A person walks along a line, starting from a sink node (e.g., a base-station), and proceeds towards a source node (e.g., a sensor) which is at an a priori unknown location. At equally spaced locations, he makes link quality measurements to the previous relay, and deploys relays at some of these locations, with the aim to connect the source to the sink by a multihop wireless path. In this paper, we consider two approaches for impromptu deployment: (i) the deployment agent can only move forward (which we call a pure as-you-go approach), and (ii) the deployment agent can make measurements over several consecutive steps before selecting a placement location among them (the explore-forward approach). We consider a very light traffic regime, and formulate the problem as a Markov decision process, where the trade-off is among the power used by the nodes, the outage probabilities in the links, and the number of relays placed per unit distance. We obtain the structures of the optimal policies for the pure as-you-go approach as well as for the explore-forward approach. We also consider natural heuristic algorithms, for comparison. Numerical examples show that the explore-forward approach significantly outperforms the pure as-you-go approach in terms of network cost. Next, we propose two learning algorithms for the explore-forward approach, based on Stochastic Approximation, which asymptotically converge to the set of optimal policies, without using any knowledge of the radio propagation model. We demonstrate numerically that the learning algorithms can converge (as deployment progresses) to the set of optimal policies reasonably fast and, hence, can be practical model-free algorithms for deployment over large regions. Finally, we demonstrate the end-to-end traffic carrying capability of such networks via field deployment.

Measurement Based As-You-Go Deployment of Two-Connected Wireless Relay Networks

Motivated by the need for impromptu or as-you-go deployment of wireless sensor networks in some situations, we study the problem of optimal sequential deployment of wireless sensors and relays along a line (e.g., a forest trail) of unknown length. Starting from the sink node (e.g., a base station), a ”deployment agent„ walks along the line, stops at equally spaced points (”potential„ relay locations), placing relays at some of these points, until he reaches a location at which the source node (i.e., the sensor) needs to be placed, the objective being to create a multihop wireless relay network between the source and the sink. The deployment agent decides whether to place a relay or not at each of the potential locations, depending upon the link quality measurements to the previously placed relays. In this article, we seek to design efficient deployment algorithms for this class of problems, to achieve the objective of 2-connectivity in the deployed network. We ensure multi-connectivity by allowing each node to communicate with more than one neighbouring node. By proposing a network cost objective that is additive over the deployed relays, we formulate the relay placement problem as a Markov decision process. We provide structural results for the optimal policy and evaluate the performance of the optimal policy via numerical exploration. Computation of such an optimal deployment policy requires a statistical model for radio propagation; we extract this model from the raw data collected via measurements in a forestlike environment. To validate the results obtained from the numerical study, we provide an experimental study of algorithms for 2-connected network deployment.

Hybrid MAC Protocols for Low-Delay Scheduling

We consider the Medium Access Control (MAC) problem in resource-constrained ad-hoc wireless networks typical of the Internet of Things (IoT). Due to the delay-sensitive nature of emerging IoT applications, there has been increasing interest in developing medium access control (TDMA) protocols in a slotted framework. The design of such MAC protocols must keep in mind the need for contention access at light traffic, and scheduled access in heavy traffic (leading to the long-standing interest in hybrid, adaptive MACs. In this paper, we consider the collocated node setting and require that each node acts autonomously only on the basis of locally available information. We propose EZMAC, a simple extension of ZMAC, and QZMAC which is designed using motivations from our extensions of certain delay-optimality and throughput-optimality theory from the literature. Practical implementation issues are outlined. Finally, we show, through simulations, that both protocols achieve mean delays much lower than those achieved by ZMAC and indeed, QZMAC provides mean delays very close to the minimum achievable in this setting, i.e., that of the centralized complete knowledge scheduler.

Past queue length based low-overhead link scheduling in multi-beam wireless mesh networks

Wireless mesh networks with multi-beam capability at each node through the use of multi-antenna beamforming are becoming practical and attracting increased research attention. Increased capacity due to spatial reuse and increased transmission range are potential benefits in using multiple directional beams in each node. In this paper, we are interested in low-complexity scheduling algorithms in such multi-beam wireless networks. In particular, we present a scheduling algorithm based on queue length information of the past slots in multi-beam networks, and prove its stability. We present a distributed implementation of this proposed algorithm. Numerical results show that significant improvement in delay performance is achieved using the proposed multi-beam scheduling compared to omni-beam scheduling. In addition, the proposed algorithm is shown to achieve a significant reduction in the signaling overhead compared to a current slot queue length approach.