arXiv subjects

Mohamad Assaad

Publications and source records attributed to Mohamad Assaad.

At least 55 records · Page 3Linked to original sources

arXiv2021

Minimizing the Age of Incorrect Information for Real-time Tracking of Markov Remote Sources

The age of Incorrect Information (AoII) has been introduced recently to address the shortcomings of the standard Age of information metric (AoI) in real-time monitoring applications. In this paper, we consider the problem of monitoring the states of remote sources that evolve according to a Markovian Process. A central scheduler selects at each time slot which sources should send their updates in such a way to minimize the Mean Age of Incorrect Information (MAoII). The difficulty of the problem lies in the fact that the scheduler cannot know the states of the sources before receiving the updates and it has then to optimally balance the exploitation-exploration trade-off. We show that the problem can be modeled as a partially Observable Markov Decision Process Problem framework. We develop a new scheduling scheme based on Whittle's index policy. The scheduling decision is made by updating a belief value of the states of the sources, which is to the best of our knowledge has not been considered before in the Age of Information area. To that extent, we proceed by using the Lagrangian Relaxation Approach, and prove that the dual problem has an optimal threshold policy. Building on that, we shown that the problem is indexable and compute the expressions of the Whittle's indices. Finally, we provide some numerical results to highlight the performance of our derived policy compared to the classical AoI metric.

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arXiv2021

On the Global Optimality of Whittle's index policy for minimizing the age of information

This paper examines the average age minimization problem where only a fraction of the network users can transmit simultaneously over unreliable channels. Finding the optimal scheduling scheme, in this case, is known to be challenging. Accordingly, the Whittle's index policy was proposed in the literature as a low-complexity heuristic to the problem. Although simple to implement, characterizing this policy's performance is recognized to be a notoriously tricky task. In the sequel, we provide a new mathematical approach to establish its optimality in the many-users regime for specific network settings. Our novel approach is based on intricate techniques, and unlike previous works in the literature, it is free of any mathematical assumptions. These findings showcase that the Whittle's index policy has analytically provable asymptotic optimality for the AoI minimization problem. Finally, we lay out numerical results that corroborate our theoretical findings and demonstrate the policy's notable performance in the many-users regime.

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arXiv2020

Age of Information in a Decentralized Network of Parallel Queues with Routing and Packets Losses

The paper deals with Age of Information (AoI) in a network of multiple sources and parallel queues with buffering capabilities, preemption in service and losses in served packets. The queues do not communicate between each other and the packets are dispatched through the queues according to a predefined probabilistic routing. By making use of the Stochastic Hybrid System (SHS) method, we provide a derivation of the average AoI of a system of two parallel queues (with and without buffer capabilities) and compare the results with those of a single queue. We show that known results of packets delay in Queuing Theory do not hold for the AoI. Unfortunately, the complexity of computing the average AoI using the SHS method increases highly with the number of queues. We therefore provide an upper bound of the average AoI in a system of an arbitrary number of M/M/1/(N+1) queues and show its tightness in various regimes. This upper bound allows providing a tight approximation of the average AoI with a very low complexity. We then provide a game framework that allows each source to determine its best probabilistic routing decision. By using Mean Field Games, we provide an analysis of the routing game framework, propose an efficient iterative method to find the routing decision of each source and prove its convergence to the desired equilibrium.

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arXiv2020

A Dynamic and Incentive Policy for Selecting D2D Mobile Relays

User-to-network relaying enabled via Device-to-Device communications (D2D) is a promising technique for improving the performance of cellular networks. Since in practice relays are in mobility, a dynamic relay selection scheme is unavoidable. In this paper, we propose a dynamic relay selection policy that maximizes the performance of cellular networks (e.g. throughput, reliability, coverage) under cost constraints (e.g. transmission power, power budget). We represent the relays' dynamics as a Markov Decision Process (MDP) and assume that only the locations of the selected relays are observable. Therefore, the dynamic relay selection process is modeled as a Constrained Partially Observed Markov Decision Process (CPOMDP). Since the exact solution of such framework is intractable to find, we develop a point-based value iteration solution and evaluate its performance. In addition, we prove the submodularity property of both the reward and cost value functions and deduce a greedy solution which is scalable with the number of discovered relays. For the muti-user scenario, a distributed approach is introduced in order to reduce the complexity and the overhead of the proposed solution. We illustrate the numerical results of the scenario where throughput is maximized under energy constraint and evaluate the gain that the proposed relay selection policy achieves compared to a traditional cellular network.

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arXiv2020

The Age of Incorrect Information: A New Performance Metric for Status Updates

In this paper, we introduce a new performance metric in the framework of status updates that we will refer to as the Age of Incorrect Information (AoII). This new metric deals with the shortcomings of both the Age of Information (AoI) and the conventional error penalty functions as it neatly extends the notion of fresh updates to that of fresh "informative" updates. The word informative in this context refers to updates that bring new and correct information to the monitor side. After properly motivating the new metric, and with the aim of minimizing its average, we formulate a Markov Decision Process (MDP) in a transmitter-receiver pair scenario where packets are sent over an unreliable channel. We show that a simple "always update" policy minimizes the aforementioned average penalty along with the average age and prediction error. We then tackle the general, and more realistic case, where the transmitter cannot surpass a specific power budget. The problem is formulated as a Constrained Markov Decision Process (CMDP) for which we provide a Lagrangian approach to solve. After characterizing the optimal transmission policy of the Lagrangian problem, we provide a rigorous mathematical proof to showcase that a mixture of two Lagrange policies is optimal for the CMDP in question. Equipped with this, we provide a low complexity algorithm that finds the AoII-optimal operating point of the system in the constrained scenario. Lastly, simulation results are laid out to showcase the performance of the proposed policy and highlight the differences with the AoI framework.

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arXiv2020

Asymptotically Optimal Delay-aware Scheduling in Queueing Systems

In this paper, we investigate a general delay-aware channel allocation problem where the number of channels is less than that of users. Due to the proliferation of delay sensitive applications, the objective of our problem is chosen to be the minimization of the total average backlog queues of the network in question. First, we show that our problem falls in the framework of Restless Bandit Problems (RBP), for which obtaining the optimal solution is known to be out of reach. To circumvent this difficulty, we tackle the problem by adopting a Whittle index approach. To that extent, we employ a Lagrangian relaxation of the original problem and prove it to be decomposable into multiple one-dimensional independent subproblems. Afterwards, we provide structural results on the optimal policy of each of the subproblems. More specifically, we prove that a threshold policy is able to achieve the optimal operating point of the considered subproblem. Armed with that, we show the indexability of the subproblems and characterize the Whittle's indices which are the basis of our proposed heuristic. We then provide a rigorous mathematical proof that our policy is optimal in the infinitely many users regime. Finally, we provide numerical results that showcase the remarkable good performance of our proposed policy and that corroborate the theoretical findings.

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arXiv2020

Status Updates with Priorities: Lexicographic Optimality

In this paper, we consider a transmission scheduling problem, in which several streams of status update packets with diverse priority levels are sent through a shared channel to their destinations. We introduce a notion of Lexicographic age optimality, or simply lex-age-optimality, to evaluate the performance of multi-class status update policies. In particular, a lex-age-optimal scheduling policy first minimizes the Age of Information (AoI) metrics for high-priority streams, and then, within the set of optimal policies for high-priority streams, achieves the minimum AoI metrics for low-priority streams. We propose a new scheduling policy named Preemptive Priority, Maximum Age First, Last-Generated, First-Served (PP-MAF-LGFS), and prove that the PP-MAF-LGFS scheduling policy is lex-age-optimal. This result holds (i) for minimizing any time-dependent, symmetric, and non-decreasing age penalty function; (ii) for minimizing any non-decreasing functional of the stochastic process formed by the age penalty function; and (iii) for the cases where different priority classes have distinct arrival traffic patterns, age penalty functions, and age penalty functionals. For example, the PP-MAF-LGFS scheduling policy is lex-age-optimal for minimizing the mean peak age of a high-priority stream and the time-average age of a low-priority stream. Numerical results are provided to illustrate our theoretical findings.

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arXiv2020

On The Optimality of The Whittle's Index Policy For Minimizing The Age of Information

In this paper, we consider the average age minimization problem where a central entity schedules M users among the N available users for transmission over unreliable channels. It is well-known that obtaining the optimal policy, in this case, is out of reach. Accordingly, the Whittle's index policy has been suggested in earlier works as a heuristic for this problem. However, the analysis of its performance remained elusive. In the sequel, we overcome these difficulties and provide rigorous results on its asymptotic optimality in the many-users regime. Specifically, we first establish its optimality in the neighborhood of a specific system's state. Next, we extend our proof to the global case under a recurrence assumption, which we verify numerically. These findings showcase that the Whittle's index policy has analytically provable optimality in the many-users regime for the AoI minimization problem. Finally, numerical results that showcase its performance and corroborate our theoretical findings are presented.

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arXiv2019

Distributed Power Control for Large Energy Harvesting Networks: A Multi-Agent Deep Reinforcement Learning Approach

In this paper, we develop a multi-agent reinforcement learning (MARL) framework to obtain online power control policies for a large energy harvesting (EH) multiple access channel, when only causal information about the EH process and wireless channel is available. In the proposed framework, we model the online power control problem as a discrete-time mean-field game (MFG), and analytically show that the MFG has a unique stationary solution. Next, we leverage the fictitious play property of the mean-field games, and the deep reinforcement learning technique to learn the stationary solution of the game, in a completely distributed fashion. We analytically show that the proposed procedure converges to the unique stationary solution of the MFG. This, in turn, ensures that the optimal policies can be learned in a completely distributed fashion. In order to benchmark the performance of the distributed policies, we also develop a deep neural network (DNN) based centralized as well as distributed online power control schemes. Our simulation results show the efficacy of the proposed power control policies. In particular, the DNN based centralized power control policies provide a very good performance for large EH networks for which the design of optimal policies is intractable using the conventional methods such as Markov decision processes. Further, performance of both the distributed policies is close to the throughput achieved by the centralized policies.

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arXiv2019

Energy Efficient and Throughput Optimal CSMA Scheme

Carrier Sense Multiple Access (CSMA) is widely used as a Medium Access Control (MAC) in wireless networks due to its simplicity and distributed nature. This motivated researchers to find CSMA schemes that achieve throughput optimality. In 2008, it has been shown that a simple CSMA-type algorithm is able to achieve optimality in terms of throughput and has been given the name "adaptive" CSMA. Lately, new technologies emerged where prolonged battery life is crucial such as environment and industrial monitoring. This inspired the foundation of new CSMA based MAC schemes where links are allowed to transition into sleep mode to reduce the power consumption. However, throughput optimality of these schemes was not established. This paper therefore aims to find a new CSMA scheme that combines both throughput optimality and energy efficiency by adapting to the throughput and power consumption needs of each link. This is done by controlling operational parameters such as back-off and sleeping timers with the aim of optimizing a certain objective function. The resulting CSMA scheme is characterized by being asynchronous, completely distributed and being able to adapt to different power consumption profiles required by each link while still ensuring throughput optimality. The performance gain in terms of energy efficiency compared to the conventional adaptive CSMA scheme is demonstrated through computer simulations.

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arXiv2019

On Optimal Scheduling for Joint Spatial Division and Multiplexing Approach in FDD Massive MIMO

Massive MIMO is widely considered as a key enabler of the next generation 5G networks. With a large number of antennas at the Base Station, both spectral and energy efficiencies can be enhanced. Unfortunately, the downlink channel estimation overhead scales linearly with the number of antennas. This burden is easily mitigated in TDD systems by the use of the channel reciprocity property. However, this is unfeasible for FDD systems and the method of two-stage beamforming was therefore developed to reduce the amount of channel state information feedback. The performance of this scheme being highly dependent on the users grouping and scheduling mechanims, we introduce in this paper a new similarity measure coupled with a novel clustering procedure to achieve the appropriate users grouping. We also proceed to formulate the optimal users scheduling policy in JSDM and prove that it is NP-hard. This result is of paramount importance since it suggests that, unless P=NP, there are no polynomial time algorithms that solve the general scheduling problem to global optimality and the use of sub-optimal scheduling strategies is more realistic in practice. We therefore use graph theory to develop a sub-optimal users scheduling scheme that runs in polynomial time and outperforms the scheduling schemes previously introduced in the literature for JSDM in both sum-rate and throughput fairness.

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arXiv2019

Deep Learning Based Online Power Control for Large Energy Harvesting Networks

In this paper, we propose a deep learning based approach to design online power control policies for large EH networks, which are often intractable stochastic control problems. In the proposed approach, for a given EH network, the optimal online power control rule is learned by training a deep neural network (DNN), using the solution of offline policy design problem. Under the proposed scheme, in a given time slot, the transmit power is obtained by feeding the current system state to the trained DNN. Our results illustrate that the DNN based online power control scheme outperforms a Markov decision process based policy. In general, the proposed deep learning based approach can be used to find solutions to large intractable stochastic control problems.

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arXiv2019

Distributed vs. Centralized Scheduling in D2D-enabled Cellular Networks

Employing channel adaptive resource allocation can yield to a large enhancement in almost any performance metric of Device-to-Device (D2D) communications. We observe that D2D users are able to estimate their local Channel State Information (CSI), however the base station needs some signaling exchange to acquire this information. Based on the D2D users' knowledge of their local CSI, we provide a scheduling framework that shows how distributed approach outperforms centralized one. We start by proposing a centralized scheduling that requires the knowledge of D2D links' CSI at the base station level. This CSI reporting suffers from the limited number of resources available for feedback transmission. Therefore, we benefit from the users' knowledge of their local CSI to develop a distributed algorithm for D2D resource allocation. In distributed approach, collisions may occur between the different CSI reporting; thus a collision reduction algorithm is proposed. We give a description on how both centralized and distributed algorithms can be implemented in practice. Furthermore, numerical results are presented to corroborate our claims and demonstrate the gain that the proposed scheduling algorithms bring to cellular networks.

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arXiv2019

Whittle Index Policy for Multichannel Scheduling in Queueing Systems

In this paper, we consider a queueing system with multiple channels (or servers) and multiple classes of users. We aim at allocating the available channels among the users in such a way to minimize the expected total average queue length of the system. This known scheduling problem falls in the framework of Restless Bandit Problems (RBP) for which an optimal solution is known to be out of reach for the general case. The contributions of this paper are as follows. We rely on the Lagrangian relaxation method to characterize the Whittle index values and to develop an index-based heuristic for the original scheduling problem. The main difficulty lies in the fact that, for some queue states, deriving the Whittle's index requires introducing a new approach which consists in introducing a new expected discounted cost function and deriving the Whittle's index values with respect to the discount parameter $β$. We then deduce the Whittle's indices for the original problem (i.e. with total average queue length minimization) by taking the limit $β\rightarrow 1$. The numerical results provided in this paper show that this policy performs very well and is very close to the optimal solution for high number of users.

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arXiv2019

Minimizing The Age of Information: NOMA or OMA?

In this paper, we examine the potentials of Non- Orthogonal Multiple Access (NOMA), currently rivaling Orthogonal Multiple Access (OMA) in 3rd Generation Partnership Project (3GPP) standardization for future 5G networks Machine Type Communications (MTC), in the framework of minimizing the average Age of Information (AoI). By leveraging the notion of Stochastic Hybrid Systems (SHS), we find the total average AoI of the network in simple NOMA and conventional OMA environments. Armed with this, we provide a comparison between the two schemes in terms of average AoI. Interestingly, it will be shown that even when NOMA achieves better spectral efficiency in comparison to OMA, this does not necessarily translates into a lower average AoI in the network.

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arXiv2019

Age of Information With Prioritized Streams: When to Buffer Preempted Packets?

In this paper, we consider N information streams sharing a common service facility. The streams are supposed to have different priorities based on their sensitivity. A higher priority stream will always preempt the service of a lower priority packet. By leveraging the notion of Stochastic Hybrid Systems (SHS), we investigate the Age of Information (AoI) in the case where each stream has its own waiting room; when preempted by a higher priority stream, the packet is stored in the waiting room for future resume. Interestingly, it will be shown that a "no waiting room" scenario, and consequently discarding preempted packets, is better in terms of average AoI in some cases. The exact cases where this happen are discussed and numerical results that corroborate the theoretical findings and highlight this trade-off are provided.

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arXiv2019

Minimizing The Age of Information in a CSMA Environment

In this paper, we investigate a network of N interfering links contending for the channel to send their data by employing the well-known Carrier Sense Multiple Access (CSMA) scheme. By leveraging the notion of stochastic hybrid systems, we find a closed form of the total average age of the network in this setting. Armed with this expression, we formulate the optimization problem of minimizing the total average age of the network by calibrating the back-off time of each link. By analyzing its structure, the optimization problem is then converted to an equivalent convex problem that can be solved efficiently to find the optimal back-off time of each link. Insights on the interaction between the links is provided and numerical implementations of our optimized CSMA scheme in an IEEE 802.11 environment is presented to highlight its performance. We also show that, although optimized, the standard CSMA scheme still lacks behind other distributed schemes in terms of average age in some special cases. These results suggest the necessity to find new distributed schemes to further minimize the average age of any general network.

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arXiv2018

Matrix Exponential Learning Schemes with Low Informational Exchange

We consider a distributed resource allocation problem in networks where each transmitter-receiver pair aims at maximizing its local utility function by adjusting its action matrix, which belongs to a given feasible set. This problem has been addressed recently by applying a matrix exponential learning (MXL) algorithm which has a very appealing convergence rate. In this learning algorithm, however, each transmitter must know an estimate of the gradient matrix of the local utility. The knowledge of the gradient matrix at the transmitters incurs a high signaling overhead especially that the matrix size increases with the dimension of the action matrix. In this paper, we therefore investigate two strategies in order to decrease the informational exchange per iteration of the algorithm. In the first strategy, each receiver sends at each iteration part of the elements of the gradient matrix with respect to a certain probability. In the second strategy, each receiver feeds back sporadically the whole gradient matrix. We focus on the analysis of the convergence of the MXL algorithm to optimum under these two strategies. We prove that the algorithm can still converge to optimum almost surely. Upper bounds of the average convergence rate are also derived in both situations with general step-size setting, from which we can clearly see the impact of the incompleteness of the feedback information. The proposed algorithms are applied to solve the energy efficiency maximization problem in a multicarrier multi-user MIMO network. Simulation results further corroborate our claim.

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