arXiv subjects

Nail Akar

Publications and source records attributed to Nail Akar.

At least 19 recordsLinked to original sources

arXiv2026

Squeezing the Most Out of Preemption for AoI Minimization: Single-source Case

In this work, we study a single-source single-server continuous-time status update system where the updates arrive according to a Poisson process and update service times are generally distributed. In our proposed setting, a preemption policy refers to one where a new update preempts the ongoing one with a probability depending on the age of the update in service. We first propose an analytical method to derive the average age of information (AoI) and average peak AoI (PAoI) for any such preemption policy. This analysis is then utilized to tune two particular preemption policies: (i) probabilistic preemption (PP), in which preemption takes place according to a fixed probability regardless of the update age, (ii) threshold-based preemption (TP), for which preemption is incurred when the update age exceeds a certain threshold, both using one-dimensional line search. The effectiveness of policy tuning for the PP and TP policies is validated using lognormal-distributed update service times.

cs.IT↗

arXiv2026

Dual-Regime Absorbing Markov Chain Theory in Remote Estimation: Age-Minimizing Push Policies

For a remote estimation system, we study the optimization of age of incorrect information (AoII), which is a recently proposed semantic-aware information freshness metric. In particular, we assume an information source that observes a discrete-time finite-state Markov chain (DTMC), and occasionally transmits status update packets to a remote monitor which is tasked with remote estimation of the source. For the forward channel from the source to the monitor, we assume the channel delay to be modeled by a general discrete-time phase-type (DPH) distribution, whereas the reverse channel from the monitor to the source is assumed to be perfect, ensuring that the source has perfect information on the AoII and the remote estimate at the monitor, at all times. Push-based transmissions are initiated when AoII exceeds a threshold depending on the current estimation value, i.e., multi-threshold policy. In this very general setting, our goal is to minimize a weighted sum of the time average of a polynomial function of AoII, depending on the remote estimate, and energy consumption from transmissions. We formulate the problem as a semi-Markov decision process (SMDP) with the same state-space of the original DTMC to obtain the optimal multi-threshold policy, whereas the parameters of the SMDP are obtained by using a novel stochastic tool called dual-regime absorbing Markov chain (DR-AMC), and its corresponding absorption time distribution named as dual-regime DPH (DR-DPH). The proposed method is validated with numerical examples using comparisons against other policies obtained by exhaustive search, and also various benchmark policies.

cs.IT↗

arXiv2026

When and Which Sensor to Observe? Timely Tracking of a Joint Markov Source

We investigate the problem of remote estimation (at a monitor) of a discrete-time joint Markov process with individual components which can be observed with dedicated sensors. At a given time slot, the monitor has the option of staying idle or sending a pull request to one of the sensors to obtain a partial state value, while the sensors are assumed to have heterogeneous sampling costs. Our goal is to develop a monitor pull policy, i.e., determining when and towards which sensor to send a pull request, in order to minimize a weighted sum of average age of incorrect information (AoII), or in short age, and sampling costs. As the communication model, we assume an erasure channel with a fixed one-slot delay from each sensor to the monitor. In this setting, the monitor does not perfectly know either the state of the process or the age, at any given time. We first obtain a sufficient statistic, namely belief, representing the joint distribution of the age and the current state of the observed process, by using the history of all pull requests and observations. Then, we formulate the optimization problem as a continuous state-space Markov decision process (MDP), namely belief-MDP, for the solution of which we propose two model predictive control (MPC) methods, namely MPC without terminal costs (MPC-WTC), and reinforcement learning MPC (RL-MPC). The effectiveness of the proposed methods is validated by numerical examples.

cs.IT↗

arXiv2026

Preemption Revisited: Multi-Threshold Preemption Policies for AoI Minimization

The study of optimal preemption policies for status update systems has been a recurring topic in the age of information (AoI) literature, where threshold-based structures have been shown to be optimal under a generate-at-will update generation model under certain assumptions. In this work, we study the effectiveness of threshold-based policies for a system with random update arrivals. In this regard, we introduce an analytical framework for evaluating the AoI of multi-threshold preemption policies and present interesting characteristics of the structure of the optimal preemption policy. We show the effectiveness of these threshold-based policies over the traditional probabilistic preemption policies and single-threshold policies, where we observe that significant gains in terms of AoI can be obtained by utilizing both the age of the packet and the age of the system when designing these preemption policies.

cs.IT↗

arXiv2026

Beyond Martingale Estimators: Structured Estimators for Maximizing Information Freshness in Query-Based Update Systems

This paper investigates information freshness in a remote estimation system in which the remote information source is a continuous-time Markov chain (CTMC). For such systems, estimators have been mainly restricted to the class of martingale estimators in which the remote estimate at any time is equal to the value of the most recently received update. This is mainly due to the simplicity and ease of analysis of martingale estimators, which however are far from optimal, especially in query-based (i.e., pull-based) update systems. In such systems, maximum a-posteriori probability (MAP) estimators are optimal. However, MAP estimators can be challenging to analyze in continuous-time settings. In this paper, we introduce a new class of estimators, called structured estimators, which can seamlessly shift from a martingale estimator to a MAP estimator, enabling them to retain useful characteristics of the MAP estimate, while still being analytically tractable. Particularly, we introduce a new estimator termed as the $p$-MAP estimator which is a piecewise-constant approximation of the MAP estimator with finitely many discontinuities, bringing us closer to a full characterization of MAP estimators when modeling information freshness. In fact, we show that for time-reversible CTMCs, the MAP estimator reduces to a $p$-MAP estimator. Using the binary freshness (BF) process for the characterization of information freshness, we derive the freshness expressions and provide optimal state-dependent sampling policies (i.e., querying policies) for maximizing the mean BF (MBF) for pull-based remote estimation of a single CTMC information source, when structured estimators are used. Moreover, we provide optimal query rate allocation policies when a monitor pulls information from multiple heterogeneous CTMCs with a constraint on the overall query rate.

cs.IT↗

arXiv2026

Multi-Stage Structured Estimators for Information Freshness

Most of the contemporary literature on information freshness solely focuses on the analysis of freshness for martingale estimators, which simply use the most recently received update as the current estimate. While martingale estimators are easier to analyze, they are far from optimal, especially in pull-based update systems, where maximum aposteriori probability (MAP) estimators are known to be optimal, but are analytically challenging. In this work, we introduce a new class of estimators called $p$-MAP estimators, which enable us to model the MAP estimator as a piecewise constant function with finitely many stages, bringing us closer to a full characterization of the MAP estimators when modeling information freshness.

cs.IT↗

arXiv2026

Utilizing the Perceived Age to Maximize Freshness in Query-Based Update Systems

Query-based sampling has become an increasingly popular technique for monitoring Markov sources in pull-based update systems. However, most of the contemporary literature on this assumes an exponential distribution for query delay and often relies on the assumption that the feedback or replies to the queries are instantaneous. In this work, we relax both of these assumptions and find optimal sampling policies for monitoring continuous-time Markov chains (CTMC) under generic delay distributions. In particular, we show that one can obtain significant gains in terms of mean binary freshness (MBF) by employing a waiting based strategy for query-based sampling.

cs.IT↗

arXiv2025

Age of Information with Age-Dependent Server Selection

In this paper, we consider a single-source multi-server generate-at-will discrete-time non-preemptive status update system where update packets are transmitted using {\em only one} of the available servers, according to a server selection policy. In particular, when a transmission is complete, the update system makes a threshold-based decision on whether to wait or transmit, and if latter, which server to use for transmissions, on the basis of the instantaneous value of the age of information (AoI) process. In our setting, servers have general heterogeneous discrete phase-type (DPH) distributed service times, and also heterogeneous transmission costs. The goal is to find an age-dependent multi-threshold policy that minimizes the AoI cost with a constraint on transmission costs, the former cost defined in terms of the time average of an arbitrary function of AoI. For this purpose, we propose a novel tool called \emph{multi-regime absorbing Markov chain} (MR-AMC) in discrete time. Using the MR-AMC framework, we exactly obtain the distribution of AoI, and subsequently the costs associated with AoI and transmissions. With the exact analysis in hand, optimum thresholds can be obtained in the case of a few servers, by exhaustive search. We validate the proposed analytical model, and also demonstrate the benefits of age-dependent server selection, with numerical examples.

cs.IT↗

arXiv2025

Semi-Markov Decision Process Framework for Age of Incorrect Information Minimization

For a remote estimation system, we study age of incorrect information (AoII), which is a recently proposed semantic-aware freshness metric. In particular, we assume an information source observing a discrete-time finite-state Markov chain (DTMC) and employing push-based transmissions of status update packets towards the monitor which is tasked with remote estimation of the source. The source-to-monitor channel delay is assumed to have a general discrete-time phase-type (DPH) distribution, whereas the zero-delay reverse channel ensures that the source has perfect information on AoII and the remote estimate. A multi-threshold transmission policy is employed where packet transmissions are initiated when the AoII process exceeds a threshold which may be different for each estimation value. In this general setting, our goal is to minimize the weighted sum of time average of an arbitrary function of AoII and estimation, and transmission costs, by suitable choice of the thresholds. We formulate the problem as a semi-Markov decision process (SMDP) with the same state-space as the original DTMC to obtain the optimum multi-threshold policy whereas the parameters of the SMDP are obtained by using a novel stochastic tool called dual-regime absorbing Markov chain (DR-AMC), and its corresponding absorption time distribution named as dual-regime DPH (DR-DPH).

cs.IT↗

arXiv2025

Absorbing Markov Chain-Based Analysis of Age of Information in Discrete-Time Dual-Queue Systems

Status update systems require the timely collection of sensing information for which deploying multiple sensors/servers to obtain diversity gains is considered as a promising solution. In this work, we construct an absorbing Markov chain (AMC) to exactly model Age of Information (AoI) in a discretetime dual-queue (DTDQ) status update system with generate at will (GAW) status updates, discrete phase-type (DPH-type) distributed service times and transmission freezing. Specifically, transmission is frozen for a certain number of slots following the initiation of a transmission, after which one of the two servers is allowed to simultaneously sample the monitored physical process and transmit a status update packet, according to the availabilities and priorities of the two servers. Based on the discrete-time AMC, we provide the exact distributions of both AoI and peak AoI (PAoI), enabling the derivation of arbitrary order moments. In addition, we analytically study the role of freezing using several typical service time distributions, including geometric, uniform, and triangular distributions. The introduction of freezing for DTDQ systems is demonstrated to be significantly beneficial in reducing the mean AoI for various service time distributions. Additionally, we study the impact of the statistical parameters of the service times and heterogeneity between the two servers on the freezing gain, i.e., reduction in mean AoI attained with optimum freezing policies.

cs.IT↗

arXiv2025

Structured Estimators: A New Perspective on Information Freshness

In recent literature, when modeling for information freshness in remote estimation settings, estimators have been mainly restricted to the class of martingale estimators, meaning the remote estimate at any time is equal to the most recently received update. This is mainly due to its simplicity and ease of analysis. However, these martingale estimators are far from optimal in some cases, especially in pull-based update systems. For such systems, maximum aposteriori probability (MAP) estimators are optimum, but can be challenging to analyze. Here, we introduce a new class of estimators, called structured estimators, which retain useful characteristics from a MAP estimate while still being analytically tractable. Our proposed estimators move seamlessly from a martingale estimator to a MAP estimator.

cs.IT↗

arXiv2025

Minimizing Functions of Age of Incorrect Information for Remote Estimation

The age of incorrect information (AoII) process which keeps track of the time since the source and monitor processes are in sync, has been extensively used in remote estimation problems. In this paper, we consider a push-based remote estimation system with a discrete-time Markov chain (DTMC) information source transmitting status update packets towards the monitor once the AoII process exceeds a certain estimation-based threshold. In this paper, the time average of an arbitrary function of AoII is taken as the AoII cost, as opposed to using the average AoII as the mismatch metric, whereas this function is also allowed to depend on the estimation value. In this very general setting, our goal is to minimize a weighted sum of AoII and transmission costs. For this purpose, we formulate a discrete-time semi-Markov decision process (SMDP) regarding the multi-threshold status update policy. We propose a novel tool in discrete-time called 'dual-regime absorbing Markov chain' (DR-AMC) and its corresponding absorption time distribution named as 'dual-regime phase-type' (DR-PH) distribution, to obtain the characterizing parameters of the SMDP, which allows us to obtain the distribution of the AoII process for a given policy, and hence the average of any function of AoII. The proposed method is validated with numerical results by which we compare our proposed method against other policies obtained by exhaustive-search, and also various benchmark policies.

cs.IT↗

arXiv2025

How to Maximize Efficiency in Systems with Exhausted Workers

We consider the problem of assigning tasks efficiently to a set of workers that can exhaust themselves as a result of processing tasks. If a worker is exhausted, it will take a longer time to recover. To model efficiency of workers with exhaustion, we use a continuous-time Markov chain (CTMC). By taking samples from the internal states of the workers, the source assigns tasks to the workers when they are found to be in their efficient states. We consider two different settings where (i) the source can assign tasks to the workers only when they are in their most efficient state, and (ii) it can assign tasks to workers when they are also moderately efficient in spite of a potentially reduced success probability. In the former case, we find the optimal policy to be a threshold-based sampling policy where the thresholds depend on the workers' recovery and exhaustion rates. In the latter case, we solve a non-convex sum-of-ratios problem using a branch-and-bound approach which performs well compared with the globally optimal solution.

cs.IT↗

arXiv2025

Which Sensor to Observe? Timely Tracking of a Joint Markov Source with Model Predictive Control

In this paper, we investigate the problem of remote estimation of a discrete-time joint Markov process using multiple sensors. Each sensor observes a different component of the joint Markov process, and in each time slot, the monitor obtains a partial state value by sending a pull request to one of the sensors. The monitor chooses the sequence of sensors to observe with the goal of minimizing the mean of age of incorrect information (MAoII) by using the partial state observations obtained, which have different freshness levels. For instance, a monitor may be interested in tracking the location of an object by obtaining observations from two sensors, which observe the $x$ and $y$ coordinates of the object separately, in different time slots. The monitor, then, needs to decide which coordinate to observe in the next time slot given the history. In addition to this partial observability of the state of Markov process, there is an erasure channel with a fixed one-slot delay between each sensor and the monitor. First, we obtain a sufficient statistic, namely the \emph{belief}, representing the joint distribution of the age of incorrect information (AoII) and the current state of the observed process by using the history of all pull requests and observations. Then, we formulate the problem with a continuous state-space Markov decision problem (MDP), namely belief MDP. To solve the problem, we propose two model predictive control (MPC) methods, namely MPC without terminal costs (MPC-WTC) and reinforcement learning MPC (RL-MPC), that have different advantages in implementation.

cs.IT↗

arXiv2025

Fully Decentralized Computation Offloading in Priority-Driven Edge Computing Systems

We develop a novel framework for fully decentralized offloading policy design in multi-access edge computing (MEC) systems. The system comprises $N$ power-constrained user equipments (UEs) assisted by an edge server (ES) to process incoming tasks. Tasks are labeled with urgency flags, and in this paper, we classify them under three urgency levels, namely, high, moderate, and low urgency. We formulate the problem of designing computation decisions for the UEs within a large population noncooperative game framework, where each UE selfishly decides on how to split task execution between its local onboard processor and the ES. We employ the weighted average age of information (AoI) metric to quantify information freshness at the UEs. Increased onboard processing consumes more local power, while increased offloading may potentially incur a higher average AoI due to other UEs' packets being offloaded to the same ES. Thus, we use the mean-field game (MFG) formulation to compute approximate decentralized Nash equilibrium offloading and local computation policies for the UEs to balance between the information freshness and local power consumption. Finally, we provide a projected gradient descent-based algorithm to numerically assess the merits of our approach.

cs.IT↗

arXiv2024

Double Spending Analysis of Nakamoto Consensus for Time-Varying Mining Rates with Ruin Theory

Theoretical guarantees for double spending probabilities for the Nakamoto consensus under the $k$-deep confirmation rule have been extensively studied for zero/bounded network delays and fixed mining rates. In this paper, we introduce a ruin-theoretical model of double spending for Nakamoto consensus under the $k$-deep confirmation rule when the honest mining rate is allowed to be an arbitrary function of time including the block delivery periods, i.e., time periods during which mined blocks are being delivered to all other participants of the network. Time-varying mining rates are considered to capture the intrinsic characteristics of the peer to peer network delays as well as dynamic participation of miners such as the gap game and switching between different cryptocurrencies. Ruin theory is leveraged to obtain the double spend probabilities and numerical examples are presented to validate the effectiveness of the proposed analytical method.

cs.CR↗

arXiv2024

Joint Age-State Belief is All You Need: Minimizing AoII via Pull-Based Remote Estimation

Age of incorrect information (AoII) is a recently proposed freshness and mismatch metric that penalizes an incorrect estimation along with its duration. Therefore, keeping track of AoII requires the knowledge of both the source and estimation processes. In this paper, we consider a time-slotted pull-based remote estimation system under a sampling rate constraint where the information source is a general discrete-time Markov chain (DTMC) process. Moreover, packet transmission times from the source to the monitor are non-zero which disallows the monitor to have perfect information on the actual AoII process at any time. Hence, for this pull-based system, we propose the monitor to maintain a sufficient statistic called {\em belief} which stands for the joint distribution of the age and source processes to be obtained from the history of all observations. Using belief, we first propose a maximum a posteriori (MAP) estimator to be used at the monitor as opposed to existing martingale estimators in the literature. Second, we obtain the optimality equations from the belief-MDP (Markov decision process) formulation. Finally, we propose two belief-dependent policies one of which is based on deep reinforcement learning, and the other one is a threshold-based policy based on the instantaneous expected AoII.

cs.IT↗

arXiv2024

Scheduling Policies in a Multi-Source Status Update System with Dedicated and Shared Servers

Use of multi-path network topologies has become a prominent technique to assert timeliness in terms of age of information (AoI) and to improve resilience to link disruptions in communication systems. However, establishing multiple dedicated communication links among network nodes is a costly endeavor. Therefore, quite often, these secondary communication links are shared among multiple entities. Moreover, these multi-path networks come with the added challenge of out-of-order transmissions. In this paper, we study an amalgamation of the above two aspects, i.e., multi-path transmissions and link sharing. In contrast to the existing literature where the main focus has been scheduling multiple sources on a single shared server, we delve into the realm where each source sharing the shared server is also supplemented with its dedicated server so as to improve its timeliness. In this multi-path link sharing setting with generate-at-will transmissions, we first present the optimal probabilistic scheduler, and then propose several heuristic-based cyclic scheduling algorithms for the shared server, to minimize the weighted average age of information of the sources.

cs.IT↗