arXiv subjects

Ismail Cosandal

Publications and source records attributed to Ismail Cosandal.

15 recordsLinked to original sources

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.

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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.

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arXiv2026

How Far Back in Time a Digital Twin Reflects the State of the Physical Object: Age of Staleness

The groundbreaking metric age of information (AoI) has been introduced to measure information freshness in communication networks. As transformational as it is, AoI metric falls short in some applications, such as remote monitoring, since it is a semantic-agnostic metric which does not consider the dynamics of the random process. There is a need to quantify the performance of a remote estimator via a metric that combines freshness and semantic aspects. To this end, in this paper, we introduce a novel metric coined age of staleness (AoS) that measures when the last time that the current estimation was correct. First, we analyze a simple scenario where an $n$-ary symmetric Markov source is observed by a monitor via a constant sampling rate, obtain a closed-form expression for the AoS, and show that it is a monotonically decreasing function of the sampling rate. Next, we consider multiple distinct Markov sources, and formulate an optimization problem, where the remote monitor allocates the total sampling rate to tracking the sources. Although the optimization problem is non-convex, its structure is suitable for obtaining a near-optimal solution using the polyblock algorithm, which leverages the monotonicity of the objective function. While the new AoS metric could be applicable in many scenarios, we believe it is particularly well-suited for a digital twin network (DTN) where multiple physical objects (POs) are monitored with a total sampling rate constraint to maintain a digital representation of them, namely, their digital twin (DT).

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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.

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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).

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arXiv2025

Optimal Source Coding of Markov Chains for Real-Time Remote Estimation

We revisit the source coding problem for a Markov chain under the assumption that the transmission times and how fast the Markov chain transitions its state happen at the same time-scale. Specifically, we assume that the transmission of each bit takes a single time slot, and the Markov chain updates its state in the same time slot. Thus, the length of the codeword assigned to a symbol determines the number of non-transmitted symbols, as well as, the probability of the realization of the next symbol to be transmitted. We aim to minimize the average transmission duration over an infinite horizon by proposing an optimal source coding policy based on the last transmitted symbol and its transmission duration. To find the optimal policy, we formulate the problem with a Markov decision process (MDP) by augmenting the symbols alongside the transmission duration of the symbols. Finally, we analyze two Huffman-based benchmark policies and compare their performances with the proposed optimal policy. We observe that, in randomly generated processes, our proposed optimal policy decreases the average transmission duration compared to benchmark policies. The performance gain varies based on the parameters of the Markov process.

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arXiv2025

Timely Tracking of a Wiener Process With Single Bit Quantization

We consider the problem of timely tracking of a Wiener process via an energy-conserving sensor by utilizing a single bit quantization strategy under periodic sampling. Contrary to conventional single bit quantizers which only utilize the transmitted bit to convey information, in our codebook, we use an additional `$\emptyset$' symbol to encode the event of \emph{not transmitting}. Thus, our quantization functions are composed of three decision regions as opposed to the conventional two regions. First, we propose an optimum quantization method in which the optimum quantization functions are obtained by tracking the distributions of the quantization error. However, this method requires a high computational cost and might not be applicable for energy-conserving sensors. Thus, we propose two additional low complexity methods. In the last-bit aware method, three predefined quantization functions are available to both devices, and they switch the quantization function based on the last transmitted bit. With the Gaussian approximation method, we calculate a single quantization function by assuming that the quantization error can be approximated as Gaussian. While previous methods require a constant delay assumption, this method also works for random delay. We observe that all three methods perform similarly in terms of mean-squared error and transmission cost.

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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.

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arXiv2025

Source Coding for a Wiener Process

We develop a novel source coding strategy for sampling and monitoring of a Wiener process. For the encoding process, we employ a four level ``quantization'' scheme, which employs monotone function thresholds as opposed to fixed constant thresholds. Leveraging the hitting times of the Wiener process with these thresholds, we devise a sampling and encoding strategy which does not incur any quantization errors. We give analytical expressions for the mean squared error (MSE) and find the optimal source code lengths to minimize the MSE under this monotone function threshold scheme, subject to a sampling rate constraint.

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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.

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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.

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arXiv2024

Multi-Threshold AoII-Optimum Sampling Policies for CTMC Information Sources

We study push-based sampling and transmission policies for a status update system consisting of a general finite-state continuous-time Markov chain (CTMC) information source with known dynamics, with the goal of minimizing the average age of incorrect information (AoII). The problem setting we investigate involves an exponentially distributed delay channel for transmissions and a constraint on the average sampling rate. We first show that the optimum sampling and transmission policy is a 'multi-threshold policy', where the thresholds depend on both the estimation value and the state of the original process, and sampling and transmission need to be initiated when the instantaneous AoII exceeds the corresponding threshold, called the estimation- and state-aware transmission (ESAT) policy. Subsequently, we formulate the problem of finding the thresholds as a constrained semi-Markov decision process (CSMDP) and the Lagrangian approach. Additionally, we propose two lower complexity sub-optimum policies, namely the estimation-aware transmission (EAT) policy, and the single-threshold (ST) policy, for which it is possible to obtain these thresholds for CTMCs with relatively larger number of states. The underlying CSMDP formulation relies on the 'multi-regime phase-type' (MRPH) distribution which is a generalization of the well-known phase-type distribution, which allows us to obtain the distribution of time until absorption in a CTMC whose transition rates change with respect to time in a piece-wise manner. The effectiveness of the proposed ESAT, EAT and ST sampling and transmission policies are shown through numerical examples, along with comparisons with a baseline scheme that transmits packets according to a Poisson process in out-of-sync periods.

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arXiv2024

AoII-Optimum Sampling of CTMC Information Sources Under Sampling Rate Constraints

We consider a sensor that samples an $N$-state continuous-time Markov chain (CTMC)-based information source process, and transmits the observed state of the source, to a remote monitor tasked with timely tracking of the source process. The mismatch between the source and monitor processes is quantified by age of incorrect information (AoII), which penalizes the mismatch as it stays longer, and our objective is to minimize the average AoII under an average sampling rate constraint. We assume a perfect reverse channel and hence the sensor has information of the estimate while initiating a transmission or preempting an ongoing transmission. First, by modeling the problem as an average cost constrained semi-Markov decision process (CSMDP), we show that the structure of the problem gives rise to an optimum threshold policy for which the sensor initiates a transmission once the AoII exceeds a threshold depending on the instantaneous values of both the source and monitor processes. However, due to the high complexity of obtaining the optimum policy in this general setting, we consider a relaxed problem where the thresholds are allowed to be dependent only on the estimate. We show that this relaxed problem can be solved with a novel CSMDP formulation based on the theory of absorbing MCs, with a computational complexity of $\mathcal{O}(N^4)$, allowing one to obtain optimum policies for general CTMCs with over a hundred states.

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arXiv2024

Modeling AoII in Push- and Pull-Based Sampling of Continuous Time Markov Chains

Age of incorrect information (AoII) has recently been proposed as an alternative to existing information freshness metrics for real-time sampling and estimation problems involving information sources that are tracked by remote monitors. Different from existing metrics, AoII penalizes the incorrect information by increasing linearly with time as long as the source and the monitor are de-synchronized, and is reset when they are synchronized back. While AoII has generally been investigated for discrete time information sources, we develop a novel analytical model in this paper for push- and pull-based sampling and transmission of a continuous time Markov chain (CTMC) process. In the pull-based model, the sensor starts transmitting information on the observed CTMC only when a pull request from the monitor is received. On the other hand, in the push-based scenario, the sensor, being aware of the AoII process, samples and transmits when the AoII process exceeds a random threshold. The proposed analytical model for both scenarios is based on the construction of a discrete time MC (DTMC) making state transitions at the embedded epochs of synchronization points, using the theory of absorbing CTMCs, and in particular phase-type distributions. For a given sampling policy, analytical models to obtain the mean AoII and the average sampling rate are developed. Numerical results are presented to validate the analytical model as well as to provide insight on optimal sampling policies under sampling rate constraints.

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arXiv2023

Timely Multi-Goal Transmissions With an Intermittently Failing Sensor

A sensor observes a random phenomenon and transmits updates about the observed phenomenon to a remote monitor. The sensor may experience intermittent failures in which case the monitor will not receive any updates until the sensor has recovered. The monitor wants to keep a timely view of the observed process, as well as to detect any sensor failures, using the timings of the updates. We analyze this system model from a goal-oriented and semantic communication point of view, where the communication has multiple goals and multiple meanings/semantics. For the first goal, the performance is quantified by the age of information of the observed process at the monitor. For the second goal, the performance is quantified by the probability of error of the monitor's estimation of the sensor's failure status. Each arriving update packet brings both an information update and an indication about the sensor's status. The monitor estimates the failure status of the sensor by using the timings of the received updates. This estimation is subject to error, since a long period without any update receptions may be due to a low update rate or a failure of the sensor. We examine the trade-off between these two goals. We show that the probability of error of estimating a sensor failure decreases with increased update rate, however, the age of information is minimized with an intermediate update rate (not too low or high).

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