Browsing by Author "Ulukus, Sennur"

Now showing 1 - 7 of 7

Open Access
AoII-optimum sampling of CTMC information sources under sampling rate constraints
(IEEE, 2024) Cosanda, Ismail; Akar, Nail; Ulukus, Sennur
We consider a sensor that samples an $N-\mathbf{state}$ 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.
Open Access
Controlling age of ınformation in a dual-server system with transmission freezing and preemption
(IEEE, 2024-12-16) Akar, Nail; Ulukus, Sennur
We study age of information (AoI) in a status update system for the generate-at-will (GAW) scenario, consisting of a single information source, dual heterogeneous servers, and a monitor. For this system, stochastic hybrid systems (SHS) were used to obtain the mean AoI for the work-conserving zero wait (ZW) policy with out-of-order packet discarding at the monitor. In this paper, we propose a non-work-conserving freeze/preempt (F/P) policy for which the sampling and transmission process is frozen for an Erlang-distributed duration upon each new transmission, and out-of-order (obsolete) packets are preempted at the source, rather than being discarded at the monitor upon reception. We use the absorbing Markov chain (AMC) method to obtain the exact distributions of AoI and also the peak AoI (PAoI) processes, for the F/P policy. Numerical results are presented for the validation of the proposed analytical model and a comparative evaluation of ZW and F/P policies.
Open Access
Cyclic scheduling for age of information minimization with generate at will status updates
(IEEE, 2024-04-02) Gamgam, Ege Orkun; Akar, Nail; Ulukus, Sennur; Akar, Nail
We study the scheduling problem in a status update system composed of multiple information sources with different service time distributions and weights, for the purpose of minimizing the weighted sum age of information (AoI). In particular, we study open-loop schedulers which rely only on the statistics (specifically, only on the first two moments) of the source service times, in contrast to closed-loop schedulers that also make use of the actual realizations of the service times and the AoI processes in making scheduling decisions. We consider the generate-at-will (GAW) model, and develop an analytical method to calculate the exact AoI for probabilistic and cyclic open-loop schedulers. In both cases, the server initiates the sampling of a source and the ensuing transmission of the update packet from the source to the server in an open-loop manner; either based on a certain probability (probabilistic scheme) or according to a deterministic cyclic pattern (cyclic scheme). We derive the optimum open-loop cyclic scheduling policy in closed form for the specific case of N = 2 sources and propose well-performing heuristic cyclic schedulers for general number of sources, i.e., N > 2. Numerical examples are provided to validate the existing methods.
Open Access
Modeling AoII in push- and pull-based sampling of continuous time Markov chains
(IEEE, 2024) Cosandal, Ismail; Akar, Nail; Ulukus, Sennur
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 models as well as to provide insight on optimal sampling policies under sampling rate constraints.
Open Access
Modeling interfering sources in shared queues for timely computations in edge computing systems
(Association for Computing Machinery, 2024-10-17) Akar, Nail; Baştopçu, Melih; Ulukus, Sennur; Başar, Tamer
Most existing stochastic models on age of information (AoI) focus on a single shared server serving status update packets from N > 1 sources where each packet update stream is Poisson, i.e., single-hop scenario. In the current work, we study a two-hop edge computing system for which status updates from the information sources are still Poisson but they are not immediately available at the shared edge server, but instead they need to first receive service from a transmission server dedicated to each source. For exponentially distributed and heterogeneous service times for both the dedicated servers and the edge server, and bufferless preemptive resource management, we develop an analytical model using absorbing Markov chains (AMC) for obtaining the distribution of AoI for any source in the system. Moreover, for a given tagged source, the traffic arriving at the shared server from the N − 1 un-tagged sources, namely the interference traffic, is not Poisson any more, but is instead a Markov modulated Poisson process (MMPP) whose state space grows exponentially with N. Therefore, we propose to employ a model reduction technique that approximates the behavior of the MMPP interference traffic with two states only, making it possible to approximately obtain the AoI statistics even for a very large number of sources. Numerical examples are presented to validate the proposed exact and approximate models.
Open Access
Scalable cyclic shedulers for age of information optimization in large-scale status update systems
(IEEE, 2024) Akar, Nail; Liyanaarachchi, Sahan; Ulukus, Sennur
We study open-loop cyclic scheduling for generate-at-will (GAW) multi-source status update systems with heteroge-neous service times and packet drop probabilities, with the goal of minimizing the weighted sum age of information (AoI), called system AoI, or the weighted sum peak AoI (PAoI), called system PAoI. In particular, we propose an offline method to obtain a well-performing cyclic schedule, which can scale to very large number of information sources. Moreover, the proposed schedule has a very low online implementation complexity. The proposed schedules are comparatively studied against existing age-agnostic scheduling algorithms in terms of computational load and system AoI/PAoI performance, to validate their effectiveness
Open Access
Timely monitoring of Markov chains under sampling rate constraints
(IEEE, 2024) Akar, Nail; Ulukus, Sennur
We study a pull-based monitoring system in which a common remote monitor queries the states of a collection of heterogeneous finite-state irreducible continuous time Markov chain (CTMC) based information sources, according to a Poisson process with different per-source sampling rates, in order to maintain remote estimates of the states. Three information freshness models are considered to quantify the accuracy of the remote estimates: fresh when equal (FWE), fresh when sampled (FWS) and fresh when close (FWC). For each of these freshness models, closed-form expressions are derived for mean information freshness for each source, as a function of the sampling rate. Using these expressions, optimum sampling rates for all sources are obtained using water-filling based optimization for maximizing the weighted sum freshness of the monitoring system, under an overall sampling rate constraint. Numerical examples are presented to validate the effectiveness of the proposed method by comparing it to several baseline sampling policies.