Modeling AoII in Push- and Pull-Based Sampling of Continuous Time Markov Chains (2401.04098v2)
Abstract: 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.
- The age of information: Real-time status updating by multiple sources. IEEE Transactions on Information Theory, 65(3):1807–1827, March 2019.
- Age of information: An introduction and survey. IEEE Jour. Sel. Areas in Comm., 39(5):1183–1210, May 2020.
- The age of incorrect information: A new performance metric for status updates. IEEE/ACM Trans. on Networking, 28(5):2215–2228, October 2020.
- Query age of information: Freshness in pull-based communication. IEEE Trans. Comm., 70(3):1606–1622, January 2022.
- Detecting state transitions of a Markov source: Sampling frequency and age trade-off. IEEE Transactions on Communications, 70(5):3081–3095, March 2022.
- N. Akar and S. Ulukus. Optimum monitoring of heterogeneous continuous time Markov chains. Available online at arXiv:2310.02223.
- Age of incorrect information for remote estimation of a binary Markov source. In IEEE Infocom, July 2020.
- S. Kriouile and M. Assaad. Minimizing the age of incorrect information for real-time tracking of Markov remote sources. In IEEE ISIT, July 2021.
- S. Kriouile and M. Assaad. When to pull data from sensors for minimum distance-based age of incorrect information metric. Available online at arXiv:2202.02878.
- Y. Chen and A. Ephremides. Minimizing age of incorrect information for unreliable channel with power constraint. In IEEE Globecom, December 2021.
- M. Bastopcu and S. Ulukus. Timely tracking of infection status of individuals in a population. In IEEE Infocom, May 2021.
- Y. Inoue and T. Takine. AoI perspective on the accuracy of monitoring systems for continuous-time Markovian sources. In IEEE Infocom, April 2019.
- G. Latouche and V. Ramaswami. Introduction to matrix analytic methods in stochastic modeling. SIAM, 1999.
- N. Akar and E. O. Gamgam. Distribution of age of information in status update systems with heterogeneous information sources: An absorbing Markov chain-based approach. IEEE Communications Letters, 27(8):2024–2028, May 2023.
- State-aware resource allocation for wireless closed-loop control systems. IEEE Trans. on Comm., 69(10):6604–6619, July 2021.
- Finite Markov chains. Springer, 1960.