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A Complex Model via Phase-Type Distributions to Study Random Telegraph Noise in Resistive Memories

Author

Listed:
  • Juan E. Ruiz-Castro

    (Department of Statistics and O.R. and Math Institute, University of Granada, 18071 Granada, Spain)

  • Christian Acal

    (Department of Statistics and O.R. and Math Institute, University of Granada, 18071 Granada, Spain)

  • Ana M. Aguilera

    (Department of Statistics and O.R. and Math Institute, University of Granada, 18071 Granada, Spain)

  • Juan B. Roldán

    (Department of Electronics and Computing Technology, University of Granada, 18071 Granada, Spain)

Abstract

A new stochastic process was developed by considering the internal performance of macro-states in which the sojourn time in each one is phase-type distributed depending on time. The stationary distribution was calculated through matrix-algorithmic methods and multiple interesting measures were worked out. The number of visits distribution to a determine macro-state were analyzed from the respective differential equations and the Laplace transform. The mean number of visits to a macro-state between any two times was given. The results were implemented computationally and were successfully applied to study random telegraph noise (RTN) in resistive memories. RTN is an important concern in resistive random access memory (RRAM) operation. On one hand, it could limit some of the technological applications of these devices; on the other hand, RTN can be used for the physical characterization. Therefore, an in-depth statistical analysis to model the behavior of these devices is of essential importance.

Suggested Citation

  • Juan E. Ruiz-Castro & Christian Acal & Ana M. Aguilera & Juan B. Roldán, 2021. "A Complex Model via Phase-Type Distributions to Study Random Telegraph Noise in Resistive Memories," Mathematics, MDPI, vol. 9(4), pages 1-16, February.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:4:p:390-:d:499923
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    References listed on IDEAS

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    1. Alonso, F.J. & Maldonado, D. & Aguilera, A.M. & Roldán, J.B., 2021. "Memristor variability and stochastic physical properties modeling from a multivariate time series approach," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    2. Aguilera-Morillo, M. Carmen & Aguilera, Ana M. & Jiménez-Molinos, Francisco & Roldán, Juan B., 2019. "Stochastic modeling of Random Access Memories reset transitions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 159(C), pages 197-209.
    3. Ruiz-Castro, Juan Eloy, 2016. "Complex multi-state systems modelled through marked Markovian arrival processes," European Journal of Operational Research, Elsevier, vol. 252(3), pages 852-865.
    4. Ruiz-Castro, Juan Eloy, 2020. "A complex multi-state k-out-of-n: G system with preventive maintenance and loss of units," Reliability Engineering and System Safety, Elsevier, vol. 197(C).
    5. Visser, Ingmar & Speekenbrink, Maarten, 2010. "depmixS4: An R Package for Hidden Markov Models," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 36(i07).
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    Cited by:

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    2. Gabriel Ciobanu, 2023. "Analyzing Non-Markovian Systems by Using a Stochastic Process Calculus and a Probabilistic Model Checker," Mathematics, MDPI, vol. 11(2), pages 1-17, January.

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