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Optimal Digital Twinning of Random Systems with Twinning Rate Constraints

Caglar Tunc

TL;DR

The proposed methodology is the first to investigate the optimal twinning problem with random PSs and twinning rate constraints, and serves as a guideline for real-world implementations on how frequently PSs should be twinned.

Abstract

With the massive advancements in processing power, Digital Twins (DTs) have become powerful tools to monitor and analyze physical entities. However, due to the potentially very high number of Physical Systems (PSs) to be tracked and emulated, for instance, in a factory environment or an Internet of Things (IoT) network, continuous twinning might become infeasible. In this paper, a DT system is investigated with a set of random PSs, where the twinning rate is limited due to resource constraints. Three cost functions are considered to quantify and penalize the twinning delay. For these cost functions, the optimal twinning problem under twinning rate constraints is formulated. In a numerical example, the proposed cost functions are evaluated for two, one push-based and one pull-based, benchmark twinning policies. The proposed methodology is the first to investigate the optimal twinning problem with random PSs and twinning rate constraints, and serves as a guideline for real-world implementations on how frequently PSs should be twinned.

Optimal Digital Twinning of Random Systems with Twinning Rate Constraints

TL;DR

The proposed methodology is the first to investigate the optimal twinning problem with random PSs and twinning rate constraints, and serves as a guideline for real-world implementations on how frequently PSs should be twinned.

Abstract

With the massive advancements in processing power, Digital Twins (DTs) have become powerful tools to monitor and analyze physical entities. However, due to the potentially very high number of Physical Systems (PSs) to be tracked and emulated, for instance, in a factory environment or an Internet of Things (IoT) network, continuous twinning might become infeasible. In this paper, a DT system is investigated with a set of random PSs, where the twinning rate is limited due to resource constraints. Three cost functions are considered to quantify and penalize the twinning delay. For these cost functions, the optimal twinning problem under twinning rate constraints is formulated. In a numerical example, the proposed cost functions are evaluated for two, one push-based and one pull-based, benchmark twinning policies. The proposed methodology is the first to investigate the optimal twinning problem with random PSs and twinning rate constraints, and serves as a guideline for real-world implementations on how frequently PSs should be twinned.
Paper Structure (6 sections, 2 theorems, 14 equations, 4 figures)

This paper contains 6 sections, 2 theorems, 14 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Related Work
  3. System Model
  4. Optimal Monitoring Problem Formulation
  5. Numerical Example
  6. Conclusion

Key Result

Theorem 1

Assuming an initial twinning instance of $t_0=0$, expected value of $C_1(t)$ is given by the following expression: where $\mathbb{E}[\cdot]$ denotes the expectation operator, $\pi_{ik}$ is the steady-state probability of state $k$ for PS $i$, $Q_i$ is the transition rate matrix for PS $i$, and $(e^{(\cdot)})_{kk}$ is the entry at the $k$-th row and $k$-th column of the exponential matrix $e^{(\cd

Figures (4)

  • Figure 1: Monitoring and twinning of the physical systems.
  • Figure 2: Sample path for the states of the PSs and DTs, and the corresponding values of the cost functions.
  • Figure 3: Average values for the cost functions (a) $C_1(t)$, (b) $C_2(t)$, and (c) $C_3(t)$, for varying values of synchronization delay $\Delta$ and average twinning rate $\lambda_{avg}$, for PRTP.
  • Figure 4: Average values for the cost functions (a) $C_1(t)$, (b) $C_2(t)$, and (c) $C_3(t)$, for varying values of synchronization delay $\Delta$ and average twinning rate $\lambda_{avg}$, for PPTP.

Theorems & Definitions (4)

  • Theorem 1
  • proof
  • Theorem 2
  • proof