The Effects of Digital Twins Development on System’s Long-Term

Performance, Potential Capabilities, and Possible Beneﬁts

Ahmed Habib

and Michael W. Grenn

Department of Engineering Management and Systems Engineering,

The George Washington University, Washington, District of Columbia, U.S.A.

Keywords:

Digital Twin, Systems Architecture, Hastings-Metropolis, Markov-Chain, Monte-Carlo Algorithm, Systems

Engineering.

Abstract:

Practitioners who are working in Digital Engineering applications and especially the applications involving

Digital Twins are concerned with maintaining the twinning state between the cyber and physical entities

throughout the system’s life cycle. Although this level of granularity during the operation mode is required

to maintain the state of the Digital Twin, in many cases, it negatively impacts the emergent behavior of the

system in the long run. This effort explores the beneﬁts of the architecture interfaces of the system, assuming

the preservation of the twinning state, to uncover the convergence of the latent system in behavior which can

offer insights to systems engineers and decision makers to guide current twinning arrangements toward the

desired system behavior in the long run. The effort will explore Hastings-Metropolis, Markov-Chain, Monte-

Carlo Algorithm at interface sampling level and discuss the expansion potential beyond systems’ interfaces

architecture through empirical analysis example and discussing future research potentials.

1 INTRODUCTION

In recent years, Digital Twins (DT) have grown in

popularity among researchers and practitioners who

operate in domains such as digital engineering, sys-

tems engineering, and Cyber-Physical Systems (CPS)

(Zhang et al., 2022; Rathore et al., 2021). The lit-

erature exhibits many examples of the potential of

DTs and the integration possibility that covers a wide

range of applications (Zhang et al., 2022; Peladarinos

et al., 2023), together with instances of direct imple-

mentation in production (Lauer-Schmaltz et al., 2024;

Othman and Yang, 2023). Industries started to pay at-

tention to the importance of DTs. For instance, the

International Council on Systems Engineering (IN-

COSE) has added in its 2035 vision the goals for

integrating DTs into the discipline of Systems Engi-

neering (INCOSE, 2023). Other types of authorita-

tive bodies started initiatives, policies that encourage

the development and implementation of digital prac-

tices in various aspects of their entities, like the Dig-

ital Platform Commission Act of 2023 in the United

States, new GDPR-like regulations state-level, such

as the California Privacy Rights Act and the Utah

Consumer Privacy Act, and the Cybersecurity Law of

https://orcid.org/0000-0002-0504-7698

the People’s Republic of China, to name a few (Pfeif-

fer et al., 2024; DoD, 2023).

The broad potential utility that DT technology can

bring to a wide range of applications drew the at-

tention of policy makers and recognized its impor-

tance, where many policy artifacts and instructions

were made to guide the evolution of DTs (DoD, 2023;

Sch

oppenthau et al., 2023; Pfeiffer et al., 2024).

At the industry level, authoritative bodies re-

sponded positively to the calls of governments and

policy makers and began to embed into their abroad

guides, procedures, standards, and visions the impor-

tance of DTs to insight the relative communities or re-

search and practice of the importance of DTs (Rocha-

acome et al., 2021; Fraga-Lamas et al., 2022; IN-

COSE, 2023).

As a consequence, there is an increase in activity

in the research and development of DTs across many

domains (Fuller et al., 2020; Lauer-Schmaltz et al.,

2024).

1.1 Brief Background of DTs

The literature offers many deﬁnitions for DTs, for in-

stance, (Barbie and Hasselbring, 2024) shared a col-

lection of deﬁnitions for DTs and its internal com-

300

Habib, A. and Grenn, M. W.

The Effects of Digital Twins Development on System’s Long-Term Performance, Potential Capabilities, and Possible Beneﬁts.

DOI: 10.5220/0013406300003929

In Proceedings of the 27th International Conference on Enterprise Information Systems (ICEIS 2025) - Volume 2, pages 300-307

ISBN: 978-989-758-749-8; ISSN: 2184-4992

ponents in their literature review; however, the au-

thors desired to focus on deﬁnitions that hinges on

the twinning state for its relevance to this work: ”... A

change in state of the physical object directly leads

to a change in state of the digital object and vice

versa.” (Kritzinger et al., 2018) From the deﬁnition

above, realizing and sustaining the state of DT is a

difﬁcult task, due to the nature of dynamic systems

overtime, especially with cases in which the systems

are complex, have human-input dependency (non-

automated processes and triggers), or may have un-

certain components due to the nature of reality. The

difﬁcult task of maintaining the twinning state of the

DT may force engineers to lose focus on appreciat-

ing the long-term operations, or system’s emergent

behaviors (Saad et al., 2020).

1.2 Possible Challenges

DT environments can be described as heterogeneous

systems, as in many cases, being connected to other

elements, systems, and networks. It’s important for

DT designers to gain a deeper understanding of the

environment and how the systems may interact with

its environment (Fuller et al., 2020). The understand-

ing should be extended to cover the human-aspect,

connected systems, and even the enterprise environ-

ment.

There are many instances in the literature where

DT designers were able to develop and integrate DTs

into systems or applications; however, the focus in

the bulk of the work was on establishing the DT as

the product, that is, prioritizing the immediate com-

pliance of the system to maintain the DT state (Saad

et al., 2020). Rightfully so, establishing and maintain-

ing the twinning state is a very important aspect and

shouldn’t be neglected; nevertheless, this may cause

the designers to overlook the long-running behavior

of the system. For those reasons, this paper is set to

address two main questions:

(1) What is the percentage of time spent at a system’s

interfaces for a DT given its architecture interface

network?

(2) Given the architecture interfaces of a DT system,

what is the percentage of resources utilized by the

system in the long-run?

This effort attempts to address posed questions by

introducing the Hastings-Metropolis, Markov-Chain,

Monte-Carlo (Hastings-Metropolis MCMC) Algo-

rithm (Ross, 2013), a technique widely used in the

Discrete-Events Simulations ﬁeld.

Paper Organization: Section 2 provides general

background information on the proposed methodol-

ogy. Sections 3 provide a simple numerical example

that motivates the methodology. Section 4 communi-

cates the ﬁndings, offer a brief discussion followed by

communicating possible limitations. Section 5 Con-

vey the conclusions of the paper and highlight propo-

sitions for future work.

2 METHODOLOGY

2.1 Uncovering Latent Behaviors of

Systems

The main motivation from this work is to encourage

practitioners and researchers to expand the scope of

the desired outcomes beyond the conventional imple-

mentation of DT’s, and to include the long-term per-

formance of the system that may uncover inefﬁcien-

cies. The idea is that if DTs were developed and de-

ployed, there is a need to learn how the system will

behave beyond the immediate concerns of maintain-

ing the twinning state and to extend the learning to

cover the systems resources and organizational plan-

ning. There are cases where the DT is developed and

deployed, and gaining insights about the system’s per-

formance is a matter of analyzing the historical data,

logs , and system’s artifacts over an extended period

of time; however, making changes to the system at

that latent state is costly. The purpose is to learn as

much as possible about the system at an earlier stage

in development.

2.2 Hastings-Metropolis MCMC

Algorithm

Consider the system interface architecture diagram

illustrated in Figure 1 (left), where the upper trian-

gular matrix represents the feedforward interfaces,

the lower triangular matrix represents the feedback

interfaces, and the diagonal entries represent the

self-loop interfaces, if any. The interfaces represent

the ﬂow of information, or messages, etc., from a

component in the system to another corresponding

component, column and row labels. The interfaces in

Figure 1 are represented in a gray circular shape.

Assumption 1. Digital Twins implementation in

the system existed in this work.

Starting with expressing the Hastings-Metropolis

MCMC Algorithm, in terms of a pseudocode rep-

resented in Algorithm 1, motivated by a conceptual

example, then walk through the requirements, con-

straints, and comment on the process.

The Effects of Digital Twins Development on System’s Long-Term Performance, Potential Capabilities, and Possible Beneﬁts

301

GFEDCBA

Figure 1: Abstract adjacency matrix represents system’s interfaces, pre-processing (left), post-processing (right).

Algorithm 1: Hastings-Metropolis, MCMC Algorithm.

Data: P,π,q(x), T

Result: π

initialization: x

;

for t = 1 to T do

Sample x

′

∼ q(x

′

);

α = min

π(x

′

)q(x

′

)

π(x

)q(x

′

)

;

Sample u ∼ U(0, 1);

if u < α then

t+1

← x

′

;

else

t+1

← x

end

where: P the adjacency matrix, π(x) the target dis-

tribution, q(x) proposal distribution (user deﬁned), T

the maximum number of iterations, and α is the ac-

ceptance ratio. In addition:

• P, π ∈ R

(N×N)

i, j

,π

i, j

= P

j,i

,π

j,i

dim(P) = dim (π) ;

• t ∈ T,T = {t : t ∈ 1 ≤ T }, ∀t,T ∈ N

The matrix P needs to conform to Markov-Chain Er-

godic requirements (Ross, 2013), where:

• p

i j

= (t) > 0 ⇒ t = ×k (Aperiodic), k ∈ T being

the period count;

• π

i, j

= π

j,i

(Irreducible), π the steady-state of

the system;

•

∑

(n) = ∞ (Recurrent).

The process starts with sampling from the adja-

cency matrix P

at time t

subject to the sampling

from the user-supplied target distribution q(x), the ra-

tio of the sample from q(x

′

) in the next state over the

sample from the previous state q(x), i.e. the Bayesian

posterior, being compared with the value of 1, that

value α is the acceptance/rejection criteria, which is

part of the Hastings-Metropolis part of the algorithm .

Taking the minimum value to be assigned to the vari-

able of α. The next step in the process is to draw a

sample u from a Uniform distribution U(0,1). If the

sample u is less than the acceptance ratio α, then ad-

vance the clock, t, and the next state will get x

′

; other-

wise, advance the clock and the next state will get x,

that is, the next state will carry the value of the current

state. The process will continue until it reaches the

maximum number of iterations, T , which is a value

provided by the user.

In terms of the overall performance of Algorithm

1, since Markov-Chains are being implemented, the

process is considered memory-less, that is, the fu-

ture is independent of the past, given the present.

This property can be beneﬁcial in reducing the space-

complexity, where the main information is stored in P

while updating the values in π when iterating through

t. In terms of time-complexity for the algorithm, the

Monte-Carlo aspect of the algorithm will be the main

contributor with estimation of O(1/n) (Ross, 2013).

At t = T , the algorithm will stop and the steady-

state π matrix is reached as illustrated in Figure 1,

post-processing (right). The difference in gradient of

the gray-color represents the tendency of the archi-

tecture interfaces to be utilized by the system in the

long-run. The next section will implement the algo-

rithm using a simpliﬁed example.

3 EVALUATION

To demonstrate the proposed methodology expressed

in Section 2, a small sample was collected from a

network that represents the topology of the Western

States Power Grid of the United States (Watts and

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Figure 2: Adjacency matrix represents system’s interfaces, pre-processing. where, system labels represents the index in the

data set.

Strogatz, 1998). The sample size is 38 nodes out

of 4, 940 nodes from the original data set, undirected

and unweighted. The graphical representation illus-

trated in Figure 2. The selection of the interfaces was

based on Markov-Chain ergodic requirements listed

in Section 2. The number of iterations used was set

to T = 50000. For reproducibility, the labeling of the

selected nodes carries the indices of the node from the

original data set. Figure 2, is the visual illustration of

the selected data, where the black squares represent an

interface between two nodes, 0 for white otherwise.

Applying Algorithm 1, on the selected adjacency

matrix data illustrated in Figure 2, along with the

mentioned speciﬁcations, the output can be seen in

Figure 3.

4 DISCUSSION

4.1 Analysis of Systems Behavior

Applying the methodology speciﬁed in Section 2, en-

gineers can have a preview of how the system may be-

have in the long-run. From Figure 2, the darker gray

color the interface is, the more time is being spent

at. This observation answers the ﬁrst posed question

(1), in other words, which interface is more impor-

tant? The gained knowledge is useful in many cases

if the system, or components of it, are being hosted

in the cloud. By learning which interface the system

would spend most of the time on, infrastructure and

resources provisioning can be made to accommodate

for such expected activity, hence, identifying the sys-

tem’s architecture ﬂow bottlenecks. Other potential

beneﬁts such as by increasing the learning about the

most used interfaces will better inform the process of

failure mode analysis, and reliability analysis to name

a few.

The Effects of Digital Twins Development on System’s Long-Term Performance, Potential Capabilities, and Possible Beneﬁts

303

Figure 3: Adjacency matrix represents system’s interfaces, post-processing. where, system labels represents the index in the

data set.

4.2 Potential System Utilization

The other way that increases the learning about the

proposed DT architecture is that Algorithm 1 helps

uncovering the expected utilization at element-level,

over the long-run. Figure 4 (bottom), underscores the

nodes, elements, and their relative utilization with re-

spect to the entire system. To deliver a relative com-

parison between the pre-process and post-process,

the authors sought to compute the percentage degree

against percentage state-frequency.

Figure 4 (top) represents the node degrees of the

adjacency matrix, computed by:

π(x

)

∑

j=1

π(x

)

× 100 (1)

where (1) represents the Percentage Degree, PD, that

communicates the degree π(x

) = deg(x

) relative to

the total degree of all nodes N, the denominator.

The graphical output for (1) is illustrated in Figure 4

(top). To produce Figure 4 (bottom), the following

was used:

V (x

) =

∑

i=1

(2)

where V (x

) is the number of visits to state x

, T is

the total number of iterations, x

, the state of Markov-

Chain at time t, 1

an indicator function that

equates to 1 if x

= x

; 0, otherwise. Applying (2)

into (3):

f (x

) =

V (x

)

× 100 (3)

where f (x

) is the state frequency, which was used

in producing Figure 4 (bottom). The visual examina-

tion of Figure 4 can help DT designers to gain under-

standing on how system’s internal components may

behave. Components with labels 138, 205, and 207

are in agreement in terms of the most percentage in

both cases; however, components 139 and 140 are the

second highest percentage in terms of state-frequency

analysis and clearly was not the case when compared

with its counterpart in the percentage degree analy-

sis. The information gained from Figure 4 helped in

addressing the question posed in 1.2.

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To optimize key variables such as cost, availabil-

ity, and organizational efﬁciency, this methodology

provides valuable insights into the utilization of the

human component within the system beyond the DT.

For instance, as shown in Figure 4 (bottom), it is

recommended to analyze system elements based on

their relative percentage utilization against available

resources, mainly when human interaction with DTs

is a critical to the process. This method aims to deter-

mine whether the relative state-frequencies of com-

ponent utilization are feasible given the dedicated hu-

man resources for the tasks. For example, the state-

frequency percentages of elements 138, 205, and 207

(Figure 4, bottom) ought to be compared to the cor-

responding human resources assigned to handle asso-

ciated tasks. On the other hand, elements 153, 157,

and 36 show high percentage utilization yet low state-

frequency, signifying a different trend worth inves-

tigating. In both cases, DT designers can leverage

this analysis to evaluate other system’s aspects. This

analysis could also support organizational talent ac-

quisition by empowering planning for better talent

alignment and determining the appropriate quantity

of personnel required for the system given DT im-

plementation. Additionally, this method extends be-

yond the human aspect to any process or sub-process

inﬂuenced by delays or queue dependencies. For in-

stance, elements 138, 205, and 207 may warrant re-

view for potentially low usage frequency, which could

indicate underutilized human resources dedicated to

those tasks. Implementing DTs into existed organi-

zations may warrant decision makers to rethink how

organizations can accommodate DTs.

4.3 As-Is vs. To-Be DT Architecture

Based on the analysis presented in Sections 4.1

and 4.2, the next logical step for DT architects is to

consider whether the proposed system interface archi-

tecture is in alignment with the expected performance.

This question prompts DT architects to evaluate the

system’s feasibility in delivering the desired capabili-

ties over the long-run. Additionally, it encourages the

consideration of speciﬁc objectives the system must

achieve within the system’s lifecycle to arrive at the

To-Be architecture. This methodology serves as a

valuable tool to support DT designers during the early

stages of DT development.

4.4 Challenges and Possible Limitations

The purpose of selecting a sample for the numerical

implementation with symmetry in the interfaces from

the dataset is to conform to Markov-Chain ergodic re-

quirements; however, in reality many systems do not

enjoy such conditions. Many interface networks have

self-directing edges, e.g., going from node A to node

A, which implies a perfect correlation in this edge

case.

Many interface network architectures have associ-

ated weights, and in many cases, those weights are not

balanced, which may need designer’s interventions to

allow the sampling in the next iteration to be less re-

stricted.

Other cases where networks by design are gov-

erned by processes that require events to not be re-

current, for instance, the case of user-to-platform ac-

cess with the event of user inputting incorrect access

credentials like wrong password or username. The

access to the system’s network must be denied, and

only interfaces that are involved with this activity are

needed. What the authors are trying to communicate

is that the Hastings-Metropolis MCMC algorithm is a

powerful tool, and its utility was demonstrated in this

section and there is a potential to investigate ways to

overcome the mentioned limitations.

5 CONCLUSIONS

In this paper, we introduced the Hasting-Metropolis

MCMC algorithm and showed how to apply it on an

interface architecture matrix for a DT system. Then

followed by an empirical analysis to answer the two

main posed questions stated in Section 1. Gained in-

sights from the analysis and expanded on how it can

help with enhancing the understanding of the system.

Followed by a discussion about the attributes and pos-

sible limitations of the method. The objective of this

work is to encourage DT architects to think outside

the scope of the implementations of systems and of-

fer a valuable tool to learn about the design and how

it may behave in the long-run.

5.1 Future Research Outlook

The results are promising and calls for further re-

search to enhance the algorithm’s inclusivity, en-

abling it to address a wider range of complex applica-

tions, as brieﬂy discussed in Section 4.4. Moreover,

there are instances in the literature advocating for the

expansion of DTs to operate at higher levels of ab-

straction.

For instance, there is a proposition of the DT-

base Automation Pyramid (AP) model for a complete

company application. They require that all AP levels

must be integrated with the DT, in an attempt to gain

improvements at manufacturing system as illustrated

The Effects of Digital Twins Development on System’s Long-Term Performance, Potential Capabilities, and Possible Beneﬁts

305

Figure 4: System’s percentage degree analysis in a comparative evaluation, pre-processing (Top), System’s percentage state-

frequency analysis, post-processing (Bottom).

PLCs

SCADA, HMI

MES

ERP

Management Level

Planning Level

Supervisory Level

Control Level

Field Level

Level 4:

Business &

Logistics

Level 3: Manufacturing

Operation Planning

Level 2: Monitoring &

Supervising

Machinery,

Sensors, etc.

Level 1: Sensing & Manipulating the

Production Process

Level 0: Physical Production Process

Figure 5: Automation Pyramid Drivers, adopted from ANSI/ISA 95 Standard.

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306

on Figure 5, (Martinez et al., 2021). The proposed

settings were adopted by the authors from standard

ANSI/ISA 95, the logical placement of DTs can be

found at the Control level, i.e., Level 1 where Sensing

and manipulating the product process.

There is another approach that can be used in as-

sessing DT systems, inspired by the work of (Wei

et al., 2024). They offered a guideline for the

construction of a multi-domain, and multi-level ST

model. The proposition is more like a reference ar-

chitecture which is composed of hierarchical multi-

model constructs such as part, component, assembly

unit, and system equipment models, and within there

are additional models at the subsystem level. Explor-

ing the application of Hastings-Metropolis MCMC

Algorithm on the domain-level, and at the model-

level can be a future research venue.

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