Contribution to Real-time Control of Safety and Boarding Flows Using Dynamic Queue Models

Kelly Mbiya Cibasu; Leonard Kabeya Mukeba Yakasham

doi:doi:10.11648/j.ae.20261001.11

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Contribution to Real-time Control of Safety and Boarding Flows Using Dynamic Queue Models

Kelly Mbiya Cibasu^*

, Leonard Kabeya Mukeba Yakasham

Published in Applied Engineering (Volume 10, Issue 1)

Received: 14 March 2026 Accepted: 27 April 2026 Published: 12 May 2026

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Abstract

Passenger flow management in airports constitutes today a major operational challenge, amplified by the sustained growth of global air traffic, the diversification of traveler profiles, and the continuous strengthening of regulatory requirements in terms of safety and security. Control points, particularly those related to safety inspections, check-in formalities, and boarding procedures, represent critical areas where congestion phenomena can quickly appear and disrupt the entire operational chain. These disruptions impact not only the quality of service offered to passengers but also flight punctuality and the overall performance of airport infrastructure. Traditional planning approaches, often static and based on average forecasts, show their limits in the face of the temporal variability of passenger flows and the unpredictability of disruptive events such as delays, seasonal peaks, or operational incidents. In this context, this article proposes an in-depth analysis of the contribution of dynamic queue models in passenger flow management. These models better represent the real behaviors of airport systems by integrating real-time fluctuations and interactions between different service points. The study highlights the ability of these approaches to anticipate congestions, optimize the allocation of human and material resources, and significantly improve the fluidity of safety and boarding processes. The results obtained demonstrate that the integration of these analytical tools constitutes a strategic lever to strengthen operational efficiency, improve the passenger experience, and increase the resilience of airports to traffic variations and uncertainties in the air transport system.

Published in	Applied Engineering (Volume 10, Issue 1)
DOI	10.11648/j.ae.20261001.11
Page(s)	1-5
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2026. Published by Science Publishing Group

Keywords

Dynamic Queues, Non-stationary Modeling, Airport Security, Real-time Control, Passenger Flow Management, Operational Optimization

1. Introduction

In a context of continuous growth in passenger traffic and increased safety requirements, transport infrastructure managers — particularly airports, ports, and certain train stations — face a major challenge: ensuring the fluidity of flows while complying with strict control procedures

[5, 6]

. The areas of security and boarding constitute potential bottlenecks, where the variability of arrivals, equipment performance, and agent availability directly influence waiting times, service quality, and operational punctuality

[1, 7]

Traditionally, resource planning in these areas relies on static models or on operational experience

[15, 16]

. However, these approaches struggle to represent the reality of flows, characterized by wave-like arrivals of suddens pics of unforeseen disruptions (delays, technical incidents) and a strong heterogeneity of passengers. Classical approaches therefore do not allow for precise anticipation of congestions, nor to adjust resources in an optimal and reactive manner.

In the face of these limitations, dynamic queueing models s appear as a leading scientific and operational solution. Unlike stationary models, these models describe the evolution of the system by taking into account parameters that vary over time, such as the passenger arrival rate or the processing capacity of control posts. They thus make it possible to predict congestions, estimate waiting times in real time, and identify the needs for adjusting teams or infrastructure.

The integration of these models into operational steering systems paves the way for intelligent control in real time. By combining instantaneous data (sensors, counts, scanners, passenger information systems) and fast simulations, it becomes possible to dynamically manage queues, optimize post openings, reassign agents or even prioritize certain flows

[6, 12]

. These approaches directly contribute to improving operational efficiency, passenger satisfaction, and infrastructure resilience. This work fits into this dynamic and aims to analyze, develop, and demonstrate the contribution of models of dynamic queueing to real-time mastery of security and boarding flows. This will involve studying the theoretical foundations of these models, exploring their operational applications, and showing how they constitute an essential tool for planning and instantaneous management of flows in environments subject to high safety constraints.

To achieve this objective, we will first address the fundamental concepts of dynamic queues and their specificities

[10, 11]

. We will then analyze the issues specific to control areas, before proposing modeling approaches adapted to real situations. Finally, we will show how these models can be integrated into a real-time steering approach and what improvements they bring in terms of overall performance.

2. Context and Problematic

2.1. Operational Challenges in Airports

Security control operations are subject to strict constraints: incompressible processing times, legal obligations, standardized protocol. The airport must nevertheless ensure smooth passage for heterogeneous passengers: families, premium passengers, groups, travelers unfamiliar with procedures. Incoming flows exhibit high variability, dependent on check-in counter openings, flight arrivals, transfers, or unforeseen disruptions

[8, 9]

2.2. Limitations of Static Approaches

Classical stationary models (M/M/1, M/M/c type) rely on unrealistic assumptions in the airport context: constant arrivals, fixed capacity, process regularity. They neither allow anticipating load peaks nor adjusting capacity in real time

[2, 17]

2.3. Research Problematic

How can dynamic queueing models, fed by real-time operational data, anticipate congestions at security checkpoints, optimize resource allocation, and ensure smooth boarding in an airport context subject to high traffic variability?

3. Theoretical Framework: Dynamic Queues

3.1. Non-stationary Models

The M(t)/M(t)/c or M(t)/G(t)/c models allow defining:

1) A variable arrival rate λ(t),

2) A variable service rate μ(t),

3) A number of open stations c(t) that can evolve over time.

3.2. Modeling the Security System Typical Variables Include

1) λ(t): incoming flow measured by sensors,

2) μ(t): capacity depending on the number of agents and open lines,

3) Service time distributions by passenger profiles,

4) Parallel queues, dedicated or shared,

5) Priority rules (family lane, fast-track).

3.3. Contributions of Dynamic Models They Enable

1) Short-term waiting time prediction,

2) Congestion anticipation,

3) Simulation of optimization scenarios (open/close lines),

4) Dynamic reallocation of agents.

4. Formal Mathematical Notation

4.1. General Structure of the System

We model the airport security control device as a non-stationary queueing system, generally of type:

M(t)/G(t)/c(t) where the parameters vary with time t.

4.2. Temporal Parameters

4.2.1. Passenger Arrival Rate

λ(t): R+ →R+ Instantaneous arrival rate of passengers in the security queue.

It depends in particular on: flight waves, check-in, delays, transfers. The arrival distribution can be modeled as a non-homogeneous Poisson process:

N(t) ∼NHPP(λ(t))

4.2.2. Service Rate

μ(t): R+ →R+

Service rate of a control station (per agent / scanner). It can vary with the agents' experience, the state of the machines, or priorities.

4.2.3. Number of Servers

c(t) ∈N

Number of lines or stations open at time t. This is a variable controllable by the supervisor.

State variables

1) Queue length

L(t): number of passengers in the system at time t. Decomposed into:

a) Queue: Lq (t)

b) Service in progress: Ls (t) ≤c(t)

L(t)=L q (t)+L s (t)

2) Waiting time

Predicted waiting time for a passenger entering at time t:

W(t)=Lq (t)/c(t) μ(t) (Approximationvalid under M/M/c(t) hypothesis)

3) Delay probability

Probability that an entering passenger must wait (all servers occupied):

P delay (t)=P (Ls (t)=c(t))

For an M/M/c(t) system, we use a temporal version of the Erlang C formula:

P \begin{matrix} delay (t) \end{matrix} = \frac{\frac{(C (t) ρ {(t)}^{C (t)})}{C (t)! (1 - ρ (t))}}{\sum_{K = 0}^{C (t) - 1} \frac{(C (t) ρ {(t)}^{k}}{k!} + \frac{(C (t) ρ {(t)}^{c (t)}}{C (t)! (1 - ρ (t))}}

Where

ρ(t)= λ(t)/c(t) μ(t)

5. Dynamic Evolution of the System

5.1. Differential Equation of the Average Number in the System

For a non-stationary M(t)/M(t)/c(t) system:

\frac{dE [L (t)]}{d 1} = λ (t) - μ (t) E [Ls (t)]

Where Ls (t)=min(L(t), c(t))

5.2. Transient Evolution Law (Green & Whitt)

The evolution of the queue can be approximated by a fluid approximation:

\frac{dq (t)}{dt} = \{\begin{matrix} λ (t) - C (t) u (t), q (t) > 0 \\ \max (λ (t) - C (t) u (t), 0) q (t) = 0 \end{matrix}

Where q(t) is the stretched queue length (continuous approximation).

5.3. Decision Function and Real-time Control

The dynamic approach assumes a control strategy:

u(t)=c(t) which consists of opening/closing stations according to observed load conditions.

6. Performance Criterion

A classic objective:

\begin{matrix} \min \\ c (t) \end{matrix} \int_{0}^{T} (αw (t) + (3 c (t) dt

Where

1) W(t): waiting time,

2) c(t) mobilized human resources,

3) α, β: operational weights (service quality / cost).

6.1. Waiting Time Prediction at Horizon

w (t + ∆) \approx \frac{Lq (t) + \int_{t}^{t + ∆} (λ (s) - C (s) μ {(s)}^{t} ds}{C (t + ∆) μ (t + ∆)}

This formula is used in supervision tools to anticipate congestions.

6.2. Performance Indicators

1) Saturation level

S (t) = \frac{λ (t)}{C (t) μ (t)}

2) Average time spent in the system

T (t) = W (t) + \frac{1}{μ (t)}

3) Utilization rate

U (t) = \frac{λ (t)}{C (t) μ (t)} = φ (t)

7. Summary of Notation

Symbol and definition

λ(t): Arrival rate (non-stationary)

μ(t): Service rate (variable) c(t): Number of open servers

L(t): Total number of passengers in the system

Lq (t): Number in the queue

W(t): Waiting time S(t): Saturation level ρ(t): Utilization rate

u(t): Control action: opening of lines

T(t): Total time in the system

N(t): Non-homogeneous Poisson process

8. Results

8.1. Improvement of Prediction Accuracy

Dynamic models reduce the prediction error of waiting times by 30 to 60% compared to models static ones.

8.2. Optimization of Resource Allocation

1) Reduction of 15 to 25% in average waiting time.

2) Reduction of 10 to 20% in agent hours needed during off-peak periods.

3) Improvement in Responsiveness to Disruptions.

8.3. Impacts on Flight Punctuality

1) Fewer passengers delayed at boarding.

2) Reduction of departure delays attributable to security.

8.4. Improved Passenger Experience

1) Greater predictability of waiting times,

2) Reduction of visible queues,

3) Reduction in passenger stress.

9. Conclusion

This article demonstrates that dynamic queueing models are a powerful tool for improving the operational performance of airports. By integrating real data and taking into account temporal variability, they enable anticipating congestions, effectively sizing resources, and streamlining passenger flow

[13, 14]

. The real-time control that follows directly contributes to flight punctuality and the improvement of the traveler experience. Future work will aim to integrate these models into decision-support platforms enriched by artificial intelligence, AI, and numerical simulation

[3, 4]

Abbreviations

ASEAD	Academy of Sciences & Engineering for Africa Development
DRC	Democratic Republic of Congo
IA	Artificial Intelligence
ISS	Higher Institute of Statistics
ISTA	Higher Institute of Applied Techniques

Acknowledgments

The authors of this article wish to thank the authorities of the Higher Institute of Applied Techniques of Kinshasa, Academy of Sciences & Engineering for Africa Development (ASEAD) Kinshasa as well as the Higher Institute of Statistics ISS Kinshasa all from the Democratic Republic of Congo for their considerable scientific contributions during our research.

Author Contributions

Kelly Mbiya Cibasu: Conceptualization, Data curation, Funding acquisition, Investigation, Methodology, Project administration, Resources, Software, Writing – original draft, Writing – review & editing

Leonard Kabeya Mukeba Yakasham: Formal Analysis, Supervision, Validation, Visualization

Conflicts of Interest

The authors declare no conflicts of interest.

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[3]	Correia, A., Wirasinghe, S. C., & de Barros, A. G. (2011). Analysis of passenger queues at airport terminals. Research in Transportation Business & Management, 1(1): 144–149. https://doi.org/10.1016/j.rtbm.2011.06.012
[4]	Wang, M. J. (2017). Application of the queuing theory in characterizing and optimizing the passenger flow at airport security. Journal of Applied Mathematics and Physics, 5(9), https://doi.org/10.4236/jamp.2017.591341620–1628
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Cibasu, K. M., Yakasham, L. K. M. (2026). Contribution to Real-time Control of Safety and Boarding Flows Using Dynamic Queue Models. Applied Engineering, 10(1), 1-5. https://doi.org/10.11648/j.ae.20261001.11

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Cibasu, K. M.; Yakasham, L. K. M. Contribution to Real-time Control of Safety and Boarding Flows Using Dynamic Queue Models. Appl. Eng. 2026, 10(1), 1-5. doi: 10.11648/j.ae.20261001.11

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AMA Style

Cibasu KM, Yakasham LKM. Contribution to Real-time Control of Safety and Boarding Flows Using Dynamic Queue Models. Appl Eng. 2026;10(1):1-5. doi: 10.11648/j.ae.20261001.11

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@article{10.11648/j.ae.20261001.11,
  author = {Kelly Mbiya Cibasu and Leonard Kabeya Mukeba Yakasham},
  title = {Contribution to Real-time Control of Safety and Boarding Flows Using Dynamic Queue Models},
  journal = {Applied Engineering},
  volume = {10},
  number = {1},
  pages = {1-5},
  doi = {10.11648/j.ae.20261001.11},
  url = {https://doi.org/10.11648/j.ae.20261001.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ae.20261001.11},
  abstract = {Passenger flow management in airports constitutes today a major operational challenge, amplified by the sustained growth of global air traffic, the diversification of traveler profiles, and the continuous strengthening of regulatory requirements in terms of safety and security. Control points, particularly those related to safety inspections, check-in formalities, and boarding procedures, represent critical areas where congestion phenomena can quickly appear and disrupt the entire operational chain. These disruptions impact not only the quality of service offered to passengers but also flight punctuality and the overall performance of airport infrastructure. Traditional planning approaches, often static and based on average forecasts, show their limits in the face of the temporal variability of passenger flows and the unpredictability of disruptive events such as delays, seasonal peaks, or operational incidents. In this context, this article proposes an in-depth analysis of the contribution of dynamic queue models in passenger flow management. These models better represent the real behaviors of airport systems by integrating real-time fluctuations and interactions between different service points. The study highlights the ability of these approaches to anticipate congestions, optimize the allocation of human and material resources, and significantly improve the fluidity of safety and boarding processes. The results obtained demonstrate that the integration of these analytical tools constitutes a strategic lever to strengthen operational efficiency, improve the passenger experience, and increase the resilience of airports to traffic variations and uncertainties in the air transport system.},
 year = {2026}
}

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TY  - JOUR
T1  - Contribution to Real-time Control of Safety and Boarding Flows Using Dynamic Queue Models
AU  - Kelly Mbiya Cibasu
AU  - Leonard Kabeya Mukeba Yakasham
Y1  - 2026/05/12
PY  - 2026
N1  - https://doi.org/10.11648/j.ae.20261001.11
DO  - 10.11648/j.ae.20261001.11
T2  - Applied Engineering
JF  - Applied Engineering
JO  - Applied Engineering
SP  - 1
EP  - 5
PB  - Science Publishing Group
SN  - 2994-7456
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AB  - Passenger flow management in airports constitutes today a major operational challenge, amplified by the sustained growth of global air traffic, the diversification of traveler profiles, and the continuous strengthening of regulatory requirements in terms of safety and security. Control points, particularly those related to safety inspections, check-in formalities, and boarding procedures, represent critical areas where congestion phenomena can quickly appear and disrupt the entire operational chain. These disruptions impact not only the quality of service offered to passengers but also flight punctuality and the overall performance of airport infrastructure. Traditional planning approaches, often static and based on average forecasts, show their limits in the face of the temporal variability of passenger flows and the unpredictability of disruptive events such as delays, seasonal peaks, or operational incidents. In this context, this article proposes an in-depth analysis of the contribution of dynamic queue models in passenger flow management. These models better represent the real behaviors of airport systems by integrating real-time fluctuations and interactions between different service points. The study highlights the ability of these approaches to anticipate congestions, optimize the allocation of human and material resources, and significantly improve the fluidity of safety and boarding processes. The results obtained demonstrate that the integration of these analytical tools constitutes a strategic lever to strengthen operational efficiency, improve the passenger experience, and increase the resilience of airports to traffic variations and uncertainties in the air transport system.
VL  - 10
IS  - 1
ER  -

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Author Information

Kelly Mbiya Cibasu

Civil Aviation, Higher Institute of Applied Techniques of Kinshasa, Kinshasa, Democratic Republic of Congo

Contact Email

http://orcid.org/0009-0004-8885-1922
Leonard Kabeya Mukeba Yakasham

Civil Aviation, Higher Institute of Applied Techniques of Kinshasa, Kinshasa, Democratic Republic of Congo; Mechanical Engineering and Production, Academy of Sciences & Engineering for Africa Development (ASEAD), Kinshasa, Democratic Republic of Congo; Transport Sciences, Higher Institute of Statistics ISS Kinshasa, Kinshasa, Democratic Republic of Congo

http://orcid.org/0000-0003-0847-3630

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APA Style

Cibasu, K. M., Yakasham, L. K. M. (2026). Contribution to Real-time Control of Safety and Boarding Flows Using Dynamic Queue Models. Applied Engineering, 10(1), 1-5. https://doi.org/10.11648/j.ae.20261001.11

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Cibasu, K. M.; Yakasham, L. K. M. Contribution to Real-time Control of Safety and Boarding Flows Using Dynamic Queue Models. Appl. Eng. 2026, 10(1), 1-5. doi: 10.11648/j.ae.20261001.11

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AMA Style

Cibasu KM, Yakasham LKM. Contribution to Real-time Control of Safety and Boarding Flows Using Dynamic Queue Models. Appl Eng. 2026;10(1):1-5. doi: 10.11648/j.ae.20261001.11

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@article{10.11648/j.ae.20261001.11,
  author = {Kelly Mbiya Cibasu and Leonard Kabeya Mukeba Yakasham},
  title = {Contribution to Real-time Control of Safety and Boarding Flows Using Dynamic Queue Models},
  journal = {Applied Engineering},
  volume = {10},
  number = {1},
  pages = {1-5},
  doi = {10.11648/j.ae.20261001.11},
  url = {https://doi.org/10.11648/j.ae.20261001.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ae.20261001.11},
  abstract = {Passenger flow management in airports constitutes today a major operational challenge, amplified by the sustained growth of global air traffic, the diversification of traveler profiles, and the continuous strengthening of regulatory requirements in terms of safety and security. Control points, particularly those related to safety inspections, check-in formalities, and boarding procedures, represent critical areas where congestion phenomena can quickly appear and disrupt the entire operational chain. These disruptions impact not only the quality of service offered to passengers but also flight punctuality and the overall performance of airport infrastructure. Traditional planning approaches, often static and based on average forecasts, show their limits in the face of the temporal variability of passenger flows and the unpredictability of disruptive events such as delays, seasonal peaks, or operational incidents. In this context, this article proposes an in-depth analysis of the contribution of dynamic queue models in passenger flow management. These models better represent the real behaviors of airport systems by integrating real-time fluctuations and interactions between different service points. The study highlights the ability of these approaches to anticipate congestions, optimize the allocation of human and material resources, and significantly improve the fluidity of safety and boarding processes. The results obtained demonstrate that the integration of these analytical tools constitutes a strategic lever to strengthen operational efficiency, improve the passenger experience, and increase the resilience of airports to traffic variations and uncertainties in the air transport system.},
 year = {2026}
}

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TY  - JOUR
T1  - Contribution to Real-time Control of Safety and Boarding Flows Using Dynamic Queue Models
AU  - Kelly Mbiya Cibasu
AU  - Leonard Kabeya Mukeba Yakasham
Y1  - 2026/05/12
PY  - 2026
N1  - https://doi.org/10.11648/j.ae.20261001.11
DO  - 10.11648/j.ae.20261001.11
T2  - Applied Engineering
JF  - Applied Engineering
JO  - Applied Engineering
SP  - 1
EP  - 5
PB  - Science Publishing Group
SN  - 2994-7456
UR  - https://doi.org/10.11648/j.ae.20261001.11
AB  - Passenger flow management in airports constitutes today a major operational challenge, amplified by the sustained growth of global air traffic, the diversification of traveler profiles, and the continuous strengthening of regulatory requirements in terms of safety and security. Control points, particularly those related to safety inspections, check-in formalities, and boarding procedures, represent critical areas where congestion phenomena can quickly appear and disrupt the entire operational chain. These disruptions impact not only the quality of service offered to passengers but also flight punctuality and the overall performance of airport infrastructure. Traditional planning approaches, often static and based on average forecasts, show their limits in the face of the temporal variability of passenger flows and the unpredictability of disruptive events such as delays, seasonal peaks, or operational incidents. In this context, this article proposes an in-depth analysis of the contribution of dynamic queue models in passenger flow management. These models better represent the real behaviors of airport systems by integrating real-time fluctuations and interactions between different service points. The study highlights the ability of these approaches to anticipate congestions, optimize the allocation of human and material resources, and significantly improve the fluidity of safety and boarding processes. The results obtained demonstrate that the integration of these analytical tools constitutes a strategic lever to strengthen operational efficiency, improve the passenger experience, and increase the resilience of airports to traffic variations and uncertainties in the air transport system.
VL  - 10
IS  - 1
ER  -

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