Optimizing Performance of Molecular Communication System using Congestion Control Mechanisms.

1. Introduction

In the field of molecular communication (MC), the efficient transport of molecules between transmitter and receiver is of paramount importance for applications like targeted drug delivery, environmental monitoring, and synthetic biology. Among these, MC has shown immense potential for targeted drug delivery in cancer therapy due to its ability to transmit drug molecules directly to malignant cells with high precision, minimizing harm to healthy tissues. However, achieving an optimal communication flow rate while maintaining minimal congestion at the receiver end remains a significant challenge. Congestion reduces throughput and leads to molecule wastage, undermining the effectiveness of therapeutic intervention. Addressing these challenges requires a robust congestion control mechanism to balance the trade-off between throughput optimization and congestion avoidance. In MC, the number of molecules emitted by the transmitter can overwhelm the receiver's capacity, resulting in congestion and reduced communication efficiency.

This necessitates strategies that dynamically regulate molecule emission based on real-time feedback from the receiver, thereby ensuring a smooth and efficient flow of molecules. This research introduces a feedback-driven framework for controlling congestion in MC systems, emphasizing the dual objectives of maximizing throughput and minimizing molecule wastage. The receiver continuously monitors the congestion level and sends feedback to the transmitter, which dynamically adjusts the emission rate of molecules to optimize the flow rate. The framework integrates innovative congestion control strategies, including adaptive thresholds, predictive modeling, and state-transition mechanisms inspired by TCP's TAHOE algorithm, tailored to address the unique dynamics of MC. This study explores five distinct congestion control mechanisms through a combination of computational modeling, simulation using COMSOL, and Python-based strategy testing. Each strategy is rigorously evaluated to demonstrate its effectiveness in optimizing flow rate while avoiding cyclic behavior or congestion spikes. The results provide valuable insights into designing efficient MC systems for real-world applications like cancer drug delivery, offering a pathway to enhance therapeutic outcomes.

"Figure 1" illustrates a closed system of MC, where information is transmitted through the release and reception of molecules.

The transmitter represents the source of information and is responsible for generating and emitting molecules. The molecules themselves carry the encoded data, traveling through the medium as they disperse.

The receiver is the destination, detecting and interpreting the incoming molecules to extract the transmitted information. This closed-loop process enables the exchange of data through the molecular channel.

1.1. Related studies

Molecular Communication (MC) has emerged as a transformative domain of research, particularly in targeted drug delivery, environmental sensing, and synthetic biology. This field offers a novel approach to precise molecular transmission, which is crucial in therapeutic contexts, such as cancer treatment, where targeted delivery reduces harm to healthy tissues. A recurring challenge in MC systems lies in managing throughput, the efficient transport of molecules, while addressing congestion at the receiver end. Congestion can disrupt the molecular flow, leading to inefficient delivery and waste. Early works, such as those by Akyildiz et al. [1] have emphasized the importance of robust congestion control mechanisms to balance throughput optimization and congestion avoidance. These studies advocate for the use of dynamic feedback systems to modulate molecule emission rates based on real-time conditions at the receiver. In [2], Byun focuses on a feedback-controlled adaptive method for signal detection, improving performance without high time costs or computational complexity. This paper introduces a straightforward and practical approach that allows receiver nanomachines to autonomously estimate signal detection times based on observed molecular concentrations and weighted feedback error measurements. Nakano et al. [3] emphasize performance parameters, throughput, and efficiency, and the study found that throughput rises with increased transmission rates, whereas efficiency peaks at an optimal transmission rate for maximum performance. The paper does not address feedback-driven congestion control strategies in MC. Feedback-based control schemes were further introduced to enable dynamic rate adaptation, striking a balance between throughput and efficiency. Zhao et al. [4] optimized and enhanced the drug release rate of nanomachines to achieve a complete drug response in localized targeted drug delivery. This approach involves utilizing a drug reception model based on the M/M/c/c queue and a response model grounded in diffusion channels. These models work to refine and optimize the drug delivery process for maximum efficacy. Femminella et al. [5] examine the factors contributing to congestion in MC systems. This study can be applied to develop rate control algorithms that efficiently determine the optimal release rate of molecules for drug delivery applications. Felicetti et al. [6] focus on regulating the release rate in MC to deliver an exact dosage of the drug to target cells within a defined timeframe while minimizing potential side effects. Felicetti et al. [7] suggested a connection-oriented protocol that utilizes TCP-like probing to determine the optimal transmission rate between the transmitter and receiver, effectively preventing congestion at the receiver. Salehi et al. [8] focus on diffusion-based MC channels, especially in the presence of probabilistic absorbers, which pose distinct challenges and opportunities for system design. This analysis focuses on the single receptor model and examines congestion effects, elucidating how absorbing targets impact the efficiency of MC. An analytical solution was developed by Damrath et al. [9] to model the controlled release of drugs transported by extracellular vesicles. This solution was validated through numerical simulations using a comprehensive end-to-end system model. Additionally, the quasiconvex/quasiconcave characteristics of a bilevel optimization problem were demonstrated and confirmed. Kotsuka et al. [10] proposed a control-theoretic framework for bidirectional molecular communication systems. Frequency response analysis offers valuable design guidelines for molecular communication channels. Ningthoujam et al. [11] propose feedback channels to enhance performance by determining channel states (good or bad) based on received ACKs or NACKs. This feedback informs whether to employ single-path or multipath techniques for optimal molecule transmission. The multipath approach performs better in poor channel conditions, while the single-path strategy is more effective in ideal channel conditions. Ghavami et al. [12] analyzed the information rate of ASK-based MC systems and evaluated the impact of feedback on communication efficiency. Mitzman et al. [13] investigates feedback-based reliable MC using Stop-and-Wait Automatic Repeat Request (SW-ARQ) protocols. This approach enhances message delivery reliability and reduces latency in noisy intrabody environments by utilizing two-way channels to transmit both information and acknowledgment molecules between bio-nanomachines. Ozen et al. [14] proposed an integer linear programming approach for network learning that incorporates biological dynamics and feedback paths effectively. Additionally, works such as Nakano et al. [15] investigated throughput and efficiency trade-offs, revealing that transmission rates must be carefully controlled to prevent molecule loss and Rx saturation. Aghababaiyan et al. [16] have focused on advanced channel modeling to account for ISI, mobility, and co-channel interference, providing insights into optimal system design under realistic conditions.

Recent research has also broadened the scope of optimization towards application-driven scenarios. Controlled-release mechanisms proposed by Cao et al. [17] and Sun et al. [18] have been applied to drug delivery systems, while network-layer frameworks such as hierarchical MC architectures by Tan et al. [19] have abstracted biological processes into communication paradigms for targeted therapeutics. Energy efficiency has gained growing attention as well, with new Tx designs leveraging molecular reservoirs to minimize resource usage, as shown by Jing et al. [20]. Finally, performance analysis studies complement these optimization efforts by providing rigorous mathematical tools for evaluating reliability, capacity, and error performance, as done by Sharma et al. [21]and Chouhan et al. [22].

Researchers have applied machine learning techniques in MC to model channel behavior and improve detection and decoding performance. Hochreiter et al. [23] emphasized the importance of selecting optimal decoding thresholds and introduced a self-adaptive algorithm that reduced bit error rates (BER) by up to 90%. Building on this idea, Birkan et al. [24] employed artificial neural networks (ANNs) to model received signals from a spherical transmitter, and further demonstrated that convolutional neural networks (CNNs) could significantly improve demodulation efficiency, achieving data rates of 5.5 bits/s. Experimental validation followed with Koo et al. [25], who analyzed single-bit transmissions in blood vessel environments using CNN-based detection. Their setup achieved rates of up to 2 bits/s, though BERs remained as high as 19% at low transmission frequencies, highlighting both the promise and challenges of deep learning in realistic biological settings. Extending this work, Bartunik et al. [26-27] proposed neural network demodulators for higher-order modulation schemes, achieving data rates beyond 5.5 bits/s with rapid training times (under two minutes) and strong adaptability to varying transmission parameters.

Although MC differs fundamentally from conventional communication systems, congestion control and rate adaptation principles developed for classical networks provide valuable insights for MC system design. Several studies have investigated congestion control and throughput optimization in traditional communication networks. Li et al.[28] proposed a precise feedback-based congestion control algorithm for named data networking that dynamically adjusts the transmission rate according to congestion information, achieving improved throughput and reduced delay. Farahani et al. [29] developed control-theoretic congestion control schemes for delayed networks and demonstrated that stability can be achieved through adaptive rate regulation. Machine learning-based congestion control has also been explored for constrained networks. Demir and Abut [30] introduced an adaptive congestion control mechanism for CoAP-based IoT systems that improves throughput by learning network conditions. Queue-based congestion control approaches were investigated by Ahmed and Arshad [31], who showed that feedback derived from queue length can effectively mitigate throughput collapse in data center networks. Furthermore, Paul et al. [32] implemented optimization techniques to reduce network congestion in power systems using a metaheuristic algorithm, demonstrating methods for congestion mitigation that can inspire optimization strategies in communication systems. Karabulut et al. [33] investigated discharge flow rate patterns under varying traffic conditions, emphasizing the role of dynamic flow regulation in congestion mitigation. Similarly, Nesamalar et al. [34] proposed an optimization-based congestion management approach incorporating renewable energy sources, demonstrating improved system efficiency under constrained conditions. In addition, Hojjat et al. [35] introduced a stochastic congestion management framework that accounts for system uncertainties using chance-constrained programming. These studies reinforce the importance of adaptive, predictive, and optimization-based congestion control strategies, aligning with the approach proposed in this work.

Although these works address electromagnetic communication networks rather than molecular channels, their core concepts, like adaptive rate control, congestion feedback, and stability-oriented control, apply to MC systems. Motivated by these principles, the present study adapts congestion control mechanisms to the MC domain and evaluates their effectiveness under diffusion-based transport conditions.

Overall, related studies focus on frameworks and computational modeling methods that have gained traction as effective tools for improving MC systems. Adaptive thresholding and predictive modeling approaches have been explored to enhance system responsiveness and stability. Together, these advancements highlight the necessity of integrating adaptive control strategies with computational tools to ensure the efficiency and reliability of molecular transport in therapeutic and environmental applications.

Existing approaches primarily focus on static or predetermined control mechanisms, which fail to adapt dynamically to varying network conditions, leading to suboptimal performance and inefficiencies in congestion management. Current congestion control strategies often rely on fixed thresholds, as seen in studies [6-7]. There is a need for dynamic threshold adjustment mechanisms that can adapt to varying channel conditions and communication requirements. Previous work has examined throughput and efficiency, but there is a notable lack of comprehensive comparative analysis of various congestion control strategies under diverse conditions and time durations. Although works explore network learning, the application of predictive modeling for proactive congestion control in molecular communication remains largely unexplored. This paper addresses these research gaps through the following contributions:

Development of a comprehensive feedback-driven framework that monitors and regulates molecular emission rates based on congestion feedback. Introduction of five distinct congestion control strategies, ranging from simple fixed thresholds to sophisticated predictive modeling approaches, providing a comparative analysis of their effectiveness.

Implementation of adaptive thresholding mechanisms that dynamically adjust based on system conditions, improving upon existing static threshold approaches. Integration of TCP TAHOE-inspired state transitions with molecular communication, offering a novel approach to congestion management.

An extensive performance evaluation using COMSOL Multiphysics simulations to validate the effectiveness of proposed strategies across different operational conditions.

1.2. System model

"Figure 2" depicts a system model diagram of an MC system with feedback-driven congestion control. The Transmitter (TX) releases molecules, represented as blue dots, which diffuse through the medium towards the Receiver (RX). The RX detects the incoming molecules. A feedback path, marked with a red dashed line, carries congestion information from the RX back to the TX. This feedback mechanism helps regulate the flow of molecules, ensuring efficient communication and preventing congestion within the system.

2. Method

This study aims to optimize MC by employing feedback-based congestion control mechanisms, evaluated through both simulation and computational modeling. The methodology is divided into three key phases: simulation of MC, development of congestion control strategies, and analysis of flow rate optimization.

2.1. Simulation setup using COMSOL Multiphysics

COMSOL was utilized to create a simulated testbed for MC. The setup emulates the transmitter-receiver dynamics in a controlled environment, with a specific focus on how varying molecule emission rates impact congestion at the receiver side.

The simulation of MC was conducted in COMSOL Multiphysics to model the dynamics of flow rate and congestion within a microfluidic system. The setup employed a flow rate of 3*10-10 m3/s, with a particle density of 1300 kg/m3, representing the physical properties of the molecules. The particle size varied between 1.5*[10.sup.-6] m and 1.1*[10.sup.-5]m, accounting for natural variability in molecule diameters. The geometry of the microfluidic system featured inlets with a length of 0.6 mm and a width of 0.1 mm, positioned at a 60-degree angle to facilitate efficient mixing and flow distribution. This configuration directed the molecules into a microchannel with a length of 140 [micro]m and a width of 20 [micro]m, ensuring precise control over the molecular pathway. The flow was modeled under laminar conditions, reflective of the smooth and controlled motion typical in microfluidic systems. The simulation was conducted at a physiological temperature of 310K (approximately 37[degrees]C), replicating biological environments.

The COMSOL simulation shown in "Figure 3" demonstrates the particle trajectories around the circular obstruction within the microchannel at time t=3.434 sec. The velocity magnitude (m/s) is represented using a color scale, with higher velocities concentrated near the inlet and lower velocities in regions of recirculation. The flow remains laminar, and particles are directed smoothly around the obstruction, indicating effective flow rate management at this rate.

The simulation parameters were chosen to represent realistic conditions in MC systems, particularly for applications like targeted drug delivery. The laminar flow assumption minimized turbulence, ensuring accurate transport of molecules through the micro-channel. The dimensions of the inlets and microchannel were optimized to support the required flow rate while maintaining minimal congestion. By varying the particle size within the specified range, the simulation captured the impact of molecular heterogeneity on congestion dynamics. The inclusion of physiological temperature provided an accurate representation of molecular behavior under biologically relevant conditions. These parameters formed the foundation for evaluating the dynamic congestion control strategies and their impact on optimizing flow rate while avoiding congestion.

Through these simulations, a mathematical relationship between the number of transmitted molecules and the resulting congestion was derived, expressed as given by equation 1,

[Please download the PDF to view the formula] (1)

Equation 1 was obtained by fitting a third-order polynomial to 50 data points extracted from COMSOL simulations. The equation achieved an [R.sup.2] value of 0.97, indicating a strong correlation with simulation results. The variable x represents the normalized number of transmitted molecules (scaled between 0 and 1), while the output represents the congestion level at the receiver. This equation reflects the interplay between molecule transmission, receiver capacity, and congestion over time. The derived data points served as inputs for subsequent Python-based strategy modeling.

2.2 Development of congestion control strategies

Five congestion control strategies were designed, each with unique approaches to regulating flow rate and mitigating congestion.

2.2.1. Strategy 1: Fixed congestion threshold

In Strategy 1, a static congestion threshold of 90% (or 0.9 on a normalized scale) was set to regulate the flow rate of molecules in the system. This approach is designed to maintain the system's throughput while preventing excessive congestion at the receiver. The strategy involves two main phases:

Flow rate Ramp-Up (increasing flow rate when congestion is below the threshold)

Congestion Recovery (reducing flow rate when congestion exceeds the threshold).

2.2.1.1. Key details

Flow rate Ramp-Up: When the congestion level C(t) is below the threshold (C(t) < 0.9C(t), the transmitter increases the flow rate F(t) gradually to maximize throughput. A slower ramp-up rate is employed to avoid sudden spikes in congestion, allowing the system to stabilize.

Congestion Recovery: If the congestion level reaches or exceeds the threshold (C(t) [greater than or equal to] 0.9C(t), the system enters the recovery phase. The flow rate F(t) is rapidly decreased to reduce congestion at the receiver. The ramp-down rate is faster than the ramp-up rate, ensuring a quick response to high congestion levels and preventing prolonged inefficiencies.

2.2.1.2. Equation for flow rate control

The flow rate F(t) at time t can be expressed as a piecewise function based on the congestion level C(t) given by equation 2,

[Please download the PDF to view the formula] (2)

where the first case represents the ramp-up phase and the second represents the ramp-down phase. Here, F(t): Flow rate at time t.

C(t): Congestion level at time t.

[alpha]: Ramp-up rate (a smaller value to increase the flow rate gradually).

[beta]: Ramp-down rate (a larger value for faster recovery).

2.2.1.3. Behavior of strategy 1

In the ramp-up phase, the system increases the flow rate F(t) proportionally to the available congestion margin (1-C(t)), ensuring that the increase is controlled, and congestion does not quickly reach the threshold. In the recovery phase, the flow rate is decreased by a magnitude proportional to the excess congestion (C(t)-0.9), ensuring a rapid drop in congestion while maintaining system stability. This method creates a cyclic pattern where the flow rate increases until the threshold is approached, after which it is reduced. The key advantage of Strategy 1 is its simplicity, making it easier to implement, though it may lead to suboptimal performance due to its fixed threshold and lack of adaptivity.

2.2.2. Strategy 2: Adaptive congestion threshold

In Strategy 2, the congestion threshold is no longer fixed. Instead, it is dynamically adjusted based on the current flow rate to better balance the flow rate and congestion. The key idea is to permit a higher congestion threshold at lower flow rates to maximize throughput and then gradually reduce the threshold as the flow rate increases, ensuring system stability. This adaptive behavior allows the system to respond more effectively to changes in flow rate and congestion levels, avoiding oscillations and achieving better performance compared to a static threshold.

2.2.2.1. Key details

Dynamic Threshold Adjustment: When the flow rate F(t) is low, the congestion threshold T(t) is set to a higher value, allowing the system to operate closer to maximum capacity and improve throughput. As F(t) increases, T(t) is reduced gradually to prevent excessive congestion and ensure the system remains stable.

Flow rate Control: Based on the adaptive threshold T(t), the flow rate F(t) is adjusted dynamically. A slower ramp-up rate is used as the system approaches the threshold, while a faster ramp-down rate is applied when congestion exceeds the threshold, like Strategy 1.

2.2.2.2. Equation for adaptive congestion threshold

The congestion threshold T(t) at time t is defined as a function of the current flow rate F(t) given by equation 3,

[Please download the PDF to view the formula] (3)

Where,

T_max: Maximum allowable threshold (e.g., 0.9 or 90%)

when F(t)=0.

[gamma]: Scaling factor that determines how quickly the threshold decreases as F(t) increases. F(t): Flow rate at time t.

The flow rate F(t) is then adjusted based on the congestion level C(t) and the adaptive threshold T(t) using the piecewise function given by equation 4,

[Please download the PDF to view the formula] (4)

where the first case represents the ramp-up phase and the second represents the ramp-down phase. Here, T(t): Adaptive threshold at time t.

[alpha]: Ramp-up rate (a smaller value for gradual flow rate increases).

[beta]: Ramp-down rate (a larger value for quick congestion recovery).

2.2.2.3. Behavior of strategy 2

When the flow rate is low (F(t)<<Tmax), the system permits a higher threshold, allowing more aggressive flow rate increases to maximize throughput. As the flow rate increases, the threshold T(t) is reduced dynamically. This ensures that the system avoids congestion and smoothly converges to an optimal operating point. In the ramp-up phase, the flow rate increases proportionally to the available margin (T(t)-C(t)), which decreases over time as T(t) adjusts. In the ramp-down phase, the flow rate decreases sharply when the congestion level C(t) exceeds the adaptive threshold T(t), all owing for rapid congestion recovery.

This strategy reduces the oscillatory behavior seen in Strategy 1 by adapting to system conditions. The dynamic adjustment of the congestion threshold ensures that the system operates efficiently across a range of flow rates while avoiding congestion spikes. This makes Strategy 2 more responsive and stable compared to a fixed-threshold approach.

2.2.3. Strategy 3: Feedback-controlled threshold

In Strategy 3, the congestion threshold is adaptively adjusted using feedback control based on the congestion error, enabling a more dynamic and responsive system. This approach improves upon Strategy 2 by incorporating a feedback loop to refine threshold adjustments, making the system more robust against sudden changes in congestion or flow rate. The feedback control mechanism allows the system to continuously monitor the deviation between the current congestion level and the desired threshold, dynamically modifying the threshold to achieve optimal performance. Transitions between flow rate increase and decrease phases are also optimized, minimizing oscillations and ensuring stable operation.

2.2.3.1. Key details

Feedback Mechanism: A congestion error E(t) is defined as the difference between the current congestion level C(t) and the threshold T(t) given by equation 5,

E(t) = T(t) - C(t) (5)

The feedback system uses E(t) to adjust the threshold T(t+1) adaptively, ensuring that the congestion stays near the desired value over time.

Adaptive Threshold Adjustment: The congestion threshold T(t) is updated using a proportional feedback mechanism given by equation 6,

T(t+1) = T(t) + Kp*E(t) (6)

Where Kp is the proportional gain, determining how aggressively the threshold adapts to changes in E(t). This ensures the threshold dynamically responds to deviations in congestion, promoting stability and reducing oscillatory behavior.

Flow rate Control: Like Strategies 1 and 2, the flow rate F(t) is adjusted based on the congestion level C(t) and the feedback-adjusted threshold T(t). The flow rate transitions between increasing and decreasing states are further optimized. Specifically, the flow rate increases when congestion falls below a specific fraction of the threshold (e.g., 0.5*T(t)). The flow rate decreases sharply when congestion exceeds the threshold T(t).

2.2.3.2. Equation for feedback-controlled flow rate

The flow rate F(t) is adjusted using a piecewise function, like Strategies 1 and 2, but now incorporates the feedback-adjusted threshold T(t) given by equation 7,

[Please download the PDF to view the formula] (7)

where the first case represents the ramp-up phase and the second represents the ramp-down phase. Here, T(t+1): Feedback-adjusted threshold for time t+1.

E(t): Congestion error used to update T(t+1).

[alpha]: Ramp-up rate (smaller for smoother increases in flow rate).

[beta]: Ramp-down rate (larger for quicker congestion recovery).

2.2.3.3. Behavior of strategy 3

Feedback Responsiveness: The threshold T(t) is adjusted in real-time based on feedback from the current congestion error E(t), allowing the system to respond dynamically to changes in flow rate and congestion. As C(t) approaches T(t), the feedback mechanism fine-tunes T(t+1) to prevent congestion from exceeding the desired threshold.

Optimized State Transitions: The flow rate transitions from a decreasing to an increasing state when the congestion level drops below 50% of the current threshold T(t+1). This avoids prolonged periods of low flow rate and ensures a quicker return to optimal throughput.

Improved Stability: The feedback loop ensures that the system remains more stable compared to Strategies 1 and 2 by continuously correcting deviations between the desired and actual congestion levels. This reduces oscillations and prevents overshooting or prolonged congestion cycles.

By leveraging feedback control, Strategy 3 achieves a more dynamic and robust congestion optimization, adapting to changes in real-time while maintaining stability and maximizing throughput.

2.2.4. Strategy 4: TAHOE-inspired state transitions

Strategy 4 adopts a congestion control mechanism inspired by TCP's TAHOE algorithm, which divides the flow rate adjustment process into three distinct states: Slow Start, Congestion Avoidance, and Recovery. Each state governs how the flow rate evolves based on the current congestion level and provides a structured approach to balancing throughput and congestion control. By using a combination of exponential, linear, and multiplicative adjustments to flow rate, this strategy effectively manages transitions between high and low congestion conditions, ensuring optimal performance.

2.2.4.1. Key Components

1. State transitions: The system operates in one of three states at any given time. Transitions are determined by the current congestion level C(t) relative to the congestion threshold T(t):

Slow Start: Activated when congestion is low, typically C(t) < 0.5*T(t). The flow rate is increased exponentially to rapidly improve throughput.

Congestion Avoidance: Triggered when congestion reaches moderate levels, 0.5*T(t) [less than or equal to] C(t). The flow rate is increased linearly to maintain stability and avoid triggering excessive congestion.

Recovery: Initiated when congestion exceeds the threshold, C(t)[greater than or equal to]T(t). The flow rate is decreased by a multiplicative factor to quickly alleviate congestion.

3. State-specific flow rate adjustments: Each state uses a specific mathematical model to govern flow rate adjustments given by equation (8),

4. Slow start:

F(t + 1) = F(t) * 2 (8)

Where,

F(t+1): Flow rate at the next time step,

F(t): Current flow rate.

The exponential growth continues until the congestion reaches 50% of the threshold.

Congestion avoidance: Equation 9 gives the congestion avoidance phase represented by

F(t + 1) = F(t) + [alpha] (9)

Where,

[alpha]: A small constant for linear flow rate increase. This mode ensures a gradual increase in flow rate to avoid crossing the congestion threshold.

Recovery: The congestion recovery phase is given by equation 10

F(t + 1) = F(t) * [beta] (10)

Where,

[beta]<1: Multiplicative decrease factor (e.g., 0.5). The flow rate is rapidly reduced to bring the congestion level back below the threshold.

Transition Conditions: The strategy relies on congestion feedback to transition between states:

* If C(t) < 0.5 * T(t) Transition to Slow

Start.

* If 0.5 * T(t) [less than or equal to] C(t) < T(t) Transition to Congestion Avoidance.

* If C(t)[greater than or equal to]T(t) Transition to Recovery.

2.2.4.2. Behavior of the system

Rapid throughput increase (Slow start): In the initial stages, when congestion is low, the flow rate grows exponentially to maximize throughput as quickly as possible. However, the system carefully transitions to the next state once the congestion reaches 50% of the threshold, preventing overshooting.

Stability (Congestion avoidance): As the flow rate approaches the congestion threshold, the system adopts a more cautious approach by increasing the flow rate linearly. This ensures throughput continues to improve while maintaining stability and avoiding unnecessary oscillations.

Quick recovery (Recovery): If congestion exceeds the threshold, the flow rate is rapidly reduced by a multiplicative factor. This swift reduction prevents prolonged periods of high congestion and enables the system to recover efficiently.

2.2.4.3. TAHOE-Inspired equation

The state transitions and flow rate adjustments can be summarized as given by equation 11,

[Please download the PDF to view the formula] (11)

Where,

F(t+1): Adjusted flow rate.

C(t): Current congestion.

T(t): Congestion threshold.

[alpha]: Linear increment rate during congestion avoidance.

[beta]: Multiplicative decrease factor during recovery.

By mimicking TCP's TAHOE algorithm, this strategy provides a robust framework for optimizing flow rate while avoiding excessive congestion. Its multi-state design ensures adaptability and efficiency, making it suitable for dynamic flow rate management scenarios.

2.2.5. Strategy 5: Hybrid Modeling

In Strategy 5, Hybrid predictive modeling is employed to optimize the flow rate by proactively managing congestion. This strategy leverages both historical data and real-time observations to forecast congestion levels, enabling the system to adjust the flow rate preemptively rather than reactively. By anticipating congestion before it occurs, the system avoids abrupt oscillations and maintains a steady throughput. Predictive modeling integrates traffic patterns, historical trends, and real-time metrics to make informed decisions about flow rate adjustments.

2.2.5.1. Key details

Predictive congestion estimation: A congestion prediction model C(t+1) is developed based on historical and real-time flow rate data. The predicted congestion at the next time step is computed as given by equation 12,

[Please download the PDF to view the formula] (12)

Where,

F(t): Current flow rate at time t.

H(t): Historical congestion data (e.g., rolling averages or patterns).

P(t): External factors (e.g., traffic patterns, time of day, environmental conditions).

f: A predictive function (e.g., regression model, neural network, or other machine learning algorithms).

Flow rate adjustment based on prediction: Using the predicted congestion [^.C](t+1), the flow rate F(t+1)is adjusted proactively to prevent congestion from exceeding the threshold T(t). The adjustment is given by equation 13,

[Please download the PDF to view the formula] (13)

Where,

[alpha]: Small ramp-up rate for increasing flow rate in the safe zone.

[beta]: Medium ramp-down rate to mitigate congestion risk.

[gamma]: Aggressive ramp-down rate to quickly reduce flow rate in high congestion scenarios.

Dynamic congestion threshold: The congestion threshold T(t) is dynamically adjusted using insights from historical data and real-time predictions. The threshold is made more lenient (e.g., higher) during low predicted congestion and more restrictive (e.g., lower) during high predicted congestion. This ensures smoother transitions and stability in flow rate adjustments.

2.2.5.2. Predictive modeling equation

To calculate the predicted congestion [^.C](t+1), a linear regression model can be used as an example given by equation 14,

[Please download the PDF to view the formula] (14)

Where,

a1,a2,a3,a4: Regression coefficients based on historical analysis.

b: Intercept term.

H(t): A rolling average of past congestion values.

P(t): External predictive factors.

2.2.5.3. Behavior of strategy 5

Proactive adjustments: By forecasting congestion one time step ahead, the system adjusts the flow rate before the congestion threshold is breached. This reduces the reactive delay and minimizes the risk of congestion spikes.

Stable flow rate control: The predictive model ensures smoother flow rate transitions by mitigating sharp increases or decreases. Abrupt oscillations seen in reactive strategies are significantly reduced.

Data-driven optimization: Incorporating historical data (e.g., trends, patterns) and real-time data ensures that the adjustments are based on comprehensive insights, making the system more robust in dynamic conditions.

By using predictive modeling, Strategy 4 enables a proactive and data-driven approach to flow rate optimization, effectively avoiding congestion before it occurs while maintaining a steady and high throughput. This predictive mechanism enhances the overall system stability and minimizes disruptions in performance.

2.3. Evaluation and analysis

The Python programming language was used to simulate and compare the five strategies over different durations (50, 100, 150, and 200 units of time). Metrics such as throughput, efficiency (ratio of molecules received to transmitted), and area under the flow rate curve (AUC) were computed. The AUC metric quantified the cumulative flow rate, allowing for a clear comparison of strategies in terms of overall performance over time.

3. Results

The simulation results illustrate the relative performance of each strategy in optimizing molecular communication flow rate while controlling congestion. The bar charts comparing the area under the flow rate curve (AUC) across different time durations demonstrate the advantages of adaptive and dynamic strategies. For shorter durations (e.g., 50-time units), the fixed-threshold strategy exhibits competitive performance due to its rapid recovery behavior. However, as the duration increases, adaptive strategies outperform static approaches by dynamically adjusting to congestion variations.

The TAHOE-inspired strategy achieves a balanced performance, maintaining stable throughput while preventing severe congestion spikes through its state-transition mechanism. In contrast, the fixed-threshold strategy exhibits cyclic behavior, leading to periodic oscillations in flow rate and reduced long-term efficiency. The predictive modeling strategy further improves performance by anticipating congestion trends and adjusting the flow rate proactively, resulting in improved AUC values for extended durations.

"Figure 4" compares the five congestion control strategies using the Area Under the Flow Rate Curve (AUC) metric for different time durations. The AUC represents the cumulative flow rate over time and provides an overall measure of throughput performance.

"Figure 4(a)" presents result for 50-time units, where the fixed-threshold strategy achieves the highest AUC, while the remaining strategies show slightly lower but comparable performance. This indicates that static control is sufficient for short-term operation. "Figure 4(b)" shows the results for 100-time units, where the adaptive threshold strategy achieves the highest AUC, outperforming all other strategies.

"Figure 4(c)" presents the results for 150-time units, where the TAHOE-inspired strategy demonstrates balanced performance with consistently high AUC values, reflecting its ability to regulate flow rate effectively while avoiding congestion spikes. "Figure 4(d)" presents the results, which show the predictive modeling strategy attains the highest AUC. This highlights the benefit of proactive congestion prediction for long-term operation. Overall, the results indicate that simple strategies are adequate for short-term scenarios, whereas adaptive and predictive approaches provide superior performance for longer durations and more variable operating conditions.

"Figure 5" illustrates the congestion evolution over time for the five strategies. Strategy 2 (Adaptive Threshold) achieves the highest AUC value of 75.48, indicating the most effective balance between congestion regulation and throughput. After approximately 300-time units, this strategy converges toward a stable congestion level close to unity.

By contrast, Strategy 1 exhibits pronounced oscillatory behavior, with congestion levels periodically varying between 0.1 and 0.9, resulting in the lowest AUC value of 60.32. Strategies 3, 4, and 5 demonstrate moderate and stable behavior, with AUC values ranging between 61.20 and 62.27. These strategies show gradual performance improvement over time but do not reach the optimal congestion level achieved by Strategy 2. The greatest divergence in performance occurs during the 300-500 time - unit interval, where Strategy 2 maintains stable, high congestion levels while the remaining strategies continue to fluctuate or increase gradually.

"Figure 6" presents four COMSOL simulations that Figure 6 presents COMSOL simulations of particle trajectories and velocity magnitudes at different flow rates and time instances. "Figure 6(a)" shows results for a flow rate of 20 [micro]L/h at 3.434 s, where dense particle clustering indicates congestion near the receiver. In "Figure 6(b)", increasing the simulation time to 10.101 s at the same flow rate produces continued chaotic and congested particle motion. "Figure 6(c)" shows that increasing the flow rate to 25 [micro]L/h at 20 s leads to a more organized particle distribution, indicating improved transport conditions under specific operating regimes. "Figure 6(d)" demonstrates that at 20 [micro]L/h and 20 s, particle trajectories become more uniform and less densely populated, suggesting reduced congestion.

The color maps represent particle velocity magnitude, with warmer colors corresponding to higher velocities. These results indicate that inappropriate flow rates can cause molecule overcrowding and congestion, whereas properly selected flow rates enable efficient molecular transport. This highlights the importance of adaptive flow rate control to balance throughput and congestion in molecular communication systems.

4. Discussion

The comparative analysis of flow rate area and congestion optimization reveals clear performance trends across different operating conditions. Among the evaluated approaches, Strategy 2 (Adaptive Threshold) consistently demonstrates the strongest overall performance across both metrics. In the flow rate analysis, it achieves the highest cumulative flow rate for longer durations (100-200 time units), reaching approximately 50,000 area units. This advantage is further reflected in the congestion optimization results, where Strategy 2 maintains the highest stability, with an AUC of 75.48 and convergence toward optimal congestion levels after 300-time units.

Although Strategy 1 (Fixed Threshold) performs reasonably well for short durations, its congestion profile exhibits pronounced oscillatory behavior, which limits its suitability for sustained operation. The observed periodic fluctuations in congestion indicate reduced stability and potential inefficiencies under long-term conditions. In contrast, Strategies 3, 4, and 5 exhibit more stable behavior, characterized by gradual performance improvements and limited fluctuations. Their AUC values, ranging from 61.20 to 62.27, indicate reliable operation; however, their throughput performance remains lower than that achieved by Strategy 2.

From a practical perspective, Strategy 2 is the most suitable choice for applications requiring sustained high throughput and stable congestion control. Strategy 1 may be considered for short-term or low-complexity scenarios where implementation simplicity is prioritized. Strategies 3-5 provide viable alternatives when predictable behavior and moderate performance are preferred over maximum throughput.

5. Conclusion

In this study, five congestion control strategies for molecular communication systems were systematically evaluated with respect to flow rate optimization and congestion mitigation. The results demonstrate that effective system performance requires a careful balance between throughput maximization and congestion control.

Among the examined approaches, the adaptive threshold strategy (Strategy 2) achieves the best overall performance, providing the highest cumulative flow rate and the most stable congestion behavior over extended durations. The fixed threshold strategy (Strategy 1) shows acceptable performance in short-term scenarios but suffers from instability when applied over longer time periods. The hybrid and feedback-based strategies (Strategies 3-5) exhibit consistent and stable behavior; however, their performance remains below that of the adaptive threshold approach.

Overall, the findings indicate that while simpler control mechanisms may be adequate for short-duration or low-variability environments, adaptive strategies are essential for achieving optimal performance in dynamic and long-term operating conditions. The selection of a suitable congestion control strategy should therefore be guided by system requirements, with adaptive mechanisms offering the greatest advantages in terms of efficiency, stability, and throughput optimization.

Conflicts of interest

The authors declare no conflicts of interest.

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Ashwini Katkar (*1) (iD), Sunil Katkar (2) (iD), Vinitkumar Dongre (3) (iD)

(1*) Vidyavardhini's College of Engineering and Technology, Mumbai University, Electronics and Telecommunication Engineering Department, India, ashwini.katkar@vcet.edu.in

(2) Vidyavardhini's College of Engineering and Technology, Mumbai University, Computer Engineering Department, India, sunil.katkar@vcet.edu.in

(3) Thakur College of Engineering and Technology, Mumbai University, Electronics and Telecommunication Engineering Department, India,vinit.dongre@thakureducation.org

Cite this study:

Katkar, A., Katkar, S., & Dongre, V. (2026). Optimizing Throughput and Efficiency in Molecular Communication via Feedback-Based Congestion Control. Turkish Journal of Engineering, Volume (Issue), 1050-1063

Received:20.02.2026

Revised:27.05.2026

Accepted:30.06.2026

Published:30.07.2026

https://doi.org/10.31127/10.31127/tuje.1894045

ORCID: https://orcid.org/0009-0004-3783-8584

ORCID: https://orcid.org/0009-0000-2861-4600

ORCID: https://orcid.org/0009-0008-0681-698X

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Title Annotation:	Research Article
Author:	Katkar, Ashwini; Katkar, Sunil; Dongre, Vinitkumar
Publication:	Turkish Journal of Engineering (TUJE)
Article Type:	Report
Date:	Jul 1, 2026
Words:	7449
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