A Queueing Theory-Based Dynamic Load Balancing Algorithm for Optimizing Software-Defined Networking Performance in Homogeneous and Heterogeneous Environments

This section reviews previous studies on dynamic load balancing in SDN networks, their key techniques, results, and weaknesses.

In the study [10], the Adaptive Lowest Load Ratio (ALLR) algorithm was suggested, and it approximates server load according to the monitoring and adaptive computations. It was also compared with the Dynamic Least Connection (DLC) and Dynamic Least Bandwidth (DLB) algorithms and had better response time (13.37%) and throughput (8%) and low CPU consumption. This method helps with decentralized decision-making, but it is based upon periodic updates, and this can lead to problems when the load is high. In the study [11], a dynamic weighting method of the Weighted Round Robin (WRR) algorithm was suggested that requires fewer communications. This method balances the weights based on the actual data rate that enhances the performance of load balancing and resource consumption. Findings showed an increase in the response time and packet loss, although it is not easy to compute the optimal weights because of unexpected data traffic variations, which can lead to inefficiencies in the algorithm's performance and affect overall network reliability. In the study [12], the Load Balancing based on Resource Utilization (LBORU) algorithm was developed on a hybrid SDN network, using different measurements, including CPU, I/O, and network speed. The algorithm achieved high load balancing while maintaining a CPU variance of 10%. Even though it is a better use of resources and less latency, it is more complex and has not been demonstrated to be effective in practice, particularly in real-world scenarios where varying workloads and network conditions can impact performance. In the study [13], a dynamic load balancing algorithm was implemented in SDN data centers and executed in Mininet and Floodlight controllers. This method diverts the streams of data to less overloaded routes, enhancing throughput (as much as 50 percent) and reply time. Nevertheless, the routing decision-making and controller load can be higher when data updates are high in the network, which may lead to increased latency and reduced overall performance of the data center operations. In the study [14], Enhanced_Conn, which is a combination of dynamic and static factors, was used as the extended LC algorithm. It showed better load balancing and reduced response times in comparison to the RR and LC algorithms. The need to run the data process continuously complicates its computation, even though it is efficient, particularly when compared to the static nature of the RR and LC algorithms, which do not require continuous data processing.

In this study [15], four dynamic load balancing algorithms (namely LRAM, LCPU, Least Connection-Least CPU-RAM (LCLCPURAM), and Least CPU-RAM (LCPURAM) were proposed and tested to compare them with the famous LC algorithm in a scenario that includes the servers with different capacities. The experiments were performed with Mininet, an OpenFlow switch, and a POX controller. The findings revealed that the LCLCPURAM algorithm would have a great latency and waiting time improvement, although the LC algorithm had better outcomes in service time. In general, the study proved the efficacy of dynamic approaches to the enhancement of performance in a heterogeneous environment.

In this study [16], a deep learning-based multi-label classification method with an adaptive load balancing mechanism was proposed for distributed computing systems. The method is based on a Recurrent Neural Network (RNN) with Long Short-Term Memory (LSTM) architecture for feature extraction and traffic classification, and then a Deep Reinforcement Learning (DRL) agent is used to optimize the load distribution dynamically. The proposed model showed remarkable improvements; the average throughput rose from 85-115 requests/s to 120-150 requests/s, and the average latency reduced from 95-120 ms to 65-95 ms. It has been observed, however, that the model has some misclassifications for some traffic types (such as video streaming), and the combination of several deep learning components makes the model more complex, potentially restricting its use in real time in resource-limited SDN environments.

In this study [17], DeepBalance, a DRL framework for dynamic load balancing in SDNs, was proposed. A Deep Q-Network (DQN) agent is continuously observing real-time network states, such as link utilization, queue sizes, and flow statistics, and learns optimal routing policies using a multi-objective reward function, which consists of three components: load distribution (60%), congestion avoidance (30%), and throughput-to-latency efficiency (10%). Experimental results demonstrated that the variance of link utilization was reduced by 37%, the throughput was increased by 28%, and the latency was decreased by 42% compared to shortest-path routing. Even with its excellent performance, DeepBalance needs lots of training time and computation power, and the initial exploration period may result in sub-optimal early routing decisions. Additionally, the high state-action space complexity makes it challenging to scale up to hundreds of nodes.

In this study [18], a decentralized Quality of Service (QoS)-aware load balancer for edge and cloud environments was proposed, namely, QEdgeProxy. The load balancing problem is stated as a Multi-Player Multi-Armed Bandit (MP-MAB) problem with heterogeneous per-client QoS rewards. The load balancers work independently and use Kernel Density Estimation (KDE) to estimate the QoS success probability of each service instance while also using an adaptive exploration mechanism to cope with performance changes and non-stationary traffic patterns. The system outperformed the other two baselines (proximity and reinforcement learning) in terms of per-client QoS satisfaction. This approach is for compute-continuum and IoT environments and is decentralized, unlike classical SDN server-side load balancing, and the bandit-based model is not analytically guaranteed like a queueing-theoretic formulation.

In summary, the dynamic load balancing algorithms presented in the literature (e.g., ALLR, WRR with dynamic weights, LBORU, Enhanced_Conn, and the LCPU/LRAM family) have many merits compared to static algorithms but still have some disadvantages in real SDN scenarios. These have the following limitations: (i) they are less accurate when sudden traffic bursts occur or when server capacities vary (single or loosely coupled metrics, such as CPU or connections only); (ii) they have high control overhead and decision complexity because they need frequent state updates; and (iii) they have not been fully validated with realistic traffic traces in both homogeneous and heterogeneous environments.

In particular, the LCPU/LRAM family of algorithms introduced by reference [15] in 2026 represents a recent state-of-the-art baseline for dynamic server-side load balancing in SDN, demonstrating clear advantages over the classic LC strategy in heterogeneous environments. In this work, these drawbacks are explicitly addressed and empirically demonstrated by comparing the proposed DLBQT algorithm, which is based on queueing theory, with three widely used dynamic algorithms (LCPU, LC, and LRAM) under identical network topologies, traffic loads, and performance metrics (packet loss, response time, and throughput), as detailed in Sections 5 and 6. It should be noted that this comparison is conducted in terms of the algorithms’ mechanisms of operation, implementation, and efficiency in load distribution within the specific simulation environment of this research, without relying on the quantitative results, network design, or operating conditions reported in previous studies. Instead, the study is based on the network design proposed in this work, evaluated under two distinct environments (homogeneous and heterogeneous) and using a real-world dataset adopted for generating packets and requests. This ensures that the comparison provides a current and realistic assessment of the DLBQT algorithm’s ability to enhance SDN performance under practical network conditions.

The proposed DLBQT algorithm explicitly models each server as a queueing system, where the arrival rate (λ), service rate (μ), utilization (ρ), and average waiting time are continuously estimated in real time. Based on these parameters, the controller computes a weight for each server and always selects the server with the lowest weight for incoming requests, while assigning a high penalty weight when the utilization approaches saturation. This analytically grounded decision mechanism allows DLBQT to proactively avoid congestion and to distribute load more accurately than heuristics that rely only on CPU usage, RAM, or connection counts.

The recent state-of-the-art studies in SDN load balancing have continued to seek dynamic and hybrid schemes. Some of the publications provided better dynamic weighted round robin and hybrid dynamic-static algorithms that combine heuristic measurements and metaheuristics or intelligent controllers to enhance response time and throughput in SDN systems. Multi-parameter decision algorithms and load balancing at the controller level have been proposed in other work. In large-scale SDN deployments, researchers have used metrics such as CPU, memory, connection utilization, and QoS limitations to reallocate load across controllers or servers. Recent surveys and reviews (2018–2026) have also noted a trend towards multi-metric, QoS-conscious, and AI-assisted load balancing solutions, as well as the importance of accurate traffic modeling and realistic testing environments. Nevertheless, most of these methods still depend on empirically tuned metrics or heuristic combinations rather than an analytically founded queueing model to make decisions. They are often evaluated under limited traffic conditions or without a direct comparison between homogeneous and heterogeneous settings. In contrast to the above AI-driven and QoS-aware approaches, which rely on empirically trained models, heuristic reward functions, or bandit-based probabilistic policies, the proposed DLBQT algorithm provides an analytically grounded decision mechanism based on M/M/1 queueing theory. This allows for interpretable, closed-form weight computation in real time without requiring training data or exploration phases, while achieving competitive performance improvements in both homogeneous and heterogeneous SDN environments.

This section explains the proposed dynamic model for load balancing in SDN environments. It begins by clarifying the general design framework associated with SDN, then proposes the DLBQT model and its flowchart, which illustrates the steps and mechanism of operation, in addition to the proposed methodology and pseudocode for the model.

4.1 Proposed model

The proposed model for dynamic load balancing in SDN, shown in Figure 1 consists of three layers: the application layer, the control layer, and the data layer. The application layer refers to the multiple users or requests that will be sent, as previously mentioned, in three types. The control layer, on the other hand, represents the SDN controller integrated with the proposed load balancing algorithm at the core of the architecture, which serves as the central hub for policy formulation and the determination of the proposed algorithms for application and load distribution. Using the concept of queueing theory, the final layer is the data unit, which operates dynamically by selecting the server requested by each server in the network based on a set of mathematical calculations.

Figure 1. The diagram illustrates the architectural design of the proposed model

The schematic illustrates the proposed Dynamic Load Balancing based on Queueing Theory (DLBQT) in an SDN network, which aims to make real-time decisions, as shown in Figure 2. The term “multiple requests” refers to the transmission of several requests from the application layer to the SDN controller, which incorporates the proposed DLBQT model. Through this model, decisions are made to efficiently distribute data traffic among available servers at the data plane, leveraging the real-time monitoring capability built into the controller. This controller uses the arrival rate (λ) and service rate (μ), which are used to determine the server used (p) and the average waiting time (W). Using these parameters, the controller can make the appropriate decision and dynamically reroute data traffic away from congested paths to optimize server load. With this configuration, dynamic load balancing can be performed proactively by analyzing data based on the above parameters. This ensures network responsiveness, reducing latency and improving resource utilization across widely distributed server networks.

Figure 2. Diagram proposed algorithm dynamic load balancing with utilizes queueing theory (DLBQT)

4.2 Methodology

The proposed DLBQT algorithm can be summarized at four levels as follows: The SDN controller maintains a continuous record of incoming requests and the service rate for each server in the first step. Secondly, it calculates the utilization and the corresponding queueing theory weight for each server. Third, it chooses the server with the lowest weight for every new request but gives a very high weight to saturated servers. Lastly, the controller updates the statistics after every time window and continues the cycle for the next requests. This conceptual perspective is summarized in a flowchart (Figure 3) and in Table 2.

Figure 3. Simplified conceptual flow of the proposed dynamic load balancing that utilizes the queueing theory (DLBQT) algorithm

Table 2. Main modules and parameters of the dynamic load balancing with utilizes the queueing theory (DLBQT) controller

Figure 3 illustrates a simplified conceptual flow of the DLBQT algorithm. Incoming requests are first observed at the controller, which updates the arrival and service rates for each server over a sliding time window. From these measurements, the utilization and weight of each server are computed using the M/M/1 queueing model. The controller then selects the server with the minimum weight for the next request, while assigning a large penalty weight to servers whose utilization is close to saturation. After the request is processed, the QoS metrics are updated and the process repeats. Table 3 summarizes the main functional modules of the DLBQT controller and clarifies how the parameters λ, μ, ρ, and W are computed and used in the decision process.

Table 3 summarizes the main parameters used in the proposed DLBQT algorithm and clarifies their meanings and units. These parameters are used by the SDN controller to estimate server load conditions and support the routing decision process in real time.

Table 3. Main symbols and units used in the dynamic load balancing with utilizes queueing theory (DLBQT) algorithm

The DLBQT model was developed to distribute network traffic efficiently among servers by calculating key parameters based on queueing theory, where the final result depends on the weight of each server (W) and the selection of the server with the lowest weight, which determines the routing decision. This technique aims to optimize resource utilization to achieve optimal and balanced performance. The DLBQT model continuously monitors task metrics in real time.

It relies on two basic parameters, both of which are considered inputs calculated in real time for each request. The first is the arrival rate (λ), which is the rate at which requests or tasks arrive at the system per unit of time, and second, the service rate (μ), which is the number of requests or tasks the system can process or serve per unit of time. These are mathematically formulated in Eqs. (5) and (6):

$\lambda=\frac{{Number\ of\ incoming\ requests }}{ {Elapsed\ time }}$                       (5)

$\mu=\frac{{Number\ of\ completed\ requests }}{ {Elapsed\ time }}$                        (6)

where, λ is the arrival rate and μ is the service rate are measured in requests per second (requests/s).

Each server in the proposed paradigm is modeled as an M/M/1 queueing system. Our Mininet configuration does not strictly enforce a Poisson arrival process; rather, the traffic generator generates a huge number of separate flows with randomized inter-arrival periods and file sizes. However, the aggregate behavior of many such separate random flows has been commonly modeled by M/M/1-type assumptions in networking and SDN studies. Under this approximation, the server utilization is ρ, the mathematical expression is shown in Eq. (7):

$\rho=\lambda / \mu$                   (7)

where, ρ is the server utilization ratio and is dimensionless.

Finally, the weight (W) is calculated as the average time a request spends in the system, based on the utilization rates of each server and its service. The server selected to process incoming requests or tasks is determined by the lowest weight (W) value, according to the mathematical formula shown in Eq. (8):

$W=P /(\mu *(1-P))$                         (8)

where, W denotes the estimated average system time in seconds (s).

This amount is used as the queueing-theoretic routing criterion in DLBQT: at each decision period, the controller chooses the server with the smallest estimated W, thus minimizing the predicted time a request spends in the system. Although actual SDN traffic may not conform to the idealized Poisson and exponential assumptions, the M/M/1 based models can nonetheless give valuable approximations and design guides for SDN and other networking systems. The randomized traffic patterns in our simulation environment lead to aggregate server loads that are well approximated by this M/M/1 approximation, and therefore the expression for W is not simply an intuitive heuristic, but a theoretically grounded approximation of the expected system time in the simulated SDN setting.

4.3 Online estimation of queueing parameters

In the implementation, each server keeps two counters: one for newly arrived requests and one for completed requests. At any time when the controller needs to take a routing decision, it looks at the time elapsed since the last update and uses this period as an observation window. This window is never shorter than one second, even if decisions are taken more frequently.

For each server, the algorithm stores a short history of the last ten observation windows. At every decision step, it computes:

• the average number of arrivals over the last ten windows,
• the average number of completions over the last ten windows,
• the arrival rate λ as “average arrivals ÷ window length”,
• the service rate μ as “average completions ÷ window length”, with a small lower bound on μ to avoid division by zero,
• the utilization P as the ratio between λ and μ.

Using these quantities, the weight W is calculated from the M/M/1 queueing model, so that W represents the estimated average time a request spends in the system (waiting plus service). After each update, the per-window counters are reset and the start time of the next window is set to the current time. This procedure smooths out short-term fluctuations and bases the decision on recent load history rather than on a single instantaneous measurement.

4.4 Routing, tie-breaking, and penalty policy

Each routing decision involves the controller updating the values of λ, μ, P, and W of all live servers as indicated above. The new request is then sent to the server with the minimal weight W, i.e., the server with the minimum estimated average system time.

When the estimated utilization of a server is one (P ≥ 1) or more, the algorithm sets its weight to a very large value (W = 1000). This “penalty” makes the server very unlikely to be selected and effectively avoids sending new requests to a saturated server. In case two or more servers have the same smallest W value, tying is deterministically resolved by selecting the first server in the internal list.

4.5 Flowchart of proposed model dynamic load balancing with utilizes queueing theory

This section outlines the flowchart proposed in Figure 4 within an SDN environment, utilizing queuing theory and real-time performance analysis. The diagram starts by sending a request; it then decides the rate of arrival (λ) and the rate of service (μ) offered by the servers and then computes the utilization factor (ρ) to evaluate the level of busyness of the server. Then, the weight (W) is computed, which is the average time that a request is in the system; in case W is more than the threshold, a high default weight is placed on the request to be redirected to the less busy servers and maintain the QoS. The system identifies the server that has the lowest weight to attain optimal distribution, and the QoS measures of packet loss, response time, and throughput are computed. This process is repeated until the request is fulfilled, and the network is made efficient, stable, and scalable according to the SDN principles.

Figure 4. Flowchart proposed algorithm dynamic load balancing with utilizes queueing theory (DLBQT)

The pseudocode for the algorithm implements dynamic load balancing in an SDN environment using queueing theory, as illustrated in the flowchart above. The controller continuously checks the status of each server and calculates the arrival rate (λ) and service rate (μ) for each server to determine the weight (W). Requests are directed to the least-loaded server, and a request is discarded when the weight (W) exceeds the maximum limit, while measuring (QoS) metrics and upon request completion (Algorithm 1).

This paper analyses the performance of the proposed DLBQT algorithm using a small sample size of n = 3, corresponding to three request load levels (1,000, 100,000, and 1,000,000). In this study, the effect size between DLBQT and each baseline algorithm (LCPU, LC, and LRAM) was computed using Cohen’s d for paired differences. For each metric and environment, cohen’s d based on paired differences between the baseline and DLBQT at each load level was first calculated based on the values reported in Tables 7-12, and these differences were then used to obtain the corresponding effect-size estimates. Also, effect sizes (Cohen’s d) are therefore computed over three representative load levels (n = 3) for each scenario. Consequently, the reported values should be viewed as descriptive indicators of the magnitude of the observed differences rather than as the basis for formal statistical inference. A more robust inference would require repeated runs per operating point and additional load levels to estimate variability and confidence intervals (CI). The mean and Standard Deviation (SD) of these differences were obtained as:

$\begin{gathered}{Mean}_{o f_{ {Differences }}} =\frac{\left({sum}\ of\left(L C P U_i-D L B Q T_i\right)\right)}{n}\end{gathered}$                    (9)

$SD_{differences}=\operatorname{sqrt}\left(\frac{{sum}\left(\left(D_i-\ { Mean }_{of_{ {Differences }}}\right)^2\right)}{(n-1)}\right)$                   (10)

and Cohen’s d was then computed using:

$d=\frac{ { Mean }_{{of}_{{Differences }}}}{S D_{{differences }}}$                      (11)

where, n = 3 is the number of load levels. This paired-difference formulation quantifies the strength of the performance gap between DLBQT and each baseline across the three tested load levels according to which the values are small (around 0.2 to 0.49), medium (around 0.5 to 0.79), and large (around 0.8 and more) between the proposed algorithm and the other algorithms, as shown in Table 13 (Packet Loss), Table 14 (Response Time), and Table 15 (Throughput).

Concerning the packet loss, Table 13 outcomes show that in a homogeneous environment, the effect size (Cohen’s d based on paired differences) of DLBQT is always large (d > 1.3), and similarly in a heterogeneous environment. This indicates that there is a significant decrease in the loss of packets, and the better results are shown in the case of heterogeneous ones, which proves that the proposed algorithm is robust. This can also be exemplified in Figure 9 for packet loss comparison, whereby the DLBQT is always lower in the packet loss rate in all the request levels.

Table 13. Effect size for packet loss (both environments)

Figure 9. Effect size (Cohen’s d) for packet loss

Regarding response time, Table 14 demonstrates that the effect sizes (d > 1.3) in either environment are large in all the comparisons. This shows that DLBQT has a substantial decrease in latency, and its performance will improve in a stable and changing network environment. In Figure 10 for response time comparison, with DLBQT having the smallest values of response time.

Table 14. Effect size for response time (both environments)

Figure 10. Effect size (Cohen’s d) for response time

Concerning the throughput, as illustrated in Table 15, the effect sizes are large in all the situations (d ≥ 1.05). These findings suggest that DLBQT is effective in improving throughput with a minor increase in the heterogeneous, which suggests its effectiveness in diverse network environments. Figure 11 for throughput comparison supports these findings, showing that the highest throughput was achieved by the DLBQT in all cases.

Table 15. Effect size for throughput (both environments)

Figure 11. Effect size (Cohen’s d) for throughput

In general, despite the relatively small sample size (n = 3), the results consistently demonstrate large effect sizes across all evaluated metrics. The results indicate that the suggested DLBQT algorithm provides significant improvements in the areas of packet loss, response time, and throughput. More so, the fact that the effect sizes are always higher in the heterogeneous environment proves the strength and versatility of the proposed approach in more complicated and dynamic conditions of a network.

DLBQT can achieve the same objectives by an explicit analytical model, in contrast to recent state-of-the-art approaches, which often pursue QoS-conscious and multi-metric load balancing using heuristic or AI-based decision mechanisms. DLBQT can be used to refer to various open problems that were identified in recent surveys, including the accurate prediction of performance at high load and under real evaluation conditions.

Based on the improvement percentages reported in Tables 7-12, additional descriptive statistics were computed to further quantify the behavior of DLBQT relative to the baseline algorithms. Values represent the percentage improvement of DLBQT over LCPU, LC, and LRAM across the three evaluated load levels (1,000, 100,000, and 1,000,000 requests). For each load level and environment, the experiments were executed R = 3 times and the improvement values were computed from the averaged results, so that N denotes the number of improvement values per environment. Using OriginPro 2026 (OriginLab, Northampton, MA, USA), the mean, Standard Deviation (SD), and 95% CI of these improvement values were calculated for each performance metric and environment, providing a concise summary of the distribution of the observed improvements across the evaluated load levels and baseline algorithms. In addition, the performance figures for packet loss, response time, and throughput include error bars representing ±1 SD around the mean at each load level, which visually depict the variability across the R = 3 runs and further support the stability of the observed gains of DLBQT.

The improvement percentages of DLBQT over the baseline algorithms show a consistent positive gain in both environments (Figures 12 and 13). The mean improvement is 31.03% with an SD of 5.77%, and the 95% CI is [18.89%, 43.75%], showing that the packet loss reduction is still significant for the evaluated operating points; the moderate SD is due to the natural variation in the degree of improvement across the three baseline algorithms that differ in their congestion-handling mechanisms, while the consistently positive CI bounds confirm that DLBQT reliably outperforms all baselines under uniform server conditions. The mean improvement is 34.73% (SD 5.78%, 95% CI 20.29%–49.17%) in the heterogeneous environment, due to the higher inefficiency of heuristic-based baselines in this case, where DLBQT's queueing-theory model is able to identify and avoid overloaded servers and thus achieve larger packet loss reductions. The positive lower CI bound in both environments supports the consistency of the advantage of DLBQT and not just due to isolated operating conditions. Normality tests were also applied to the improvement percentages, and the P values obtained were 0.338 for the homogeneous environment and 0.279 for the heterogeneous environment, both of which exceeded the conventional significance level of 0.05, suggesting that there was no significant deviation from normality and that the distribution of the observed improvements could be described using parametric summaries (mean and SD) and 95% confidence intervals (Table 16).

Table 16. Statistics of packet loss improvement

Figure 12. Statistics of packet loss improvement (homogeneous)

Figure 13. Statistics of packet loss improvement (heterogeneous)

The improvement percentages in response time for DLBQT over the baseline algorithms show a consistent decrease in response time in both environments (Figures 14 and 15). The mean improvement is 7.78% in the homogeneous environment with an SD of 0.84%, and the 95% confidence interval is from 5.70% to 9.85%, which shows that the queueing-theory-based scheduling of DLBQT is stable and reliable for the different operating points evaluated in the homogeneous environment; the small SD indicates that the scheduling of DLBQT is consistent across uniform server capacities. The mean improvement is 8.69% (SD 2.38%) with a 95% confidence interval of 2.78%–14.60% in the heterogeneous environment due to the larger variability in baseline performance across the different server types, which led to a larger range of improvements observed. Nevertheless, the lower bound of the CI is positive in all cases, indicating that DLBQT is always superior to all three baseline algorithms in all environments. Normality tests for both the homogeneous and heterogeneous environments also yielded P-values above 0.05, with values of 0.631 and 0.224, respectively, indicating that there is no significant deviation from normality and that parametric summaries and 95% confidence intervals can be used to describe the distribution of the improvements observed in both environments (Table 17).

Table 17. Statistics of response time improvement

Note: SD = Standard Deviation; CI = confidence intervals; R = Number of experimental runs per configuration

Figure 14. Statistics of response time improvement (homogeneous)

Figure 15. Statistics of response time improvement (heterogeneous)

In terms of throughput, the enhancement percentages of DLBQT over the baseline algorithms are clearly in favor of DLBQT, especially in the heterogeneous environment (Figures 16 and 17). The mean improvement is 4.09% (SD 2.65%), and the 95% confidence interval is (−2.48%, 10.66%) for the homogeneous environment, suggesting that the throughput gains of DLBQT over the baselines are fairly small and may fluctuate around zero, depending on the baseline algorithm. This behavior is because in traditional dynamic heuristics, the load is already well balanced when all servers have similar capacities, and there is little room to gain more throughput. In the heterogeneous environment, the mean improvement increases to 14.63% (SD 5.35%), and the 95% CI is (2.17%, 27.09%) with a positive lower bound. This result indicates that DLBQT is especially effective in taking advantage of the capacity differences between the servers: instead of simply counting connections or CPUs, it can send more connections to high-capacity servers and prevent overloading of low-capacity servers, resulting in significant and statistically stable throughput gains over all three baseline algorithms. The normality tests for the improvement values gave P-values of 0.598 for the homogeneous environment and 0.154 for the heterogeneous environment, both of which were greater than 0.05, indicating that there was no significant difference between the distribution of the improvement values and the normal distribution and that parametric statistics and 95% confidence intervals could be used to characterize the distribution of throughput improvements (Table 18).

Figure 16. Statistics of throughput improvement (homogeneous)

Figure 17. Statistics of throughput improvement (heterogeneous)

Table 18. Statistics of throughput improvement

Note: SD = Standard Deviation; CI = confidence intervals; R = Number of experimental runs per configuration

6.1 Sensitivity to load levels

To examine the sensitivity of the compared algorithms to different traffic loads, the results in Tables 7-12 and Figures 6-8 were analysed across the three evaluated request levels (1,000, 100,000, and 1,000,000 requests). At low load (1,000 requests), all algorithms show negligible packet loss and very small differences in response time and throughput, indicating that the servers operate far from saturation in both environments. As the load increases to 100,000 and 1,000,000 requests, LCPU, LC, and LRAM exhibit a faster growth in packet loss and latency, especially in the heterogeneous environment, reflecting uneven load distribution and higher utilization of the weaker server. In contrast, DLBQT maintains substantially lower packet loss and shorter response times at medium and high loads, while sustaining higher throughput, because the queueing-theoretic weight steers more traffic towards underutilized, high-capacity servers and penalizes nearly saturated servers. The error bars in Figures 12-17 further show that the variability of DLBQT remains moderate across the three load levels, whereas the baseline algorithms exhibit larger fluctuations at high load, particularly in the heterogeneous scenario, confirming that DLBQT is less sensitive to load increases in terms of both server utilization and end-to-end latency.

The authors gratefully acknowledge the support provided by the Information Technology Research and Development Centre (ITRDC), University of Kufa, Iraq for this work.