MSCHF algorithm for minimizing signaling costs and enhancing vertical handover efficiency in wireless communications networks

Computational efficiency

To achieve computational efficiency, MSCHF employs a streamlined decision-making approach that approximates optimal behavior through heuristic-based dynamic adjustments. This approximation reduces computational overhead by prioritizing rapid evaluation of critical parameters—such as RSS (threshold: −85 dBm), latency (threshold: >3 ms), and buffer levels (low: 25%, high: 75% of 1,024 kB)—over exhaustive state-space exploration. Decisions are made in real-time using pre-defined rules updated over a sliding time window (last 5 s) to detect buffer trends, avoiding iterative computations. This approach reduces computation time by approximately 30% compared to non-optimized VHO methods, as evidenced by reduced handoff decision times in simulations, maintaining accuracy by focusing on high-impact factors weighted via empirical tuning. The on-time buffering strategy further minimizes resource-intensive early buffering, a typical inefficiency in traditional methods, ensuring decisions are both swift and effective. The streamlined approximation in MSCHF introduces trade-offs between computational complexity and solution accuracy. By avoiding exhaustive optimization, MSCHF reduces processing demands, making it feasible for real-time application in dynamic WLAN-5G environments where UEs require rapid handovers. However, there are rare chances of suboptimal decisions in highly volatile scenarios like a sudden network congestion spike. Simulation results across 97 trials indicate this trade-off is minimal, with MSCHF achieving a 40% signaling cost reduction and 50% lower failure rate compared to non-MSCHF, suggesting high practical accuracy. The risk of reduced precision is further mitigated by dynamic parameter adjustments, ensuring adaptability without significant computational overhead.

Hyperparameter tuning and validation in MSCHF algorithm

To ensure the robustness of the MSCHF algorithm, a systematic approach was adopted for hyperparameter tuning and performance validation. The hyperparameters, including buffer thresholds, decision score weights, and data rate adjustment factors, were tuned using an empirical search method based on preliminary simulations. A smaller dataset of 100 user traffic samples was used to test multiple parameter configurations under varied network conditions. Similarly, weight combinations for decision metrics were adjusted iteratively, prioritizing RSS and latency based on their impact on handover success in WLAN-5G transitions, assessed via trial-and-error over 50 iterations to maximize performance metrics. Validation of MSCHF’s performance was conducted using a hold-out validation approach rather than k-fold cross-validation, given the simulation-based nature of the study and the sequential dependency of handover events. The full dataset of 441 user traffic samples was split into a training set (70%, 309 samples) for initial parameter tuning and a test set (30%, 132 samples) for final performance evaluation across 97 trials. This split ensured that the algorithm was assessed on unseen data, simulating real-world applicability. Performance metrics—signaling cost, handover failure rate, and buffer consumption were measured on the test set, confirming consistent results. Also, scalability testing across user/node densities served as a form of external validation, verifying generalizability under varied conditions. These tuning and validation techniques affirm MSCHF’s reliability and adaptability in heterogeneous WLAN-5G networks, with statistical significance further supported by hypothesis testing.

Signaling cost

• 1)

  Non-MSCHF algorithm

To calculate the signaling cost for the Non-MSCHF algorithm:

(1) $$SCcandidate-RAT=S1+S2+S3+S4+S5+S6$$where SCcandidate−RAT, S1, S2, S3, S4, S5, and S6 are referred to as the signaling cost of candidate RAT, VHO triggering, and early, respectively.

(2) $$SCcurrent-RAT=S1+S2+S3+S4+S7+S8+S2+S8$$where SCcurrent−RAT, S1, S2, S3, S4, S7, S8, S2, and S8 are referred to as the signaling cost of current RAT, VHO triggering, early buffering, initiation, decision, current RAT, UE, early buffering, and UE, respectively.

From (2)

(3) $$SCcurrent-RAT=S1+2S2+S3+S4+S7+2S8$$

• 2)

  MSCHF algorithm

To calculate the signaling cost for the MSCHF algorithm:

(4) $$SCcandidate-RAT=S1+S2+S3+S4+S5+S6$$where SCcandidate–RAT, S1, S2, S3, S4, S5, and S6 represent the signaling cost of candidate RAT, VHO triggering, initiation, decision, candidate RAT, on time buffering, and execution, respectively.

(5) $$SCcurrent-RAT=S1+S2+S3+S7$$where SCcurrent–RAT, S1, S2, S3, and S7 are signaling costs of current RAT, VHO triggering, initiation, decision, and current RAT, respectively.

Handover failure

• 1)

  Non-MSCHF algorithm

To calculate the probability of handover failure for the Non-MSCHF algorithm, we use

(6) $$PHFcurrent-RAT=S2+S8$$where PHFcurrent–RAT refers to the probability of handover failure due to early buffering and keeping connected with the current RAT.

• 2)

  MSCHF algorithm

The probability of handover failure due to on-time buffering and keeping connected with the current RAT = 0, and is represented as

(7) $$PHFcurrent=0$$

Buffer consumption

• 1)

  Non-MSCHF algorithm

To calculate buffer consumption for the Non-MSCHF algorithm, we use

(8) $$BCcurrent-RAT=S2+S3+S4+S7+S8+S2+S8$$

(9) $$BCcurrent-RAT=2S2+S3+S4+S7+2xS8$$where BCcurrent−RAT is the buffer consumption due to using early buffering while maintaining connection with the current RAT.

• 2)

  MSCHF algorithm

The buffer consumption resulting from using on-time buffering and keeping connected with the current RAT in the case of MSCHF (BCcurrent−RAT ) is 0 and is represented as

(10) $$BCcurrent-RAT=0$$

Reducing signaling cost

Let’s denote Nnon and Nms as the number of signaling messages for non-MSCHF and MSCHF algorithms, respectively. The cost per message is Cm, and assume the MSCHF algorithm reduces the number of signaling messages by a factor of k, where k > 1.

(11) $$Nms=Nnon/k$$where the signaling cost for non-MSCHF and MSCHF algorithms is defined in Eqs. (12) and (13).

(12) $$Cnon=Nnon\cdot Cm$$

(13) $$Cms=Nms.Cm={\displaystyle \frac{N_{non}}{k}.Cm}$$

Reduction in signaling cost is defined through Eqs. (14), (15), and (16).

(14) $$\mathrm{\Delta }C=Cnon-Cms$$

(15) $$\mathrm{\Delta }C=Nnon.Cm-{\displaystyle \frac{N_{non}}{k}.Cm}$$

(16) $$\mathrm{\Delta }C=Nnon.Cm\left(1-{\displaystyle \frac{1}{k}}\right).$$Since k > 1, $\left(1-{\displaystyle \frac{1}{k}}\right)$ is always positive. Therefore, ΔC is positive, proving that the MSCHF algorithm reduces the signaling cost.

Reducing handover failure

Let P_f,non be the probability of handover failure for the non-MSCHF algorithm, and P_f,ms for the MSCHF algorithm. Assume the MSCHF algorithm reduces the failure probability by a factor of α, where α > 1.

(17) $$Pf,ms={\displaystyle \frac{Pf,non}{\alpha }.}$$

The reduction in handover failure is calculated using Eqs. (18), (19), and (20).

(18) $$\mathrm{\Delta }Pf=Pf,non-Pf,ms$$

(19) $$\mathrm{\Delta }Pf=Pf,non-{\displaystyle \frac{Pf,non}{\propto }}$$

(20) $$\mathrm{\Delta }Pf=Pf,non\left(1-{\displaystyle \frac{1}{\propto }}\right).$$

Since α > 1, $\left(1-{\displaystyle \frac{1}{\propto }}\right)$ is always positive. Therefore, ΔPf is positive, proving that the MSCHF algorithm reduces the handover failure rate.

Reduced resource allocation time

Let Tr, non, and Tr, ms be the resource allocation times for non-MSCHF and MSCHF algorithms, respectively. Assume the MSCHF algorithm reduces the allocation time by a factor of ϵ, where ϵ > 1.

(21) $$Tr,ms={\displaystyle \frac{Tr,non}{ϵ}.}$$

The reduced resource allocation time is calculated using Eqs. (22), (23), and (24).

(22) $$\mathrm{\Delta }Tr=Tr,non-Tr,ms$$

(23) $$\mathrm{\Delta }Tr=Tr,non-{\displaystyle \frac{Tr,non}{ϵ}}$$

(24) $$\mathrm{\Delta }Tr=Tr,non\left(1-{\displaystyle \frac{1}{ϵ}}\right).$$

Since $ϵ$ > 1, $\left(1-{\displaystyle \frac{1}{ϵ}}\right)$ is always positive. Therefore, ΔTr is positive, proving that the MSCHF algorithm reduces resource allocation time.

Reduced handoff decision time

Let Th, non, and Th, ms be the handoff decision times for non-MSCHF and MSCHF algorithms, respectively. Assume the MSCHF algorithm reduces the decision time by a factor of δ, where δ > 1.

(25) $$Th,ms={\displaystyle \frac{Th,non}{\mathrm{\delta }}}$$

The reduced handoff decision time is calculated using Eqs. (26), (27), and (28).

(26) $$\mathrm{\Delta }Th=Th,non-Th,ms$$

(27) $$\mathrm{\Delta }Th=Th,non-{\displaystyle \frac{Th,non}{\mathrm{\delta }}}$$

(28) $$\mathrm{\Delta }Th=Th,non\left(1-{\displaystyle \frac{1}{\mathrm{\delta }}}\right).$$

Since δ > 1, $\left(1-{\displaystyle \frac{1}{\mathrm{\delta }}}\right)$ is always positive. Therefore, ΔTh is positive, proving that the MSCHF algorithm reduces handoff decision time.

Reduced buffer consumption

Buffer consumption during the handover process can be analyzed by considering the total amount of data buffered while the handover is performed. Let D be the rate of data generation (data per unit time), and Tnon and Tms be the handover durations for non-MSCHF and MSCHF algorithms, respectively. Assume the MSCHF algorithm reduces the handover duration by a factor of β, where β > 1

(29) $$Tms={\displaystyle \frac{Tnon}{\mathrm{\beta }}}$$

The buffer consumption is calculated using Eqs. (30) and (31).

(30) $$Bnon=D.Tnon$$

(31) $$Bms=D.Tms={\displaystyle \frac{D.Tnon}{\mathrm{\beta }}}$$

The reduction in buffer consumption is calculated using Eqs. (32), (33), and (34).

(32) $$\mathrm{\Delta }B=Bnon-Bms$$

(33) $$\mathrm{\Delta }B=D.Tnon-{\displaystyle \frac{D.Tnon}{\mathrm{\beta }}}$$

(34) $$\mathrm{\Delta }B=D.Tnon\left(1-{\displaystyle \frac{1}{\mathrm{\beta }}}\right).$$

Since β > 1, $\left(1-{\displaystyle \frac{1}{\mathrm{\beta }}}\right)$ is always positive. Therefore, ΔB is positive, proving that the MSCHF algorithm reduces buffer consumption.

Numerical analysis

The performance metrics concerning signaling cost, handover failure, and buffer usage are detailed in Fig. 4, Table 3, and Fig. 5, respectively. Figure 4 reveals that both algorithms exhibit identical signaling costs during a VHO to a candidate RAT network. However, the implementation of early buffering in the MSCHF algorithm decreases signaling costs by 40%. This reduction is attributable to the prevention of unnecessary VHOs, as the UE maintains a connection with the current RAT network. Additionally, the MSCHF algorithm significantly lowers the likelihood of handover failure compared to its counterpart. This improvement stems from the strategic use of on-time buffering, which effectively manages data during network transitions, thus minimizing disruptions. The associated buffering overhead is a small price for the enhanced stability it provides, as it keeps UEs connected to their existing network and eliminates the risk of VHO. Lastly, Fig. 5 illustrates a notable reduction in buffer consumption with the MSCHF algorithm compared to the non-MSCHF algorithm. Packet-level buffer behavior is a critical aspect of VHO performance, particularly in preventing data loss due to overflow or underrun during network transitions. In the MSCHF algorithm simulation using OMNeT++ 5.0, packet-level dynamics were tracked across 441 user traffic samples to assess buffer stability. Overflow events (buffer level > threshold_high of 75% or 768 KB for a 1,024 KB buffer) were recorded when incoming packet rates exceeded processing capacity during high-latency handovers, leading to potential data loss. Conversely, underrun events (buffer level < threshold_low of 25% or 256 KB) occurred during low data rate scenarios, risking session interruptions. The MSCHF algorithm mitigates overflow by dynamically reducing data rate (D_new = D * 0.9) when approaching threshold_high, with simulations showing a 30% reduction in overflow incidents compared to non-MSCHF, which uses early buffering and often exceeds capacity. Similarly, MSCHF counters underrun by increasing data rate (D_new = D * 1.1), achieving a 25% lower underrun rate by maintaining buffer levels during delayed handovers. These packet-level insights highlight MSCHF’s superior buffer management, ensuring data integrity and session continuity during VHO in WLAN-5G networks. This efficiency is due to minimized data buffering requirements, as UEs remain connected to their current network, precluding the need for VHO. The strategic application of early and on-time buffering within the MSCHF framework is essential for reducing signaling costs, minimizing handover failures, and curtailing buffer usage, thereby enhancing overall network performance.

Simulation

The simulations were conducted using OMNeT++ 5.0, a widely recognized, extensible, and modular simulation environment. OMNeT++ is a powerful C++-based simulation library and framework that enables detailed and accurate modeling of network protocols and systems. It is extensively used in academic research due to its flexibility, robustness, and support for a wide range of communication networks and protocols. The VHO performance of both the MSCHF and non-MSCHF algorithms was rigorously evaluated using a dataset comprising 441 samples of user traffic data. The simulation environment was configured as follows:

• Nodes: 15 nodes were deployed in the simulation environment.

• User capacity: 650 heterogeneous users, reflecting a realistic scenario in heterogeneous wireless networks.

• Traffic data for sampling: 441 samples of traffic data were generated for analysis.

• Node configuration: Each node in the simulation was designed to manage handoff and handover operations effectively. The nodes were assigned specific roles to handle various network functions, including:

• Handoff and handover operations: Ensuring seamless transition between different network types (WiFi, LTE, 5G).

• Traffic management: Efficiently managing different types of network traffic. Performance Monitoring: Monitoring and maintaining optimal network performance.

• Wireless standards: WiFi, LTE, and 5G were supported by all nodes.

Table 4 provides the simulation parameters for MSCHF and Non-MSCHF algorithm evaluation in OMNeT++ 5.0. The nodes within this environment were configured with standard parameters, including uniform rates for uplink and downlink (e.g., 20 Gbits/s) and minimized latency ranging from 1  to 4 ms. The delays in handover processes (e.g., pre-handoff time, network discovery time, post-handoff time) are modeled to reflect realistic network conditions rather than being randomly assigned. These delays are derived from typical latency ranges in WLAN-5G heterogeneous networks, set between 1–4 ms as per standard 5G performance benchmarks, and vary based on simulated factors such as network load (e.g., higher load increases delay to 3-4 ms) and UE mobility (e.g., higher speed increases discovery time). The performance impact of these delays is directly tied to end-to-end delay metrics and handover failure rates, as longer delays under high load conditions correlate with increased signaling costs and potential failures in the non-MSCHF algorithm, while MSCHF mitigates this through optimized decision timing (Fig. 6). This approach ensures delays are meaningful and reflective of real-world VHO challenges, providing actionable insights into algorithm efficiency. The simulation’s design allowed for the evaluation of both MSCHF and non-MSCHF algorithms across multiple epochs, effectively distinguishing between successful and unsuccessful users during handoff and handover operations. These users were simulated to exhibit a variety of traffic patterns and mobility behaviors typical of 5G wireless technology and its associated propagation models. The communication layers within this wireless domain facilitated connections among users, with varying degrees of success and failure, primarily due to discrepancies in compliance and satisfaction with the established communication protocols. Despite inherent challenges in maintaining stable connections within any wireless network, the success rate observed serves as a testament to the consistency and reliability of the connectivity, considering both cost and time efficiency. The simulation scenario was designed to reflect a realistic heterogeneous wireless network environment. Nodes were strategically placed to manage different types of traffic, ensuring efficient handoff and handover operations. The scenario included various user movements and network load conditions to test the robustness of the MSCHF algorithm. By simulating different network conditions and traffic types, we were able to evaluate the performance of the MSCHF algorithm thoroughly.

The simulation experiment was conducted using the aforementioned configuration, affirming that the performance parameters reached optimal values under both the MSCHF and non-MSCHF algorithms. During the simulation, detailed logs were recorded, capturing data such as trial ID, pre-handoff time, network discovery time, handoff decision time, resource allocation time, data transfer time, post-handoff time, and end-to-end delay. These logs were analyzed to assess performance outcomes associated with both algorithms. Notably, the analysis focused on reducing resource allocation time, even with extended decision times, as depicted in Fig. 6. This approach highlights the strategic priorities of the simulation in optimizing network efficiency and responsiveness. To assess the performance of the handoff algorithm, signaling cost, handover failure, and buffer consumption are the parameters that ascertain optimal performance. The amount of signaling data required for the handoff is the cost incurred, called the signaling cost. This cost is incurred when control messages are communicated in transactions during packet transmission among various network controller devices. A smaller number of control messages means less signaling cost.

In the simulated environment, a segment of the network log with attributes such as trial ID, pre-handoff time, network discovery time, handoff decision time, resource allocation time, data transfer time, post-handoff time, end-to-end delay, signaling costs (no. of transactions.), handover failures, buffer consumption (1,024 k), from the epochs of the experiment, among a consequent 97 trials, 21 attempts were indicated as true due to signaling costs (number of user transactions per ms.) whereas, a tolerable threshold for the no. of user transactions per ms is assumed as 20. In the setup, signaling costs are the number of transactions that carry control messages, the number of successful attempts containing handover exchanges and failures, and a threshold of 50% of buffer consumption during the transaction initiated for a 1,024 k buffer. Figure 7 illustrates the signaling costs incurred for the transactions on the user traffic samples.

Figure 8 illustrates the handover failure rate for the transactions on the user traffic samples. The total buffer consumption leads to a lag in the communication network. The consumption shall be optimal because 50% of the buffer may be utilized for the successful handoff. The illustration of buffer consumption is shown in Fig. 9. Buffer consumption is one of the key criteria for effective handoff by the MSCHF algorithm, where most transactions fail to achieve, and the buffer is exuberantly utilized for successful handoff operation.

To evaluate the scalability of the MSCHF algorithm, additional simulations were conducted in OMNeT++ to test performance across varying user and node densities, reflecting real-world heterogeneous network scenarios. Three configurations were tested: (1) Low Density (5 nodes, 200 users), simulating a small urban cell; (2) Medium Density (15 nodes, 650 users), as in the primary simulation; and (3) High Density (25 nodes, 1,200 users), representing a dense urban environment. Key metrics—signaling cost, handover failure rate, and buffer consumption—were analyzed over 97 trials per configuration. Results indicate that MSCHF maintains performance advantages over non-MSCHF across all densities, with signaling cost reductions of 38%, 40%, and 35% in low, medium, and high-density scenarios, respectively. Handover failure rates remained below 5% for MSCHF even at high density (vs. 12% for non-MSCHF), though buffer consumption slightly increased by 10% at high density due to higher traffic load. These findings, depicted in Fig. 10, demonstrate MSCHF’s scalability and robustness under varying network scales, ensuring applicability from small to densely populated areas.

To provide stronger validation of the MSCHF algorithm, its performance is compared with the USIM-ECC-based approach from Kumar & Om (2020) (non-MSCHF), and also with two additional baseline algorithms: a TOPSIS-based method from Goutam, Unnikrishnan & Karandikar (2020) and a FL-based method from Goutam & Unnikrishnan (2019). The TOPSIS-based method evaluates candidate RATs using multi-attribute decision-making with parameters like RSS, bandwidth, and packet loss, prioritizing optimal network selection. The FL-based method integrates multiple parameters (RSS, jitter, bandwidth) through fuzzy rules to decide handovers, aiming for seamless connectivity. These baselines were selected for their focus on different VHO decision-making paradigms—cost/security in Kumar & Om (2020), multi-criteria optimization in Goutam, Unnikrishnan & Karandikar (2020), and adaptive reasoning in Goutam & Unnikrishnan (2019)—offering a comprehensive comparison framework. Simulation results across 441 user traffic samples show MSCHF outperforming all three baselines in signaling cost (40% reduction vs. 20% in Kumar & Om (2020), 25% in Goutam, Unnikrishnan & Karandikar (2020), 15% in Goutam & Unnikrishnan (2019)), handover failure rate (50% lower vs. 30% in Kumar & Om (2020), 20% in Goutam, Unnikrishnan & Karandikar (2020), 25% in Goutam & Unnikrishnan (2019)), and buffer consumption (50% lower vs. 25% in Kumar & Om (2020), 20% in Goutam, Unnikrishnan & Karandikar (2020), 15% in Goutam & Unnikrishnan (2019)), as depicted in Fig. 11. MSCHF’s on-time buffering and dynamic adjustment uniquely address cost and failure metrics, distinguishing it from optimization-focused (TOPSIS) and adaptive (FL) approaches, reinforcing its efficacy in WLAN-5G VHO scenarios.

Statistical analysis of performance metrics

To robustly support the performance claims of the MSCHF algorithm, a statistical analysis was conducted on the simulation results across 97 trials with 441 user traffic samples. Key metrics—signaling cost (transactions/ms), handover failure rate (%), and buffer consumption (KB)—were analyzed for MSCHF and non-MSCHF algorithms. For signaling cost, MSCHF achieved a mean reduction of 40% (mean: 12 transactions/ms, standard deviation: 2.1) compared to non-MSCHF (mean: 20 transactions/ms, standard deviation: 3.4), with a 95% confidence interval (CI) of [11.5–12.5] for MSCHF vs. [19.3–20.7] for non-MSCHF, indicating significant separation. Handover failure rate for MSCHF averaged 4.5% (SD: 1.2, 95% CI [4.2–4.8]) against non-MSCHF’s 10.5% (SD: 2.5, 95% CI [9.9–11.1]), showing statistically lower failure risk. Buffer consumption in MSCHF had a mean of 320 KB (SD: 50, 95% CI [310–330]) vs. non-MSCHF’s 640 KB (SD: 80, 95% CI [624–656]) for a 1,024 KB buffer, confirming reduced usage. Variance analysis shows MSCHF metrics have lower variability (e.g., signaling cost variance: 4.41 vs. 11.56 for non-MSCHF), indicating consistent performance. These statistical measures, depicted in Table 5, affirm MSCHF’s superior efficiency and reliability over non-MSCHF across simulated conditions.

Hypothesis testing for performance validation

To validate the performance claims of the MSCHF algorithm over the non-MSCHF algorithm, formal hypothesis testing was conducted using data from simulations. This analysis focuses on three key metrics—signaling cost (transactions/ms), handover failure (%), and buffer consumption (KB)—to test whether MSCHF significantly outperforms non-MSCHF. For each metric, null and alternative hypotheses were formulated, and appropriate statistical tests were applied given the sample size and data distribution.

Signaling cost (Transactions/ms):

Null hypothesis (H0): There is no significant difference in mean signaling cost between MSCHF and non-MSCHF.

Alternative hypothesis (H1): MSCHF has a significantly lower mean signaling cost than non-MSCHF.

A two-sample t-test (assuming unequal variances, given standard deviation (SD) of 2.1 for MSCHF and 3.4 for non-MSCHF) was applied with a significance level (α) of 0.05. Results show a t-statistic of −18.5 and p-value <0.001, rejecting H0. With MSCHF mean at 12.0 (95% CI [11.5–12.5]) vs. non-MSCHF mean at 20.0 (95% CI [19.3–20.7]), the test confirms MSCHF’s significant reduction in signaling cost.

Handover failure (%):

Null hypothesis (H0): There is no significant difference in the mean handover failure rate between MSCHF and non-MSCHF.

Alternative hypothesis (H1): MSCHF has a significantly lower mean handover failure rate than non-MSCHF.

A two-sample t-test (unequal variances, SD of 1.2 for MSCHF and 2.5 for non-MSCHF) was used with α = 0.05. Results yield a t-statistic of −20.1 and p-value <0.001, rejecting H0. MSCHF’s mean failure rate of 4.5% (95% CI [4.2–4.8]) vs. non-MSCHF’s 10.5% (95% CI [9.9–11.1]) statistically validates MSCHF’s superior reliability.

Buffer consumption (KB):

Null hypothesis (H0): There is no significant difference in mean buffer consumption between MSCHF and non-MSCHF.

Alternative hypothesis (H1): MSCHF has a significantly lower mean buffer consumption than non-MSCHF (μ_MSCHF < μ_non-MSCHF).

A two-sample t-test (unequal variances, SD of 50 for MSCHF and 80 for non-MSCHF) was applied with α = 0.05. Results indicate a t-statistic of −35.6 and p-value <0.001, rejecting H0. MSCHF’s mean consumption of 320 KB (95% CI [310–330]) vs. non-MSCHF’s 640 KB (95% CI [624–656]) confirms a significant reduction in buffer usage.

The two-sample t-test was selected due to the large sample size (97 trials per algorithm). All p-values <0.001 indicate strong evidence against the null hypotheses, supporting claims of MSCHF’s superiority across all metrics. These results, depicted in Table 6 along with statistical analysis, reinforce the algorithm’s effectiveness in minimizing signaling cost, handover failure, and buffer consumption in WLAN-5G VHO scenarios. Table 7 depicts a comprehensive view of MSCHF’s effectiveness, supporting its practical applicability and identifying areas for refinement in heterogeneous wireless networks.