Category: 3. Business

Introduction

Peer-assisted learning, defined as “people from similar social groupings who are not professional teachings, helping each other to learn and learning themselves by teaching”, has been used across all levels of health care education for centuries.¹ It can be categorized based on group size, more specifically the student-to-student ratio (mentoring, tutoring, or didactic) and the relationship between students: either peer teaching that occurs between students of same levels of education, or near peer teaching (NPT) which takes place in a face-to-face setting with students who are at least one academic year apart.²

NPT is increasingly used in undergraduate health professional programs as it is beneficial for health training institutions, students as teachers and students as learners. At the institutional level, it represents a solution to the rising student numbers and a shortage of faculty tutors and mentors in constrained educational environments.^3,4 Regarding seniors students, several studies have shown that they not only improve their clinical knowledge and competences but also develop teaching and leadership skills.^5–7 Consequently, NPT is now formally recognized worldwide and has led to the development of “medical student-as-teachers” programs in several institutions to support students in acquiring teaching skills.^8,9 Junior students also benefit from NPT, often achieving comparable or even superior learning outcomes compared to traditional teaching methods.^10,11 NPT has proven particularly effective during the clinical years and when the content focuses on practical and procedural clinical skills.^10,12

NPT often targets clinical skills including history taking, physical exam, communication, or procedural skills such as suturing, ultrasound or basic life support. Studies evaluating the impact of NPT programs through objective structured clinical encounters (OSCE) have shown that most NPT programs support learning over time and promote consistent improvements in OSCE performance.^10,11 However, little is known about the effectiveness of a single NPT training delivered alongside traditional faculty-led clinical skills training. This study aimed to assess the impact of a single NPT session on students’ overall performance in a summative OSCE.

Method

Setting and Design

We developed and evaluated the impact of a new NPT session on third year medical students’ clinical performance at the Faculty of Medicine, Geneva University, Switzerland. The Geneva Faculty of Medicine offers a six-year curriculum divided into three pre-clinical years (bachelor’ level, 480 students) and three clinical years (master’s level, 480 students) with approximately 160 students per year. Clinical skills training takes place during the second and third years of the bachelor. During these two years, medical students practice history taking, physical examination, and communication skills, through four formative OSCEs, each focusing on a different system: abdominal, cardiac, respiratory, and neurological. Two formats are used: 1) a group format involving direct observation followed by immediate feedback. One clinical teacher supervises two or three students interacting consecutively with a standardized patient mimicking a different clinical problem, followed by group feedback from the teacher, peers, and simulated patient; 2) an individualised video-based format—where students receive delayed verbal feedback given by a clinical teacher after a videotaped encounter with a standardized patient. At the end of the third year of the bachelor, students take a summative OSCE of three stations, covering topics such as abdominal, cardiac, respiratory, musculoskeletal, neurological, gynaecological, emergency, and hematologic related conditions.

Development of the Near-Peer Clinical Skills Training

It consisted of a two-hour session during which all third-year students (junior students) could rehearse and improve clinical skills on three clinical situations. The clinical situations were related to systems for which students from previous years had shown weaker history taking and physical examination skills than in other systems at the end of the bachelor years. The first two clinical situations focused on musculoskeletal and neurological complaints for all students, and the third addressed gynaecological, emergency, or hematologic related issues. The tutor facilitated a group of three students successively role-playing the clinician, the observer, or the patient. The observer’s role was to provide feedback on the clinician’s history-taking and physical examination skills—using a grid—prior to the facilitator’s input. The clinical situations were developed by experienced clinical teachers and aligned with previously taught clinical skills. The NPT was limited to one session for feasibility and was optional, due the limited availability of both junior and senior students.

Participants

As part of a prospective study held in 2022 and 2023, near-peer teachers—fourth to sixth year medical students (senior students: approximately 160 per year)—were invited by Email to attend this optional NPT session. Fifty of them (n=26 in 2022, and n=24 in 2023) accepted the invitation and attended a two-hour session. This session included an overview of the learning objectives, content, process and organisation of the training, and their role. The second part consisted of a 90-min small group training session in which senior students practiced clinical and teaching skills such as feedback and small group facilitation. Senior students alternated roles as supervisor, the clinician interviewing the patient, or the observer during 3–5 min sequences. These sessions were led by two senior students (ASA and VT) in charge of the project. Participants then registered online to facilitate one or two NPT sessions focused on clinical skills training.

All junior (third year) medical students were invited to attend this optional NPT session via Email over two consecutive years: 246 registered (122 out of 160 in 2022 and 124 out of 160 in 2023) and 210 attended the training session (114 in 2022 and 96 in 2023).

Outcome Measures

We collected junior students overall score and sub-scores regarding history taking, physical exam, and communication skills at the end of the third year summative OSCE exam. Each of the three stations of the exam lasted 18 minutes—and assessed history taking, physical exam, and communication skills.

The study project was approved by the Ethics Committee of the Geneva University, Geneva Switzerland (CUREG-2023-03-50). All junior and senior students provided written consent for the use of their data.

Analysis

A multiple regression model was used to investigate the potential association of the OSCE scores (raw scores, ie number of points divided by the maximum of attributable points of the evaluation grid) and the following categorical variables: gender (gender influences performance in some clinical skills such as communication¹³), set of OSCEs stations used the day of the exam, and participation in the NPT.

Additional complementary analysis used the same model with two additional variables: the scores from the two formative OSCEs taken during the third year. These two variables were considered as student’s baseline performance prior to the NPT and summative OSCE.

Finally, a linear mixed effect model was used to investigate whether there was a link between the performance at every single station of the OSCE and the fact that this station had dealt with a system specifically trained during the NPT. All the OSCE station scores were normalized and taken into the model as with the following variables: gender, participation in the NPT, system specifically trained during the NPT (fixed effects), and individual-specific effect (random). The validity of the models was checked by visual inspection of the plot and quantile–quantile normal plot of the residuals.

All analyses were run on R 4.4.2 (the R Foundation for Statistical Computing, Vienna, Austria).

Results

Three hundred and nineteen students (153 in 2022 and 166 in 2023) attended the end of third year summative OSCE (57% women and 43% male). Junior medical students who participated in a near-peer teaching program significantly outperformed non-participants in the summative OSCE, independently from other variables such as gender, scores at prior third year formative OSCE, topics of the summative OSCE and across all the dimensions assessed (global score 80.01±7.64 vs 74.58±6.71 p-value < 0.0001) (Table 1 and Figure 1).

Table 1 Third Year Medical Students’ Scores at the Summative OSCE Whether They Took Part in the NPT Study or Not

Figure 1 Boxplot of the OSCE global scores according to near-peer OSCE participation (yes; n=208) or nonparticipation (no; n=111).

Performance at prior third year formative OSCEs was not different between NPT attenders and non-attenders (81.58±8.74 vs 80.35±9.13; p-value=0.6345), and integration of these results in the model led to the same conclusion regarding the difference between the NPT and the other group, apart from weaker evidence for the communication subscale.

Further sub-analysis showed that students who attended the NPT did not systematically obtain higher scores in the OSCE stations specifically related to the clinical situations for which they received additional clinical skills training (musculoskeletal-hip global score 66.70±9.89 vs 67.49±9.89 p-value 0.820; neurology global score 75.42±8.34 vs 75.94±8.03 p-value 0.695; lymphatic global score 77.17±9.67 vs 75.20±8.79 p-value 0.598 in 2022) (musculoskeletal global score 84.85±11.42 vs 77.21±12.59 p-value 0.013; neurology global score 72.44±11.2 vs 62.44±11.52 p-value 0.018; emergency global score 66.71±16.57 vs 57.74 ±15.14 p-value 0.067 in 2023) (Appendix 1).

The linear mixed effect model used to investigate whether there was a link between the performances at every single OSCE station of the exam confirmed a strong effect of the participation in the NPT (0.4075±0.0771; p<0.0001). There was, however, no evidence of any additional benefit specifically linked to the station focused on a system specifically trained during the NPT (−0.0119±0.0598; p=0.8428).

Discussion

This study aimed to assess the impact of a single NPT session on students’ overall objective performance in a summative OSCE. We were especially interested in evaluating whether students’ performance was higher for the systems specifically trained during the NPT. We showed that students who attended this new near peer led clinical skills training session obtained higher grades at the summative OSCE than non-participating students during two consecutive years, independently from other factors such as gender, scores at prior 3^rd year formative OSCEs, topics of the summative OSCE. The effect extended to all the dimensions of the OSCE (history taking, physical examination, and communication) and was independent from the clinical situations trained during the NPT session.

Improved performance at summative OSCEs may be explained by the fact that participation was optional, and that only highly motivated and already skilled students may have attended such additional training activity.^14–16 However, several studies have shown that higher grades are more associated with peer-facilitated sessions than other factors such as previous academic grades.^17,18 In our study, the absence of significant differences in prior formative OSCE scores between participants and non-participants suggests that the two groups were comparable in terms of baseline performance. Furthermore, we also found that medical students who attended this single NPT did not consistently outperform non-attenders in OSCE stations related to the clinical scenarios covered during the NPT session. Several studies have reported that peer-teachers are preferred to medical teachers for various reasons: senior students are familiar with the exam content, have completed the same curriculum and can share their own experience and highlight common pitfalls; finally, despite being less clinically experienced than Faculty educators, they deliver information relevant to the expected level.^19–21 In addition, working cooperatively, in a secure learning environment can empower students’ learning and increase their self-confidence by decreasing their anxiety and the stress related to the upcoming exam.^22,23 Similarly, peer-led learning in clinical environments has been shown to positively influence and support medical students’ clinical development during clerkships.²⁴ These elements, which refer to cognitive and social congruence may explain why this single NPT was effective despite its short duration and its limited focus. Cognitive congruence refers to the fact that as near-peer tutors are usually only one or two years apart, this makes it easier for them to identify students’ needs, share past experiences and give useful advice.^12,25 The concept of social congruence concerns senior and junior students sharing similar roles.¹⁶ Being a student helps build a rapport with students that goes beyond the traditional teacher-student dynamic and creates a more collaborative and mutually respectful interaction.⁷ A recent study evaluating the effectiveness of near-peer teaching (NPT) among third-year medical students found that participants reported an improved understanding of how their clinical skills would be assessed during OSCEs.²⁶ This further confirms that NPT not only enhances clinical skill acquisition but also provides valuable insights and strategies for preparing for OSCEs. This may explain why a single NPT improve student’s performance at OSCEs, independently from the specificity of the skills trained during the session.

There are, however, several limitations. As noted, both senior and junior student recruitment was voluntary and limited to a single institution, raising the possibility of a selection bias toward high-performing students. However, the fact that participation to this NPT was not associated with the level of performance at previous formative OSCE does not support this hypothesis. A randomized trial would have been the best design to test the effectiveness of NPT but was not possible due to the voluntary nature of the intervention. Additionally, no selection criteria were applied to senior students, and we did not collect information about their prior academic performance or teaching experience. As a result, we cannot determine whether these factors influenced the quality of the NPT sessions.

Conclusion

A single NPT session seems to improve junior students’ general performance but not specifically the scores related to the trained clinical situations at a summative OSCE. This suggests that NPT may facilitate the transfer of more generic rather than specific skills or boost students’ confidence and skill acquisition by providing opportunities to gain additional insight into how to prepare for the OSCE. Further research is needed to better understand the mechanisms that really enhance student learning in such context.

Data Sharing Statement

The datasets generated or analyzed during the current study are not publicly available due to the privacy of the students but are available from the corresponding author on reasonable request.

Ethical Approval and Consent to Participate

An ethical compliance decision was granted by the Geneva University Commission for Ethical Research (CUREG2.0) (Institutional Review Board (IRB) DECISION FORM: CUREG-2023-03-50) to the project as all methods were carried out in accordance with relevant guidelines and regulations and that all participants gave their informed consent to allow the use their anonymized data for this study.

Acknowledgment

The authors thank the junior and senior students who took part into the study and Julia Sader for improving the English quality of the manuscript. An earlier version of a first manuscript presenting initial results has been uploaded to ResearchSquare as a preprint (https://www.researchsquare.com/article/rs-3079788/v1).

Funding

This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.

Disclosure

The authors report no conflicts of interest in this work.

References

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2. Olaussen A, Reddy P, Irvine S, Williams B. Peer-assisted learning: time for nomenclature clarification. Med Educ Online. 2016;21:30974. doi:10.3402/meo.v21.30974

3. Allikmets S, Vink JP. The benefits of peer-led teaching in medical education. Adv Med Edu Pract. 2016;7:329–330. doi:10.2147/AMEP.S107776

4. Ten Cate O, Durning S. Peer teaching in medical education: twelve reasons to move from theory to practice. Med Teach. 2007;29(6):591–599. doi:10.1080/01421590701606799

5. Boud D. Making the move to peer learning. In: Boud D, Cohen R, Sampson J, editors. Peer Learning in Higher Education. 1st ed. Routledge; 2001:1–17.

6. van der Hoeven D, van der Hoeven R, Zhu L, Busaidy K, Quock RL. Integration of basic and clinical sciences: faculty perspectives at a U.S. dental school. J Dental Educ. 2018;82(4):349–355. doi:10.21815/JDE.018.038

7. Tanveer MA, Mildestvedt T, Skjaerseth IG, et al. Peer teaching in undergraduate medical education: what are the learning outputs for the student-teachers? A systematic review. Adv Med Edu Practice. 2023;14:723–739. doi:10.2147/AMEP.S401766

8. Cohen A, Steinert Y, Cea ER. Teaching medical students to teach: a narrative review and literature-informed recommendations for student-as-teacher curricula. Acad Med. 2022;97(6):909–922. doi:10.1097/ACM.0000000000004608

9. Meyer HS, Kelsey L, Anita S, et al. Teaching medical students how to teach: a scoping review. Teaching Learning Med. 2022;34(4):379–391. doi:10.1080/10401334.2021.1979006

10. Brierley C, Ellis L, Reid ER. Peer‐assisted learning in medical education: a systematic review and meta‐analysis. Med Educ. 2022;56(4):365–373. doi:10.1111/medu.14672

11. Rees EL, Quinn PJ, Davies B, Fotheringham V. How does peer teaching compare to faculty teaching? A systematic review and meta-analysis. Med Teacher. 2016;38(8):829–837. doi:10.3109/0142159X.2015.1112888

12. Williams B, Reddy P. Does peer-assisted learning improve academic performance? A scoping review. Nurse Edu Today. 2016;42:23–29. doi:10.1016/j.nedt.2016.03.024

13. Graf J, Smolka R, Simoes E, et al. Communication skills of medical students during the OSCE: gender-specific differences in a longitudinal trend study. BMC Med Edu. 2017;17(1):75. doi:10.1186/s12909-017-0913-4

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OpenAI is set to open a corporate office in the Indian capital of New Delhi in a few months, establishing a formal presence in a key growth market.

The company, known for its artificial intelligence chatbot ChatGPT, has begun hiring to expand its local team, it said in a statement Friday. It posted three sales jobs in India that required at least seven years of experience, and it could list more in future. OpenAI currently has only one employee in India — Pragya Misra, who leads public policy and partnerships in the country after joining the firm last year.

HUHTAMÄKI OYJ PRESS RELEASE 22.8.2025 AT 9.00 EEST

Huhtamäki Oyj establishes a Euro Medium Term Note programme

Huhtamäki Oyj has established a EUR 2 billion Euro Medium Term Note (“EMTN”) programme. The Central Bank of Ireland has approved the base prospectus for the EMTN programme on August 21, 2025. The base prospectus will be available on the website of Euronext Dublin at www.euronext.com/en/markets/dublin and on Huhtamaki’s website at www.huhtamaki.com/en/investors/financial-information/debt-investors.

BNP PARIBAS is acting as the arranger of the EMTN programme.

The net proceeds from the notes issued under the EMTN programme will be used for general corporate purposes.

For further information, please contact:
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BEIJING, Aug. 22 — China has registered a net increase of nearly 20 million enterprises since the beginning of the 14th Five-Year Plan period (2021-2025), the State Administration for Market Regulation said on Friday.

Since the launch of the 14th Five-Year Plan, China’s business environment has continued to improve, thereby fully stimulating entrepreneurial vitality across society, Luo Wen, head of the administration, said at a press conference highlighting the country’s achievements during the period.

The country also recorded a net increase of approximately 34 million self-employed households during the same five-year period, Luo added.

The rupee slipped 11 paise to 87.36 against the US dollar amid rising dollar demand. Positive FII inflows and lower crude prices limited losses as traders awaited US Fed Chair Jerome Powell’s remarks at the Jackson Hole Symposium.

Mumbai: The rupee declined 11 paise to 87.36 against the US dollar in early trade on Friday amid a rise in dollar demand.

However, positive FII inflows and a decline in crude oil prices prevented sharper losses in the local unit as traders awaited US Fed Chief Jerome Powell’s speech at the Jackson Hole Symposium later in the day, forex traders said.

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The domestic unit opened at 87.37 against the US dollar and inched up to 87.36, down 11 paise from its previous close.

The rupee pared initial gains on Thursday to settle lower by 18 paise at 87.25 against the greenback.

“The rupee fell yesterday (Thursday) as importers and a big public sector bank bought dollars. Rupee was unable to pierce the support of 86.92 yesterday (Thursday) as dollar buying emerged on dips though FPIs were buyers of Indian equity,” Anil Kumar Bhansali, Head of Treasury and Executive Director, Finrex Treasury Advisors LLP, said.

“Uncertainty on tariffs remained as we approach August 27, the day on which 25 per cent additional tariffs will be imposed by the US on Indian exports,” he said.

Meanwhile, the dollar index, which gauges the greenback’s strength against a basket of six currencies, gained 0.10 per cent to 98.72.

Brent crude, the global oil benchmark, was trading 0.18 per cent down at USD 67.55 per barrel in futures trade.

“Brent oil prices were steady on Friday morning amid sustained risk aversion before more cues on US monetary policy from Fed Reserve Chair Jerome Powell. Oil prices, however, headed for weekly gains amid increasing signs that peace negotiations between Russia and Ukraine were stalling,” Bhansali added.

On the domestic equity market front, stock markets declined 262.05 points to 81,738.66 in early trade, while Nifty dropped 81.55 points to 25,002.20.

Foreign Institutional Investors purchased equities worth Rs 1,246.51 crore on Thursday, according to exchange data.

In this section, we will discuss the dynamical behavior through bifurcation and sensitivity.

Bifurcation analysis

From (18), we can write as

Let (frac{alpha _1kappa ^2+alpha _4kappa -kappa omega }{alpha _1K^2}=A), (frac{alpha _3kappa +alpha _5kappa }{alpha _1K^2}=B) and (frac{alpha _2}{alpha _1K^2}=C), then we get

Using the Galilean transformation on (60), then we get dynamical system

Case 1: (A>0), (B>0), and (C>0).

We take different values of parameters (alpha _1 = 0.3), (alpha _2 = 0.5), (alpha _3 = 0.4), (alpha _4 = 0.2), (alpha _5 = 0.1), (omega = 0.1), (K = 0.5), and (kappa = 0.4), then get five equilibrium points (0, 0), (0.81, 0), ((-0.81,0)), (0.51i, 0), and ((-0.51 i,0)). As we see in Fig. 7 (0, 0) is the saddle and (0.81, 0), ((-0.81,0)) are center points.

Case 2: (A<0), (B<0), and (C<0).

We take different values of parameters (alpha _1 = 0.3), (alpha _2 = -5), (alpha _3 = 0.2), (alpha _4 = 1), (alpha _5 = 0.3), (omega = -5), (K = 2), and (kappa = -1.5), then we get five equilibrium points (0, 0), (0.17, 0), ((-0.17,0)), (0.10i, 0), and ((-0.10 i,0)). As we analyze in Fig. 8, (0, 0) is the center point.

Case 3: (A<0), (B>0), and (C>0).

We take different values of parameters (alpha _1 = 0.5), (alpha _2 =2), (alpha _3 = 0.6), (alpha _4 = -3), (alpha _5 = 0.4), (omega = 5), (K = 1), and (kappa = 0.8), then we get five equilibrium points (0, 0), ((1-0.89 i,0)), ((-1+0.89 i,0)), ((1+0.88 i,0)), and ((-1-0.88 i,0)). As we see in Fig. 9 (0, 0) is the center point.

Case 4: (A>0), (B<0), and (C>0).

We take various values of parameters (alpha _1 = 0.5), (alpha _2 =2), (alpha _3 = -1), (alpha _4 = 3.0), (alpha _5 = -0.5), (omega = 1.0), (K = 1), and (kappa = 1.2), then we get five equilibrium points (0, 0), (1.43i, 0), ((-1.43 i,0)), (1.06, 0), and ((-1.06 i,0)). As we see in Fig. 10 (0, 0) is the saddle point and (1.06, 0), ((-1.06,0)) are the center points.

Case 5: (A>0), (B>0), and (C<0).

We take diverse values of parameters (alpha _1 = 0.5), (alpha _2 =-2), (alpha _3 = 1.0), (alpha _4 = 3.0), (alpha _5 = 0.5), (omega = 1.0), (K = 1.0), and (kappa = 1.2), then get five equilibrium points (0, 0), ((0.63-0.92 i,0)), ((-0.63+0.92 i,0)), ((0.63+0.92 i,0)), and ((-0.63-0.92 i,0)). As we analyze in Fig. 11, (0, 0) is the saddle point.

Case 6: (A<0), (B<0), and (C>0).

We take various values of parameters (alpha _1 = 1), (alpha _2 =3), (alpha _3 = -2), (alpha _4 = -4), (alpha _5 = -1), (omega = 8.0), (K = 0.8), and (kappa = 1.0), then we get five equilibrium points (0, 0), ((0.81-1.03 i,0)), ((-0.81+1.03 i,0)), ((0.81+1.03 i,0)), and ((-0.81-1.03 i,0)). As we see in Fig. 12, (0, 0) is the center point.

Case 7: (A<0), (B>0), and (C<0).

We take various values of parameters (alpha _1 = 1.0), (alpha _2 =-5.21), (alpha _3 = 1.5), (alpha _4 = 22.69), (alpha _5 = 3.57), (omega = 10.0), (K = 1.0), and (kappa = 1.2), then we get five equilibrium points (0, 0), (1.57i, 0), ((-1.57 i,0)), (1.14, 0), and ((-1.14,0)). As we see in Fig. 13, (0, 0) is the center point and (1.14, 0), ((-1.14,0)) are the saddle points.

Case 8: (A>0), (B<0), and (C<0).

We take various values of parameters (alpha _1 = 0.5), (alpha _2 =-3.0), (alpha _3 = -1.0), (alpha _4 = 4.0), (alpha _5 = -0.5), (omega = 1.0), (K = 1.0), and (kappa = 1.2), then we get five equilibrium points (0, 0), ((0.86-0.67 i,0)), ((-0.86+0.67 i,0)), ((0.86+0.67 i,0)), and ((-0.86-0.67 i,0)). As we see in Fig. 14, (0, 0) is the saddle point.

Sensitivity analysis

For sensitivity analysis we will decompose the Eq. (60) into dynamical system as,

The system (62) explores how variations in initial conditions and parameters (alpha _1 = 0.8), (kappa = 2), (alpha _2 = 0.4), (K = 3), (alpha _3 = 0.3), (alpha _4 = 0.5), (alpha _5 = 0.1), and (alpha _6 = 0.5) influence the system’s behavior. The system is governed by nonlinear terms that can yield to complex dynamics, making it highly sensitive to small variation in initial conditions. In Fig. 15a, where the system starts with (0.40, 0) and a slight perturbation is introduced by changing the initial conditions to (0.45, 0.01), there is a significant divergence between the two trajectories. This shows the system’s high sensitivity to initial conditions, characteristic of unstable or chaotic systems where small changes lead to large variations in the results.

In contrast, Fig. 15b present the system with different initial conditions (1.60, 1.02) and a slight changes in the initial values. The two curves in this plot show much less divergence, showing that the system is less sensitive to changes in initial conditions. This present that the system is operating in a more stable region, where minor variations do not significantly affect its trajectory. Thus, the comparison between the two figures indicates the system shows sensitive.

Analytical modelling of the edge-IoT environment as a single-channel queueing system with controlled shift in distributions

In modern edge-oriented IoT environments, there is an increasing need for adaptive load regulation that considers constraints related to latency, energy consumption, and traffic class. This is particularly relevant for systems such as URLLC or mMTC, where response speed or transmission stability is critically important. Under such conditions, the problem of formal control over waiting time and queue length becomes pressing, without disrupting the overall flow structure. One of the key solutions involves introducing a shift parameter into the arrival and service distributions. For this purpose, let us consider single-channel queueing systems of the A/B/1 type in Kendall’s classification, where the symbols A and B denote the probability distributions of inter-arrival and service intervals respectively, and 1 indicates the number of service channels. The single-channel model is the most appropriate abstraction of an edge node. It reflects the hardware constraints of NB-IoT, LoRa, or BLE devices, which process requests sequentially rather than in parallel. Moreover, this model preserves the mathematical clarity of the analytical apparatus, particularly when using the spectral method³¹ for the Lindley equation³².

In A/B/1 queueing systems, the probability density functions (alpha left( t right)) and (beta left( t right)), corresponding to the distributions of inter-arrival times and service durations, respectively, are defined as time-shifted functions (tau), where (tau>0) is a controllable parameter characterising the minimum delay in the system

Here, (tilde {alpha }left( t right)) and (tilde {beta }left( t right)) represent the original (non-shifted) density functions of inter-arrival and service intervals, respectively. The introduction of the shift (tau) enables continuous adjustment of the expected values of the corresponding stochastic variables without altering their functional form. As a result, a controlled reduction in the coefficient of variation occurs, which is one of the main factors influencing the mean waiting time. Consequently, the parameter (tau) becomes a controllable variable that can be used to shape delays as an optimisation tool, for instance, to balance between QoS classes or minimise buffer overflow. Henceforth, it is assumed that the base densities (tilde {alpha }left( t right)) and (tilde {beta }left( t right)) belong to the class of functions that admit Laplace transformation. This is a critical requirement for applying the spectral method, which serves as the principal analytical tool used to derive the numerical-analytical characteristics of queue waiting time. As a result of introducing the controllable shift (tau) into the density functions (1), not only the expected values of the corresponding intervals are altered, but also the shape of the system’s overall variation profile is affected. In particular, increasing the mean values of the intervals while keeping the variance fixed leads to a monotonic decrease in the coefficients of variation, which has a decisive impact on queue characteristics. Since the mean waiting time in a G/G/1 system is directly proportional to the squares of the coefficients of variation of inter-arrival and service intervals, managing the shift opens the way to analytically controlled delay optimisation.

From a mathematical standpoint, a system with a regulated shift does not preserve Markovian properties, and its dynamics are described within the general G/G/1 class. In this class, the arrival and service flows may follow arbitrary structures, provided they admit a Laplace transform. To describe the distribution law of the queue waiting time, the Lindley integral equation is used in the following interpretation:

where (Wleft( x right)) is the distribution function of the queue waiting time, and (Fleft( {{v_xi }} right)) is the distribution function of the stochastic variable (rho =beta – alpha), which describes the difference between the service time (beta) and the inter-arrival interval (alpha) of two successive requests. The variable ({v_rho }) in this context is the integration variable that spans all possible values of (rho), i.e., all scenarios of relative positioning of arrival and service completion events. If ({v_rho }>0), the current request is forced to wait; if ({v_rho } leqslant 0), the service begins immediately. The controllable shift parameter (tau), introduced at the level of the distributions (alpha left( t right)) and (beta left( t right)), indirectly shapes the behaviour of the function (Fleft( {{v_rho }} right)), and thus governs the entire dynamics of request accumulation in the system.

To obtain an analytical solution to the Lindley Eq. (2) under arbitrary (non-Markovian) arrival and service distributions, it is appropriate to apply the spectral method³². This approach is widely used in the analysis of queueing systems, as well as in applied problems of mathematical physics and signal processing. In our model, this method preserves analytical controllability even in the absence of simplifying assumptions about the form of the densities. The core idea of the method is to transition into the Laplace transform domain, where the densities (alpha left( t right)) and (beta left( t right)) are represented as functions ({{rm A}^ * }left( p right)) and ({{rm B}^ * }left( p right)). This transition allows the integral Eq. (2) to be rewritten in the form of an algebraic relation:

where (p in {text{F}}) is the complex Laplace transform parameter, and (aleft( p right)), (bleft( p right)) are analytical functions (typically polynomials) that approximate the integral structure in rational form. Such a transformation enables the analysis of the system’s spectral structure, in particular the identification of its zeros and poles, which directly influence the temporal characteristics of the service process and determine the asymptotic behaviour of the waiting time.

For the subsequent analysis, we select two of the most representative distributions that combine analytical transparency with practical relevance for IoT edge subsystems – the exponential and the second-order Erlang distributions. Their selection is motivated by the fact that these distributions, on the one hand, possess closed-form Laplace transforms, and on the other hand, allow for the modelling of both reactive and multi-phase behaviour of service or arrival processes.

The exponential distribution serves as a fundamental model for memoryless stochastic events, such as spontaneous request generation by sensors or short computational tasks. Its shifted distribution function is given in

where (lambda) denotes the intensity of the exponential process. This distribution is characterised by a zero coefficient of variation, which makes it convenient for analytical anchoring and spectral interpretation of systems with constant load.

The Erlang distribution of order two, in turn, enables the modelling of structured, staged processes, particularly in cases where a request undergoes several stages of preliminary processing (filtering, authorisation, encryption). Its distribution function with adjustable shift (tau) is given in

where (mu) denotes the intensity parameter of each phase. Unlike the exponential distribution, this one exhibits a lower coefficient of variation, which allows for more precise control over load fluctuations and more efficient management of waiting times in the system.

Both distributions form a unified parametric axis, enabling a smooth transition from a fully random (exponential) to a sequential-phase (Erlang) mode without losing analytical controllability. This makes it possible, within a single spectral scheme, to model a wide range of edge scenarios () from lightweight requests with immediate service to complex transactions with sequential processing.

Within the described analytical framework, we consider queueing systems in which interarrival and service intervals are modelled by continuous stochastic variables with shifted distribution functions. Specifically, let us assume that the system dynamics are defined by two functions of the form ({F^{left( i right)}}left( t right)=left{ begin{gathered} {{tilde {F}}^{left( i right)}}left( {t – tau } right)forall t geqslant tau , hfill \ 0forall 0 leqslant t leqslant tau , hfill \ end{gathered} right.), where ({tilde {F}^{left( 1 right)}}left( t right)) and ({tilde {F}^{left( 2 right)}}left( t right)) denote the base (unshifted) distributions for arrivals and service, respectively. This formalisation generalises the previously considered exponential and Erlang cases, allowing a more abstract representation of systems with controllable delay. Interpretatively, this means that each process in the system initiates no earlier than after a fixed time interval (tau), reflecting hardware, protocol, or energy constraints typical of real-time edge nodes. Such a shift enables the reproduction of internal buffering, adaptive delays, and minimum activity intervals without disrupting the overall structure of the model. Importantly, the shifted distributions retain all key properties of classical queueing models that underpin spectral and Laplace-based methods.

After formalising the shifted form of the distribution functions (4), (5) and analysing their properties in the time domain, a natural step is to transition to the spectral representation, which is implemented via the Laplace transform. In the classical formulation, it is defined as

where (fleft( t right)) denotes the probability density function of the corresponding random variable. This transition to the complex domain enables the replacement of integral operators with algebraic ones and reveals the structure of functional relationships between model components in the form of products, quotients, and poles.

In the case of time-shifted functions (in particular, (fleft( {t – tau } right)), which equals zero for (left[ {0,tau } right))), the standard shift property ({text{L}}left[ {fleft( {t – tau } right)} right]={F^ * }left( p right)exp left( { – tau p} right)) is used, allowing the effect of controllable delay to be easily incorporated into the spectral image. This enables the previous relation (3) to be rewritten in the following form

where exponential factors associated with the shift parameter (tau) mutually cancel. As a result, the structural form of the spectral expression remains unchanged, which is a significant advantage: the shifted model does not require additional adjustment in the Laplace transform domain. This makes it possible to directly apply the spectral decomposition technique developed for classical systems, without any loss of generality or need to renormalise components.

Within the formulated model, we consider a queueing system in which both arrivals and service are described by two-phase Erlang densities with a symmetric delay structure. This approach reflects practical scenarios in which both incoming requests and their processing consist of sequential stages with a guaranteed minimum activation time, such as authentication and confirmation procedures. In the analytical representation, these densities take the form:

where (varphi ,phi>0) are the intensities of the phase components. Both densities are shifted to the right by (tau), ensuring consistency with the previously introduced logic of controllable delay.

After transitioning to the spectral domain, the corresponding Laplace transforms take the form:

where the factors (exp left( { – tau p} right)) arise as a consequence of the shift in the time domain. Since the exponential components in both transforms are synchronised, they cancel each other out within the product structure that appears in the spectral relation. After algebraic manipulation, we obtain:

where the coefficients ({k_0}), ({k_1}), ({k_2})​ depend solely on the model parameters and define the numerator as a third-degree polynomial. The pole structure of the fraction (10) is fully determined: singularities at the points (p=varphi) and (p=phi) define the dominant frequency behaviour of the system and determine the positions of the spectral peaks. This spectral localisation subsequently enables a precise analysis of the asymptotic characteristics of the waiting time.

Summarising the results of the spectral representation, we construct the Laplace transform of the waiting time function based on the rational structure of the fraction derived earlier. In the model with two-phase Erlang density distributions for arrivals and service, the corresponding transform ({W^ * }left( p right)) is given by

where ({Omega _+}left( p right)) is the regular part of the spectrum, and ({p_1}), ({p_2}) are the real positive roots of the denominator of the spectral decomposition, associated with the frequency characteristics of the system. Their presence determines the asymptotic behaviour of the waiting time function, including the dominant decay rates of the queue.

To complete the spectral construction, we refine the structure of the functions (aleft( p right)) and (bleft( p right)), which appear in relation (10) and define the spectral decomposition in the frequency domain:

where ({p_3}) is the pole of the function (bleft( p right)), located to the right on the complex axis and is the reciprocal of the characteristic time parameter of intensity (varphi). The rational form of both functions enables the efficient application of inverse transform methods and analytical approximation techniques.

The mean waiting time ({rm E}left[ W right]) is determined using the standard operator approach to the derivative of the spectral transform (11), or equivalently, through the analysis of partial fraction decomposition. We obtain:

which clearly illustrates the dependence of delay on the location of poles in the spectrum. According to formula (13), the value of ({rm E}left[ W right]) decreases with increasing ({p_1}), ({p_2})​, which, in turn, depend on the distribution parameters (primarily the mean intervals and coefficients of variation). Therefore, controlling these quantities opens the way to analytically formalised optimisation of delays in the system.

To proceed with the comparative analysis, we consider the generalised metric characteristics of the arrival and service flows. These quantities allow spectral results to be interpreted in terms of temporal scales and the dispersion properties of the system.

For the arrival flow, the corresponding values are calculated as:

where ({rm E}left[ {{T_varphi }} right]) is the mean interarrival time and ({c_varphi }) is the coefficient of variation, reflecting the degree of instability in the incoming traffic. Similarly, for the service flow we obtain:

In both cases, the coefficient of variation is a decreasing function of (tau), which confirms the earlier statement: increasing the shift stabilises the process by reducing relative dispersion and smoothing stochastic fluctuations.

In contrast to standard Erlang distributions without shift, where the coefficient of variation equals ({1 mathord{left/ {vphantom {1 {sqrt 2 }}} right. kern-0pt} {sqrt 2 }}), in the proposed model it is further reduced due to the presence of an unavailability phase. Consequently, both coefficients satisfy the inequality (0<{c_varphi },{c_phi }<0.5), indicating that the model belongs to the class of systems with limited variability, where the influence of random factors on the waiting time is significantly diminished. This creates the preconditions for predictable queue behaviour and effective real-time quality of service management.

Finally, let us consider the limiting case of the model with Erlang densities – Its transition to the exponential distribution with the same shift parameter (tau). This model corresponds to the classical M/M/1 system with activation delay, allowing an assessment of the impact of distribution order on the behaviour of the waiting time. In this case, the arrival and service densities take the form:

In contrast to the two-phase Erlang structure, this configuration exhibits memoryless behaviour with the highest possible variability (coefficient of variation (c=1)). In such a setup, the mean waiting time is determined by the classical formula for the M/M/1 model:

which, despite the presence of the shift (tau), retains its form due to the cancellation of exponential factors in the spectral domain, as demonstrated earlier.

The Laplace transforms of the densities (16) take the form:

and the product ({{rm A}^ * }left( { – p} right){{rm B}^ * }left( p right)) results in a rational fraction that describes the spectral structure of the model:

Unlike the previously considered cases, expression (19) has two simple poles, and the structure of the numerator is linear in (p), which simplifies inversion and facilitates the interpretation of queue dynamics. In this way, the shifted model remains fully compatible with the classical M/M/1 theory, while introducing a crucial element, controlled service unavailability over the interval (left[ {0,tau } right)), which is essential in realistic IoT scenarios.

In contrast to existing approaches that address task placement or energy-aware scheduling without formally modelling the internal queue structure, the proposed model introduces a parametrically controlled delay shift within a G/G/1 framework, enabling analytical control over key QoS metrics. For example, the study³³ formulates a stochastic game for distributed task coordination among UAVs, but does not explicitly model queue dynamics or device activation delay. Similarly³⁴, applies a vacation queue model to optimise application placement, yet its optimisation process is based on empirical heuristics and lacks an analytical linkage between service parameters and latency characteristics. The work³⁵ focuses on energy-efficient scheduling, but does not formalise the queue as a controllable element within the service process. The proposed model, by contrast, incorporates analytically derived expressions for mean waiting time (formula (13)) and coefficients of variation (formulas (14) and (15)), where the shift parameter (denoted (theta)) directly affects both temporal stability and service variability. The Laplace-domain representation (formulas (10) and (11)) enables spectral analysis of system behaviour under arbitrary input distributions. Furthermore, the shifted Erlang distributions defined in formula (8) allow precise modelling of activation delays typical for edge nodes. As a result, the proposed framework offers a mathematically grounded foundation for reinforcement learning that is explicitly sensitive to queue dynamics, structurally induced service delays, and decentralised real-time optimisation.

Intelligent control of the shift parameter in a queueing model for Edge-IoT environments using reinforcement learning

After formalising the analytical queueing model with a controllable shift, it is justified to proceed to the description of the mechanism for its intelligent control. The shift (tau), previously interpreted as a parameter defining the phase of system unavailability prior to processing, is hereinafter considered a controllable variable dynamically adjusted by the RL agent in response to the current system state. This is particularly relevant in edge-IoT environments, where load characteristics fluctuate unpredictably and the need to adapt to resource and timing constraints is critical.

The problem of optimal selection (tau) in this context is formalised as a Markov Decision Process (MDP), within which the RL agent observes the variation of queue parameters, selects actions from the set of admissible shifts, and receives a reward for reducing delay and improving system stability.

The state space (s) is defined by the key features of the current service configuration (S=leftlangle {q,rho ,{c_{ef}}} rightrangle), where (q) denotes the queue length, (rho ={varphi mathord{left/ {vphantom {varphi phi }} right. kern-0pt} phi }) represents the load intensity, and ({c_{ef}}) is the effective coefficient of variation. The latter can be specified as the average value between ({c_varphi }) and ({c_phi }), calculated according to formulas (14) and (15), which already incorporate the impact of the shift (tau) on the variability of incoming flows.

The action space ({rm T}) is a finite set of permitted shift values available for the agent to choose from: ({rm T}=left{ {{tau _1},{tau _2}, ldots ,{tau _n}, ldots ,{tau _N}} right}), ({tau _n} in left[ {0,{tau _{hbox{max} }}} right]). The boundaries of this set are determined by hardware, protocol, or energy constraints of edge devices, while its discrete nature allows for controlled complexity of the learning algorithms.

The reward function (Rleft( {s,{tau _n}} right)) integrates two key aspects of service performance: the average waiting time and the balance between the variability of service and arrivals. In its simplest form, it is expressed as

where ({rm E}left[ {Wleft( {{tau _n}} right)} right]) is defined by the spectral formula (13), which depends on the poles ({p_1}) and ({p_2}), indirectly influenced by the choice of shift (see expressions (10), (19)); (left| {{c_varphi } – {c_phi }} right|) serves as an indicator of variability imbalance; ({q mathord{left/ {vphantom {q {{q_{hbox{max} }}}}} right. kern-0pt} {{q_{hbox{max} }}}}) is the normalised queue length, directly reflecting the level of request accumulation; ({q_{hbox{max} }}) denotes the maximum permissible queue length; and the term (hbox{max} left( {0,rho – 1} right)) penalises situations where the arrival intensity exceeds the system’s computational capacity. The coefficients ({kappa _1},{kappa _2},{kappa _3} in {{mathbb{R}}^+}) define the relative importance of each criterion, taking into account architectural and service-level priorities.

The probabilistic transition function (Pleft( {s^{prime}left| {s,{tau _n}} right.} right)), which describes the change of state resulting from performing action ({tau _n} in {rm T}) in state (s in S), is empirically defined in most practical cases. The RL agent does not possess complete knowledge of the model; instead, it learns the queue dynamics through experience-based learning algorithms (off-policy).

The objective of the RL agent is to approximate the optimal policy ({pi ^ * }=arg mathop {hbox{max} }limits_{pi } {rm E}left[ {sumnolimits_{{t=0}}^{infty } {{gamma ^t}Rleft( {{s_t},{n_t}} right)} } right]), where (gamma in left( {0,1} right]) is the discount factor that determines the long-term significance of decisions.

The RL approach serves as a superstructure over the analytical framework outlined in subsection 2.1. It does not alter the structure of the Lindley equation or the spectrum (see expressions (3), (10), (19)), but rather uses them as a foundation for dynamic learning. Crucially, the RL agent operates not at the level of modifying the mathematical model itself, but at the level of managing its parameters, thus, enabling the system to adapt to load fluctuations and instability in incoming flows without sacrificing analytical predictability.

Function (20) formalises shift management (tau) as a MDP, in which the RL agent, interacting with the analytically grounded queuing system (see expressions (13)–(15)), develops a policy for dynamic action selection. However, in a practical edge-IoT environment, additional factors (such as buffer limitations, request losses, traffic class, and node energy capacity) play a decisive role alongside stability and service speed. Therefore, it is reasonable to introduce an extended reward function that complements function (20) with terms accounting for these application-specific requirements:

where (L={{{N_{drop}}} mathord{left/ {vphantom {{{N_{drop}}} {{N_{arrive}}}}} right. kern-0pt} {{N_{arrive}}}}) is the empirically estimated ratio of lost requests to total arrivals, (L in left[ {0,1} right]); ({L_{hbox{max} }}) is the permissible loss threshold defined by the QoS profile; (Eleft( {{tau _n},{c_{ef}}} right)) is the expected energy consumption, modelled in simplified linear form

where ({e_0},{e_1},{e_2} in {{mathbb{R}}^+}) are the parameters of the node’s energy profile corresponding to background consumption, delay cost, and processing of variable input flows; ({E_{hbox{max} }}) is the available energy consumption limit; and ({kappa _4},{kappa _5} in {{mathbb{R}}^+}) are the weighting coefficients. Each term in function (21) represents a measurable or predictable quantity calculated at the decision-making moment, ensuring a fully formalised agent policy without the need for heuristic tuning.

The extension of function (20) to the form (21) requires the construction of an agent-based architecture capable of making decisions regarding the value of the shift parameter (tau), based on observations of queue state, load characteristics, variability, losses, and energy consumption. Given that such key components of the reward as average waiting time and coefficients of variation are determined analytically (see expressions (13)–(15)), the RL agent does not approximate the service model, but rather operates as a strategic superstructure over an already adapted system.

The agent’s input is defined as a state vector (s=left( {q,rho ,{c_{ef}},L,E} right)), (s in S), where all variables are either available during execution (e.g. (q,rho)), (rho)) or computed using the mathematical framework defined in subsection 2.1. At the same time, reward components dependent on the selected action (in particular, ({rm E}left[ {Wleft( {{tau _n}} right)} right])) are not included in the state, as they are computed post hoc, after the action has been applied. As before, the RL agent’s action space is defined by the set of admissible shift values ({rm T}=left{ {{tau _i}} right}), (i=overline {{1,N}}). The discreteness of this set enables the use of tabular methods for policy learning. For such configurations, it is appropriate to apply the Q-learning algorithm, which updates the estimated utility of selecting ({tau _n} in {rm T}) in state s according to the rule:

where.(eta in left( {0,1} right]). is the learning rate, (left( {s,{tau _n}} right)) and (left( {s^{prime},{{tau ^{prime}}_n}} right)) denote the current and next states of the system, respectively; (Rleft( {s,{tau _n}} right)) is the reward function of the form (20) or (21), computed analytically based on the parameter ({tau _n}) and the observed state (s)s.

In cases where the dimensionality of the state space increases (for instance, due to the inclusion of additional QoS labels or changes in flow distributions), and the action set becomes broader, the RL agent can be implemented as a neural approximation of the Q-function, i.e. as a DQN. In this case, function (23) is modelled by a neural network with parameters (theta), which are updated by minimising the squared error between current and target estimates:

where ({theta ^ – }) denotes the parameters of the target network, updated with a delay. The DQN variant is appropriate in contexts where the management of (tau) is performed centrally using edge servers or gateway devices capable of real-time learning.

Thus, the optimal policy of the RL agent is defined as:

or, in the case of DQN:

The architecture generalised by expressions (23)–(26) implements a fully functional approach to system behaviour management without altering its internal structure. The RL agent, operating as a superstructure over the analytical core (13)–(15), performs adaptation to current load conditions, energy constraints, and service priorities (depending on the selected function (20) or (21)). This enables QoS-resilient, resource-aware control in practical edge-IoT scenarios, particularly in environments such as LoRaWAN, NB-IoT, or Smart Building Monitoring.

The construction of an effective policy for managing the shift parameter (tau) requires training the RL agent in a controlled environment that simultaneously reflects the analytical structure of the queuing model (see subsection 2.1) and allows flexible modelling of dynamic service conditions, losses, and energy consumption. Such simulation is a key instrument for validating the effectiveness of the chosen RL agent architecture and the reward function of the form (20), (21).

The simulator implements the integration of two components: the analytical core, which provides the computation of metrics (17)–(19), and the dynamic module, which updates the queue, overall costs, and energy expenditure. The current system state at step t is represented as ({s_t}=left( {{q_t},{rho _t},c_{{ef}}^{{left( t right)}},{L_t},{E_t}} right)). The RL agent selects an action ({tau _n} in {rm T}), corresponding to shift (tau _{n}^{{left( t right)}}), and the system transitions to a new state.

Within each simulation step of duration (Delta), the shift phase (tau _{n}^{{left( t right)}}) is implemented as a service delay. During this interval, arrivals continue, while processing is suspended. The new queue state is modelled according to the scheme:

where (Uleft( {tau _{n}^{{left( t right)}}} right)) is the number of new requests arriving during the shift, and (Dleft( {tau _{n}^{{left( t right)}}} right)) is the number of requests the system manages to process after the shift ends. The latter is computed as (Dleft( {tau _{n}^{{left( t right)}}} right)=hbox{min} left( {{q_t},phi left( {Delta – tau _{n}^{{left( t right)}}} right)} right)), which accounts for both queue limitations and the remaining service time. Losses are defined as the proportion of requests dropped due to buffer overflow: ({L_t}={{{N_{drop}}left( t right)} mathord{left/ {vphantom {{{N_{drop}}left( t right)} {Uleft( {tau _{n}^{{left( t right)}}} right)}}} right. kern-0pt} {Uleft( {tau _{n}^{{left( t right)}}} right)}}), and energy consumption is modelled as a linear function of the shift and flow variability: ({E_t}={e_0}+{e_1}tau _{n}^{{left( t right)}}+{e_2}c_{{ef}}^{{left( t right)}}). 

It is reasonable to train the RL agent under variable load conditions by following one of four typical scenarios:

• stationary (with constant (varphi), (phi));

• peak (with impulse load patterns);

• quasi-periodic (representing daily cycles in sensor networks);

• energy-constrained (with a variable energy budget).

To quantitatively assess the effectiveness of the strategy (pi left( s right)), the following metrics are accumulated:

where ({N_{rm T}}) denotes the number of iterations (simulation steps) during which the RL agent performs actions and the corresponding metric values are recorded.

The final stage of training the RL agent responsible for managing the shift parameter (tau) is the interpretation of the resulting policy (pi left( s right)) in terms of its stability, sensitivity to environmental changes, and generalisability beyond training scenarios. All actions of the RL agent are constrained within the discrete space ({rm T}), which ensures the preservation of the system’s spectral stability, particularly the invariance of the admissible pole placement in expression (10). The training procedure is formalised to ensure that the resulting policy (pi left( s right)) consistently reduces the average waiting time ({rm E}left[ W right]) while maintaining controlled losses ({rm E}left[ L right]) and balanced energy consumption ({rm E}left[ E right]). The sensitivity of the policy (pi left( s right)) to parametric changes was analysed through planned variation of (leftlangle {varphi ,{q_{hbox{max} }},{E_{hbox{max} }}} rightrangle) and the weighting coefficients ({kappa _i}).

To contextualise the proposed approach within the broader landscape of queueing and scheduling strategies for edge-IoT systems with strict QoS constraints, a comparative overview of relevant mathematical models is presented in the unnumbered table below. This summary outlines the structural and functional characteristics of classical stochastic queueing frameworks, threshold-based and protocol-imposed policies, task offloading schemes, and learning-driven delay management strategies. The models are compared in terms of their ability to regulate delay shifts, adapt to dynamic load conditions, and provide real-time responsiveness under decentralised operation. The final entry in the table summarises the distinctive contribution of this work, which formally integrates parameterised service delay control with reinforcement learning logic for locally autonomous decision-making.

Summary of Mathematical Models Considered in the Study.