The article proposes a novel mathematical framework for the analytical evaluation of the performance of a high-loaded 5G-IoT ecosystem operating in an environment with multiple sensor networks. The relevance of the study is driven by the rapid development of critical-use Internet of Things (IoT) systems and the necessity to ensure guaranteed Quality of Service (QoS) under conditions of high traffic intensity. The constructed model accounts for the specific features of 5G technologies, including NR Scheduling, HARQ, DRX, as well as packet fragmentation mechanisms and adaptive frequency hopping (AFH) in NRU mode. The developed approach integrates methods of mathematical modelling, queueing theory, and stochastic analysis, providing reliable predictive capabilities for key performance parameters, in particular, average response time, blocking probability, and system idleness. A comparative validation of the model was conducted using an open dataset of operational indicators from a real 5G-NB-IoT network, confirming its advantages over classical models. The findings of the study encompass models and methods for the analysis of modern information and communication technologies, intelligent traffic management, resource optimisation, and the evaluation of dependability in dynamic environments. Complex Systems & Network Data Analysis; analytical modelling; information technology; 5G-IoT ecosystem; sensor network; adaptive resource scheduling; energy efficiency; collision reduction.
Machine-Type Communications (mMTC), which are key components of 5G-IoT. Furthermore, ITU-T standards Y.3101 and Y.3113 emphasise the need for analytical evaluation of resource availability, latency, and data loss probability in critical services [5]. However, neither these standards nor traditional approaches to modelling loaded networks fully capture the specific nature of multisensor systems, which dynamically alter their topology, traffic types, and processing requirements. Consequently, there is a growing need to develop advanced analytical models capable of reliably forecasting the performance of the target information and communication system, taking into account the interaction between multiple sensor networks and 5G base stations under real-world load and constrained resource conditions. These challenges, aligned with the provisions of the aforementioned international standards, define the relevance of the present study.
Existing approaches to the analytical modelling of 5G-IoT ecosystem performance demonstrate a considerable diversity of methods – from classical queueing theory models to sophisticated hybrid frameworks that combine stochastic geometry, radio channel parameterisation, and service mechanisms [6–9]. Fundamental methods [10–12], such as the M/M/1, M/M/c, and MAP/PH/1 models and their modifications, are effective for a first approximation in modelling individual network components. However, they exhibit significant limitations in the context of 5G ecosystems due to their lack of adaptability to variable traffic loads, traffic prioritisation, NR Scheduling, and DRX/HARQ mechanisms, which are critically important for real-world operational scenarios [13].
Advanced approaches based on stochastic geometry, widely applied in LTE systems and early versions of 5G, are capable of accounting for the spatial distribution of users, signal blockage by obstacles, and environmental characteristics [14–16]. However, as noted in [17], these models insufficiently reflect the dynamics of service provision at the base station side, particularly in cases of adaptive multi-service traffic (eMBB, URLLC, mMTC). In 5G-IoT ecosystems, where sensor devices generate quasi-periodic or spontaneous traffic and transmission delay is of critical importance, there arises a need for multi-component analytical models that simultaneously cover both the physical transmission layer and service processes at the gNB level.
The study [18] proposes a two-level framework structure for modelling systems based on mmWave/THz communication, which can be adapted for 5G-IoT. The first level involves radio interface parameterisation (geometry, blockage, micro-mobility), while the second comprises a queueing service model. This approach enables the separate modelling of physical environment effects and traffic processing mechanisms at base stations. The application of such a framework facilitates the simulation of scenarios involving resource reservation, multi-connectivity, diverse traffic types, and prioritisation schemes.
Of particular interest are the models presented in [19], which are tailored to the specific requirements of URLLC and mMTC—key service categories within the 5G-IoT paradigm. Such models must account for both ultra-low latency and massive device connectivity, implying a necessary synergy between adaptive radio resource scheduling (NR Scheduling) and intelligent traffic optimisation algorithms. As stated in [20], traditional methods are incapable of accurately reflecting the effects of packet fragmentation, DRX mode switching, inter-flow prioritisation across varying levels of criticality, as well as system behaviour under excessive load conditions.
Another important trend is the advancement of analytical modelling methods for 5G networks operating in the millimetre-wave and terahertz frequency bands. The study [21] describes a modular framework that accounts for antenna directivity, atmospheric attenuation, blockage effects, and micro-mobility—factors characteristic of next-generation sensor networks. Such models can be integrated into broader 5G-IoT performance models to capture not only radio aspects but also traffic behaviour and request processing at the base station level, which is particularly relevant in scenarios characterised by high traffic density and critical latency requirements.
In addition, contemporary approaches [22], such as those involving Network Function Virtualization (NFV) and Network Slicing, introduce a new modelling paradigm in which each "slice" (logical subnetwork) is optimised for a specific traffic type. Within the context of analytical modelling, these approaches necessitate the construction of systems composed of multiple interacting service models, each with its own scheduling policy and acceptable QoS level.
In summary, existing approaches demonstrate considerable flexibility but fail to comprehensively capture all operational characteristics of real-world loaded 5G-IoT ecosystems. This underscores the need to develop new mathematical frameworks that integrate mechanisms for adaptive resource management, packet processing with fragmentation, dynamic frequency planning, and multi-channel routing services, all aimed at ensuring guaranteed Quality of Service under multisensor traffic conditions.
The object of this study is the operation of a 5G information and communication ecosystem involving the interaction of multiple sensor networks under high-load conditions.
The subject of the research is analytical models for evaluating the performance of 5G-IoT ecosystems, taking into account dynamic radio resource allocation, adaptive frequency planning, and other technologies inherent to the 5G platform relevant for the deployment of sensor networks.
The aim of the study is to develop an analytical framework for the reliable evaluation of the performance of a high-loaded 5G-IoT ecosystem, considering the specific features of radio resource scheduling, traffic typology, and the architectural characteristics of sensor networks.
To achieve this aim, the following tasks were accomplished: 1. The specific features of 5G-IoT ecosystem operation under high-load conditions were analysed.
2. A model of interaction between multiple sensor networks and a gNB base station was formulated, incorporating NR Scheduling, HARQ, and DRX.
3. Analytical expressions were formalised to evaluate blocking probabilities, system idleness, response time, and throughput.
4. The model was modified to account for packet fragmentation and its impact on communication efficiency.
5. The model was adapted to the conditions of dynamic frequency planning (AFH) in NR-U mode.
6. The proposed mathematical framework was validated using a real dataset and compared with classical models.
7. The representativeness of key performance metrics was investigated for characterising typical operational scenarios of 5G-IoT ecosystems.
2.
2.1.
In a 5G-IoT ecosystem, data transmission between the 5G base station (gNB) and sensor networks is implemented through dynamic radio resource allocation governed by NR Scheduling technology. All active sensor networks can initiate transmission via the Random Access Channel (RACH), after which the base station allocates uplink or downlink resources based on traffic demand and priority. The functioning of the 5G-IoT ecosystem during the aggregation of information flows from sensor networks can be conditionally divided into two operational modes:
- Time Division Mode (TDM) – an active traffic period during which sensor networks transmit data, and the gNB performs adaptive scheduling, allocating resources according to the current load.
- Traffic Control Mode (TCM) – a resource optimisation mode in which, under low-load conditions, the 5G base station may redistribute frequencies, enable Discontinuous Reception (DRX) for energy efficiency, or switch part of the radio resources to a low-activity state.
If, at any given moment, no sensor network has data to transmit, the system does not await the completion of TCM but can immediately activate DRX or adjust resource allocation. Consequently, TDM and TCM do not alternate according to a fixed schedule but are dynamically regulated based on current traffic conditions. Data transmission from a sensor network occurs in dedicated time slots (Transmission Time Intervals – TTI), which the gNB allocates based on real-time analysis of traffic requests. If a sensor network has data to send, it signals this through a Buffer Status Report (BSR), after which the gNB assigns the appropriate resources. Transmission success is monitored via the Hybrid Automatic Repeat Request (HARQ) mechanism, which enables retransmission with minimal delay in the event of packet loss. This approach enables flexible load management and prevents inefficient use of the radio channel. The present study considers a scenario in which the 5G base station operates under high-load conditions, where the probability of radio resource idleness due to traffic absence is negligible, and adaptive allocation mechanisms ensure a continuous flow of data from multiple sensor networks.
We describe a typical model of a 5G-IoT ecosystem designed to collect data from multiple sensor networks S 1,, S . Each sensor network s S comprises a set of Ns end devices (sensors, IoT devices) and one or more edge servers that perform preliminary data processing prior to transmission via the 5G network. In this study, we consider the most common scenarios of information interaction:
- Requests directed to the edge server within the sensor network (local internal interaction within the sensor network).
- Requests directed to an external server (in the global network) via the gNB base station. - Response transmission: either the local or external server processes the request and generates a response consisting of multiple packets, which are transmitted via the 5G connection.
Data transmission is carried out through dynamic resource allocation by the base station using NR Scheduling, while communication between sensor networks and the gNB is regulated via RACH and BSR mechanisms. If required, the HARQ mechanism ensures error correction and packet retransmission with minimal delay. This minimalist set of scenarios reliably reflects the actual data exchange mechanisms in real-world 5G-IoT ecosystems, optimising performance and minimising delays during the processing of information requests.
Since the aim of the study is to analyse the throughput of a 5G base station during data collection from multiple sensor networks, the interaction between individual sensor nodes within a local network s S and beyond is modelled in a simplified manner. A request from a sensor terminal within the network s is generated at an average interval 1 s following the reception of the last response packet from the gNB. Requests may be directed either to a local server within the sensor network or to external servers via the 5G infrastructure. External requests arrive at the base station as a Poisson flow with intensity 0 and are forwarded to the corresponding server or sensor device capable of performing the required processing. The server’s response is generated in the form of a set of packets or an aggregated Transport Block (TB) and transmitted back via the 5G connection. Within the scope of this study, it is assumed that the 5G network operates under highload conditions, where the probability of traffic absence across all sensor networks is negligible. It is also assumed that the TCM interval significantly exceeds TDM, allowing periods of low activity to be disregarded when evaluating throughput.
After passing through the 5G base station (gNB), a request is either processed by the corresponding server within the sensor network or forwarded to external computing resources via cloud infrastructure. If the request is directed to a local server within sensor network r , r 0 , it is processed internally within that network. Conversely, if the request is intended for an external system, i.e., r 0 , the transmission is carried out through the 5G infrastructure in the form of an aggregated TB or a set of packets. The routing path of the request is determined by a routing matrix Ps,r , where s 0 denotes external traffic originating from the global network. After being processed by the server r , the average response delay is 1 s,r , and the resulting response stream consists of Fs,r packets or aggregated data blocks. The response from the server is transmitted back via the 5G connection, undergoing buffering within the sensor network before being forwarded through the gNB base station. If the response originates from an external server r 0 , it is transmitted directly through the gNB to the sensor device that initiated the request. Upon receiving the final response packet, the sensor device may generate a new request to continue the data exchange process. The generation of requests and their processing by servers follow an exponential distribution, which is a typical approach for modelling high-loaded networks in 5G environments.
Based on the stated assumptions, a simulation was conducted to model the operation of a 5G base station (gNB) responsible for collecting and processing data from multiple sensor networks. Due to the high number of sensor nodes Ns and the substantial volume of responses from servers Fs,r , the simulation process proved to be resource-intensive, even for a relatively small number of sensor devices and their corresponding requests. The most effective approach for analysing the operation of a 5G-IoT ecosystem is analytical modelling, which enables the evaluation of system performance under varying load conditions. To this end, data transmission through sensor networks and the gNB is represented using a mixed exponential model, where requests from sensor devices circulate within the system as clustered data flows with dynamic routing.
In this context, each sensor network s S consists of a set of Single-Channel Sensor Devices (SCs) operating in continuous data collection and transmission mode, and Buffering Controllers (BCs) that manage request queues before data is sent to the 5G base station. An SC generates a stream of requests with an average intensity s and transmits them via the RACH to the BC, which temporarily buffers the packets if no resources are available at the gNB. Once resources are allocated, the BC forwards the packet to the gNB, which assigns processing resources through NR Scheduling. To model the interaction between sensor networks and the base station, the following variables are introduced:
- Tresp (s) Nss 1s is the average response time to a request from a sensor device within the network s ;
S - s is the total throughput of the 5G-IoT ecosystem;
s1 - Tproc s is the average processing time of requests at the sensor network server or in the cloud environment;
- s 1 Tproc s M s is the load coefficient of the BC in sensor network s prior to transmitting data through the 5G infrastructure, where M s represents the average number of requests waiting for processing in network s ;
- Pvis s, r is the visit ratio of server r by sensor network s , indicating the probability of routing a request to that server;
R - KS Pvis s, r is a non-zero visit ratio of sensor network s S , indicating the frequency r0 with which this network forwards requests to server r R , including both local and global routes.
Requests from sensor devices are received by the gNB, which assigns resources to them in accordance with NR Scheduling. The routing of requests is determined by the visit ratio matrix Pvis s, r , which specifies the target server for each request. In the case of a request directed to a local server of the sensor network r R , the average processing time is Tproc s , and the response is transmitted in the form of Frs individual packets or an aggregated Transport Block (TB). If the request requires external processing on a Cloud Server, the response arrives from the global network and is routed through the gNB to the initiating sensor device. Upon receiving the final response packet, the sensor device may generate a new request, thus maintaining a continuous flow of data. The visit ratio coefficients KS determine the frequency of traffic routing between sensor networks and servers. Fig. 1 visualises the interaction model between sensor networks and the gNB base station within the 5G-IoT ecosystem.
Considering that sensor networks may utilise various communication mechanisms (NB-IoT, LTE-M, 5G NR), delays in data processing and transmission are modelled using an exponential distribution. The analytical characterisation of the performance of the 5G-IoT ecosystem presented in Fig. 1 is conducted in the following sections.
The model of the 5G-IoT ecosystem shown in Fig. 1 is multiplicative in nature (in accordance with [23–25]). Considering this, classical methods [23] can be applied to characterise each sensor network s S in terms of performance metrics such as throughput s , average response time Tresp s , and probabilities Pidle s and Pblock s , which describe the absence of requests in the queue to the Buffering Controller (BC) of the sensor network and to the 5G base station (gNB), respectively. To carry out the evaluation, it is necessary to determine key characteristics of the target 5G-IoT infrastructure, such as the average request processing time on the sensor network server Tproc s and the waiting time for resources at the gNB TgNB s for s S .
To determine these characteristics, it is important to note that the operation of a 5G-IoT ecosystem under dynamic resource allocation resembles the structure of time-slotted networks [24]. Each sensor device within a sensor network may transmit data via the RACH, after which the gNB allocates resources in accordance with NR Scheduling. The duration of the time slot s , assigned for data transmission from sensor network s , is a stochastic variable with an average value that depends on the dynamics of request flows within the system.
Depending on the resource scheduling mechanism at the gNB, sensor network s receives resource allocations ms times during the observation period (in the case of uniform distribution – ms 1 ) for s S . The average waiting time for a resource at the gNB can then be estimated as: 1 TgNB s H gNB s qidle s S
m 2 s1 s s , where qidle s is the probability that a request arrives at an empty queue of the BC of sensor network s , and H gNB s
is the probability of successful resource assignment by the gNB for data transmission from sensor network s . The value Tproc s is determined using a similar formula, but with consideration of the data processing time at the sensor network server.
We define the average time slot duration s for sensor network s . Let us assume that the data transmission time of a packet, excluding the header, is denoted by td and is identical for all t packets, while the average packet transmission time is p . The probabilities of frame corruption for frames containing and not containing payload data are denoted as zd and z0 , respectively. Taking the introduced parameters into account, the average duration of a time slot is characterised by formula where
s Z poll s Zresp s Tack gNB ,
Z poll s td 1 Pblock st p s zˆblock s max s ,
Zresp s 1 zˆbloock s td 1 Pidle s tp s 2z0 ,
(
Zack s 1 zˆblock s 1 1Pidle s 1 1 Pblock s 1 zd ,
and Tack gNB denotes the transmission time of the acknowledgement from the gNB, s is the
signal propagation time from the gNB to sensor network s , max is the maximum propagation
delay in the system, zˆblock s Pblock s z0 1 Pblock s zd is the effective transmission blocking
probability, and the index s 1 in formula (
The probabilities of successful data transmission in the 5G-IoT ecosystem are defined by formulas
H gNB s 1 zˆblock s 1 zd 1 zˆblock s 1 , H BC s 1 zd 1 zˆidle s , where zˆidle s is determined analogously to zˆblock s , but in the context of probabilities Pidle s , and index s 1 is replaced by 1 in the case of s S ; H gNB s denotes the probability of successful resource assignment by the gNB for data transmission from sensor network s ; H BC s represents the probability of successful packet passage through the BC of sensor network s .
The probability that a request arrives at an empty queue is defined analogously to [23, 24]:
S
qidle s Pidle s s i ps,i M BC s
i0,is
(
i0,is where
S M BC s s i ps,i Fs,i i0,is ,
M gNB s s zˆ
S i ps,i i0,is , and Pidle s is the probability of no requests in the queue of the BC of sensor network s , Pblock s is the probability of transmission blocking through the gNB, s is the request generation intensity by sensor network s , ps,i is the probability of routing a request from network s to network i , and Fs,i is the average number of packets in the response after request processing at the server of network s .
Thus, considering known values of Pidle s , Pblock s , s for s S , expressions (
Pidle s 1 Tproc s M BC s , where the value of Qs is determined from the following system of equations:
1 S Qs ˆs rproc s KS rgNB s i1,is ps,i rgNB i Fs,irproc i
which 1ˆs 1s pss,,00 i1S,is pss,,ii , rproc s proc s 1 Tproc s 0 ps,0 Fs,0 ,
gNB s 1 TgNB s 0 ps,0 , rproc s QNss i1S,is QNii ps,i Fs,i proc s , rgNB s Ns K
Qs
S N S i ps,i gNB s i1,is Qi
,
and
(
Tmin tp Tack gNB 2td 0 min s s , t with p denoting the packet transmission time, transmission time, 0 is the signal propagation time, and s the maximum signal propagation time for sensor network s .
Tack gNB is the acknowledgement
By analogy with [23], for a large number of sensor nodes Ns , the order of probability Р0 is estimated using formula
is an auxiliary variable representing the average waiting time of a request prior to its
processing within the sensor network, and rgNB s is an auxiliary variable representing the
average waiting time for resource allocation by the gNB. The system of equations (
We estimate from above the probability that the gNB base station of a 5G-IoT ecosystem transitions into an energy-saving state due to the absence of packets for transmission from all sensor networks during the TCM period. The probability that the last transmitted packet was the only one across all sensor networks can be indirectly evaluated through the probability P0 of no pending requests in all BCs of the sensor networks:
PgNBidle P0TCM Tmin , S P0 exp proc s rproc s gNB s rgNB s Ns ln ˆsQs
s1 .
Expression (
P0IoT exp 2n0IoT sS1 Nˆss td 0 sS1 s . (13)
Thus, the developed analytical method can be applied if the upper bound PgNBidle computed
using expression (
To reduce the number of collisions in a 5G-IoT ecosystem, it is advisable to implement a packet
fragmentation mechanism. This approach enables retransmission of only the affected fragments in
case of channel errors, rather than the entire packet. Each packet, assuming a uniform average
n
transmission time, is divided into f fragments, where the average transmission time of all
fragments except the last is tmf (category 1), and for the final fragment – l
t f
case, expression 1 H gNB s in equation (
denote the probabilities of successful transmission of category 1 and category 2 fragments, respectively, and parameter zd is replaced with the fragment error probabilities zm and zl for categories 1 and 2.
In other equations of the mathematical framework, the parameters zd and tp are replaced with the averaged values zd f and tmean , which are determined using formulas f zd f 1 n f 11 nzfm 1 zl , (14) n f 1 1
Hs f 1 H s f 2 , where Hs f 1 and
tmfean tmf n f 11 zm tl f 1 zl
n f 11 z f 1 zl
,
(15)
f
where tmean is the average transmission time of a fragment, taking into account that the
majority of the packet consists of standard fragments of category 1 with length tmf , while only the
final fragment belongs to category 2 and has a different length tl f . In condition (
S Tmin n f 1tmfean tl f nf Tack gNB 2 td 0 s (16) s1 .
Thus, the method can be readily modified to account for the distribution of packet lengths, which is particularly relevant for sensor networks where both short messages (e.g., control signals or telemetry data) and longer packets containing aggregated or multimedia data are present.
Another modification of the proposed mathematical framework involves adaptation to dynamic frequency planning in a 5G-IoT ecosystem based on Adaptive Frequency Hopping (AFH) technology in NR-U (Unlicensed NR). In this mode, all sensor devices operate on a single frequency for a fixed time-frequency interval Tdewll , after which they are switched to a different frequency (with a switching delay tc ). During frequency switching, terminals temporarily lose synchronisation with the network. Accordingly, a sensor device waiting for resource allocation to transmit a packet (or its fragment) postpones the transmission if the expected transmission time, calculated based on the maximum signal propagation time max (including acknowledgement), exceeds the remaining time in the current frequency interval. Such a scenario is referred to as delayed transmission.
The average waiting time between a delayed transmission and the end of the frequency interval (including the switching time tc ) can be estimated using formula
tc Tmin 2 , (17) where the minimum packet transmission time is defined according to equation (16), but with max replaced by min s . In the case of fragmentation, instead of the average packet transmission t time p , the averaged value from equation (15) is used.
As shown in [24], it can be assumed (and this is confirmed by simulation modelling) that the
adaptive frequency hopping mode differs from the stationary regime only by silence periods with
an average duration at the end of each frequency interval Tdewll . Therefore, in formulas (
Let us begin this section by presenting the process and results of the verification of the mathematical framework proposed in the article. The verification involved a detailed evaluation of the adequacy of the analytical model presented, as well as empirical validation of its effectiveness and practical relevance. The objective of the verification was to empirically demonstrate that the developed model accurately describes the operation of a high-loaded 5G-IoT ecosystem, provides more reliable results compared to classical approaches, and can be effectively applied for the practical analysis of network performance.
To verify adequacy, we consistently carried out a series of actions structured into three key stages. The first stage involved the selection of classical mathematical models of network performance widely used in the field of information and communication systems. Particular attention was given to the ability of these conventional models to describe functional processes characteristic of high-loaded 5G-IoT ecosystems, with a specific focus on radio resource allocation, adaptive traffic scheduling, and dynamic request management. The second stage consisted in selecting a representative dataset containing sufficient information on the operational results of real 5G-IoT ecosystems in terms of the parameters used in the formalisation of the proposed mathematical framework. At the third stage, we visualised the comparison results between the proposed model and classical counterparts using the research-specific performance metrics, with the determination of confidence intervals and discussion of the findings. The analysis focused on key performance parameters such as latency, throughput, and request blocking probability, which are critical for the operation of a 5G-IoT ecosystem.
In implementing the first stage, we focused on selecting classical mathematical models for traffic flow and load evaluation in branched information and communication networks. Traditional Markov queueing models such as M/M/1 and M/M/c serve as fundamental analytical tools for systems with randomly arriving requests. The M/M/1 model assumes a single queue with exponentially distributed inter-arrival and service times, enabling analysis of individual network nodes. The M/M/c model extends this approach by incorporating multiple parallel service servers, offering a more adequate representation of modern multichannel 5G-IoT networks. However, these models have significant limitations, as they do not account for adaptive resource scheduling typical of 5G systems and fail to capture the impact of mechanisms such as NR Scheduling. Iterative analytical methods for evaluating network load allow for a more accurate analysis of radio resource status and allocation mechanisms. These methods are based on repeated computations of the steady state of the telecommunication system, considering dynamic load parameters and adaptive traffic control algorithms. This approach enables the estimation of request blocking probabilities and resource allocation efficiency in high-load scenarios. At the same time, classical analytical methods remain limited when dealing with the complex adaptive mechanisms of 5G-IoT, such as dynamic traffic prioritisation and the use of HARQ to minimise packet loss. In contrast, the proposed mathematical framework integrates elements of adaptive resource management and scheduling mechanisms tailored to high-loaded 5G-IoT ecosystems. This potentially offers a more realistic reflection of the functioning of such ecosystems compared to traditional approaches (M/M/1 and M/M/c).
For the verification of the proposed mathematical framework, we selected the open-access dataset “A Large-Scale Dataset of 4G, NB-IoT, and 5G Non-Standalone Network Measurements” [26]. This dataset was developed by a research team from Simula Research Laboratory, Ericsson Research, Karlstad University, Sapienza University of Rome, and other institutions. It contains results from a seven-week campaign of experimental data collection on the real-world operation of commercial mobile networks in Rome, Italy. The dataset covers three major mobile communication technologies: LTE (4G), NB-IoT, and 5G NR (Non-Standalone), and includes measurements obtained across a variety of usage scenarios—ranging from stationary to dynamic (pedestrian and vehicular) contexts. Its representativeness for our study is explained by its scale, openness, and, most importantly, the breadth of captured characteristics directly related to the performance and reliability of 5G-IoT ecosystems. Specifically, the dataset includes parameters of radio coverage (RSRP, RSRQ, SINR), channel characteristics (TBS, Modulation and Coding Scheme), as well as indicators of data transmission quality such as round-trip time (RTT), packet delay variation (PDV), interface-level interactions, packet loss, and throughput. The RTT metric was measured under real-world conditions using Speedtest sessions and online gaming traffic, making the data highly relevant for modelling latency in practical 5G-IoT scenarios.
Within the scope of our study, the RTT parameter is employed as the primary verification
metric. It is particularly critical for IoT applications with stringent response time requirements,
such as telemetry, real-time control, and automated management systems. In the proposed
mathematical framework, the response time (or the latency between request generation and receipt
of the corresponding response) is modelled by the expression Tresp s 1 s s , where s
denotes the intensity of new request generation, and s represents the actual throughput of
sensor network s S within the 5G-IoT ecosystem. This expression is presented in formula (
As previously noted, the classical analogues selected for comparison with the proposed mathematical framework are the M/M/1 and M/M/c models. The M/M/1 model is used to describe a system with a single queue and a single server. In the context of this basic model, the average time a request spends in the system (including both queueing and actual service time) is given by RTTM /M /1 1 , where represents the intensity of the Poisson arrival process, and 12 is the parameter of the exponential distribution corresponding to the average service rate of the single server. To avoid discontinuities in the corresponding function graph, a constraint was introduced. The M/M/c model is a generalisation of M/M/1 and describes a system with c parallel servers (for example, in cases where the base station processes requests in parallel across multiple channels). The RTT in the M/M/c model is defined by expression RTTM /M /c 1 c!1c c 11 , where с is the system load metric. All parameters of the classical models were selected to ensure that the RTT estimates derived from them closely approximate the real-world data from the dataset.
Fig. 2 presents a comparison of RTT estimates in a high-loaded 5G-IoT ecosystem, calculated using the proposed model (red line), the M/M/1 model (blue line), and the M/M/c model (green line). The black line represents the empirical RTT values obtained from the dataset. The grey shaded area around this curve represents the confidence interval, reflecting the fluctuation of RTT under real-world operating conditions. The high data dispersion indicates significant variability in latency across different network load scenarios.
An analysis of the real data dynamics in Fig. 2 reveals a gradual increase in RTT as the load grows, represented by the argument , which denotes the input flow intensity. In the low-load range 2 , RTT values remain low, as the system operates in a regime where the servicing capacity exceeds the volume of incoming requests, resulting in minimal delays. In the mid-load range 2 6 , a noticeable increase in RTT is observed, indicating a gradual saturation of network resources and the emergence of queue formation within the system. Under 6 , the latency continues to grow, though at a slower rate, as the system reaches a relatively stable operational region under high-load conditions. The confidence interval (grey area) reflects the variability of measured RTT values across different conditions, driven by the heterogeneity of the network environment and the influence of adaptive resource management in 5G. In the masked region 4, 6 , empirical data were unavailable; however, interpolation of the confidence interval allows for an estimation of the likely RTT distribution within this range.
The red line representing the proposed model demonstrates a high degree of alignment with the empirical data, particularly in the mid- and high-load ranges . In the low-load region 2 , the model slightly overestimates RTT, which can be attributed to its design focus on providing more accurate predictions of system behaviour under high-load conditions. It is important to note that, beyond the masked region, the proposed model naturally continues the trend of the empirical data, reinforcing its predictive capability. In contrast, the classical M/M/1 model (blue line) exhibits substantially different behaviour. It predicts a sharp increase in RTT with increasing , which is a typical characteristic of systems with a single server and an unbounded queue. This can be observed in the graph, where for 6 , the RTT values predicted by the M/M/1 model significantly exceed the empirical results. The main reason for the discrepancy between M/M/1 and the real data lies in the model’s inability to account for adaptive resource management, which is intrinsic to 5GIoT systems, as well as its lack of support for parallel request servicing. The green line, representing the M/M/c model with с 3 , exhibits a more moderate increase in RTT compared to M/M/1, which can be attributed to the presence of multiple service channels. However, RTT values in this model remain substantially lower than the empirical measurements, particularly under high-load conditions , indicating its overly optimistic assumption of uniform request distribution across service channels. In reality, in 5G-IoT ecosystems, channel load is dynamically variable and influenced by numerous factors, including traffic type, adaptive radio resource scheduling, and retransmission mechanisms (such as HARQ and ARQ), which are not considered in the M/M/c model.
To visually demonstrate the effectiveness of the proposed mathematical framework, a block of
three-dimensional visualisations was developed (see Figure 3), illustrating the dynamics of key
performance parameters of the 5G-IoT ecosystem model for a selected dataset instance under
varying operational conditions. The visualisation is based on the analytical expressions presented
in Sections 2.2 and 2.3 of the article, particularly formulas (
As independent variables, we selected the input request intensity 0.5,1.0,,10 , which characterises the load arriving at the base station from multiple sensor devices, and the number of devices in the sensor network Ns 1,10 , which influences the overall throughput of the subnet. The selected range for Ns reflects a typical volume of sensor nodes within a single communication domain in a distributed environment. The load coefficient was fixed at level Q 0.8 , simulating a near-saturation operating condition characteristic of critical applications. For the baseline performance visualisation, we considered a 5G-IoT ecosystem scenario with a single representative sensor network s S under fixed routing conditions. This setup isolates the effects of request intensity and device count on performance metrics, avoiding interference from inter-network interaction effects, which will be the subject of subsequent experiments.
The three-dimensional visualisation Tresp s , Ns presented in the block Figs. 3 revealed a
consistent increase in latency with rising input traffic intensity , particularly under conditions
where the sensor network comprises a small number of devices. This result is based on formula (
To confirm the practical effectiveness of the proposed mathematical framework, three targeted
experiments were conducted, the results of which are presented in Fig. 4. Each of these
experiments provides informative representation of a corresponding key operational scenario
within a 5G-IoT ecosystem, namely, the energy-saving mode of the base station (formula (
The objective of the first experiment was to evaluate the probability of the gNB transitioning
into the DRX energy-saving state in the absence of requests during the control period TCM. The
calculation was based on an exponential dependency (formula (
The objective of the second experiment was to determine the impact of packet fragmentation on the probability of communication channel blocking. The calculation of the effective length of a fragmented packet was performed using formula (14), taking into account the average fragment length and the length of the final segment. To evaluate the blocking probability, expression (15) was applied, which models its dependency on traffic with exponential saturation characteristics. The computational procedure was implemented in two modes: with fragmentation and without it, using the following fixed and independent parameters: n f 4 , zm 0.045 , zl 0.12 , 0.5,10 . This experiment characterises the model’s capability to account for resource holding time reduction effects resulting from traffic segmentation.
The third experiment tested the model’s adaptability to frequency dynamics under NR-U conditions. Within this scenario, the processing and response times were adjusted according to formula (16), which accounts for time losses due to frequency switching. The total response delay was evaluated using formula (17), which incorporates the non-linear influence of parameter Tdwell , varied within the range Tdwell 5,30 ms. During modelling, the values of parameters Tresp , Tproc , s were balanced using appropriate correction coefficients, which were set proportionally to changes in the available frequency window. This experiment focused on validating the model’s adequacy under adaptive frequency planning, which is typical of scenarios with high interference levels and spectrum usage constraints.
The results of the first experiment, presented in Fig. 4, demonstrate an exponential decrease in the probability of the gNB base station transitioning to the DRX energy-saving state as the number of sensor networks increases. This leads to a key practical conclusion: scaling the ecosystem by increasing the number of devices contributes to the stabilisation of its active state. As the number of nodes grows, the probability of a complete absence of global traffic drops, even when the load on each individual local sensor network remains moderate. From the second experiment, a clear distinction can be observed between the packet fragmentation and non-fragmentation modes. Fragmentation proves to be an effective strategy for reducing blocking probability, especially under moderate load conditions. This effect can be explained by the fact that dividing transmitted data reduces the resource holding time per device, which in turn lowers contention for access channels. Practically, this supports the application of fragmentation as a flexible access control mechanism in overloaded network segments, particularly at the MAC layer. The third experiment analysed response delay under AFH operation mode in the NR-U frequency band. The dependencies visualised in Fig. 4 show a sharp increase in latency as the parameter Tdwell , which defines the dwell time on a single frequency, decreases. The region below 10 ms is particularly critical, where time losses due to frequency switching begin to outweigh effective data transmission. From a practical standpoint, this highlights the need for careful tuning of frequency planning parameters in highinterference environments. Taken together, the results of the three experiments confirm the model’s capability to accurately capture the complex interplay between architectural, protocollevel, and frequency-level components of a 5G-IoT ecosystem.
The relevance of this research topic is driven by the rapid rise in the importance of 5G-IoT ecosystems in mission-critical domains, where the efficient aggregation of traffic from multiple sensor networks with guaranteed real-time Quality of Service (QoS) is a fundamental requirement for system operation. Traditional analytical approaches fail to account for the dynamic nature of such networks, which manifests in topological variability, traffic fragmentation, the need for energy efficiency, and adaptation to frequency instability. Therefore, the development of a novel mathematical model capable of accurately representing the operation of high-loaded 5G-IoT ecosystems is both scientifically justified and practically essential.
The scientific novelty of this work lies in the formalisation of a multi-component mathematical framework for the analytical evaluation of the performance of 5G-IoT ecosystems, taking into account key factors such as NR Scheduling, packet fragmentation, DRX mode, HARQ mechanisms, and adaptive frequency hopping in NR-U mode. The proposed model is the first to integrate the interaction of multiple sensor networks with a gNB base station within a generalised system of equations, enabling the estimation of blocking and idleness probabilities, average response, processing, and waiting times, as well as the evaluation of boundary operating regimes with consideration for energy-saving mechanisms.
The conducted experiments confirmed the adequacy and high effectiveness of the proposed model. Verification was performed using the open-access dataset from Simula Research Lab, which contains seven weeks of data on the real-world operation of 5G, LTE, and NB-IoT networks. The analytical estimation of the Tresp showed a deviation of less than 12% compared to empirical RTT values, and within the medium load range 2 6 , this error was only 6–9%, significantly outperforming the accuracy of classical models such as M/M/1 and M/M/c, which exhibited errors of up to 40%. Within the experimental block, it was also demonstrated that the probability of the gNB transitioning to the energy-saving DRX mode does not exceed 2% when operating with more than 30 sensor networks at a request generation intensity 1 , confirming efficient system utilisation. Moreover, packet fragmentation with parameters n f 4 , zm 0.045 , zl 0.12 resulted in a 17% reduction in channel blocking probability compared to the non-fragmented scenario. Adaptation to frequency dynamics in AFH mode, with parameters Tdwell 10 and tc 2 , led to an 8–11% reduction in effective throughput, which was accounted for in the model through modified waiting time coefficients.
The practical value of the developed analytical framework lies in its ability to safely predict system behaviour under load without the need for resource-intensive simulations. This opens promising opportunities for applying the model in real-world 5G-IoT infrastructure design, overload risk assessment, optimisation of energy-saving modes, and adaptation to frequency instability. The proposed approach accounts for dynamics at both the physical channel level and the logical traffic routing level, making it suitable for multi-service scenarios in mission-critical applications.
Future research will focus on extending the model to incorporate heterogeneous QoS traffic classes (URLLC, mMTC, eMBB), developing integrated models for multi-gNB topologies, integrating Network Slicing functionality, and designing analytical mechanisms for monitoring performance recovery following peak load conditions.
Acknowledgements
The authors are grateful to all colleagues and institutions that contributed to the research and made it possible to publish its results.
Funding
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