An IoT-Based Traffic Management System Using a Mean Fitness-Oriented Dragonfly Algorithm for Traffic Flow Prediction

he extreme urbanization experienced in recent years and the ever-growing size of the vehicular population on the road have resulted in extreme traffic conditions experienced in cities all over the globe [1]. This congestion causes a lot of economic losses, environmental pollution, and the general damping of the quality of life of commuters. With the inability of the transportation facilities to meet the rising demand, smarter traffic management systems have turned into a center of attention of contemporary urban planning. Traffic flow prediction can be considered among the numerous elements of the intelligent transportation systems (ITS) because it is capable of enabling proactive congestion management and effective resources allocation.

Traffic flow prediction is defined as the process of predicting future traffic status using the historical and current data of the traffic status. The traffic light management, recommended navigation routes, response to an emergency situation and optimization of the mass transportation may be enhanced through proper forecasting [2], as shown in Figure 1.

Despite such profits, there still exist challenges [3-5]. The deep learning models are often quite resource intensive in both their computer demands and training data requirements which may not be easily available. Furthermore, such models often resemble the black boxes and this does not create a lot of accessibility to the derivation of estimates and this is a major problem especially in situations where transparency in decision-making is influential. In addition, it would take a lot of human intervention to modify the architecture and nature of such simulations based on different urban structures or circulation patterns.

Application of traffic forecasting systems in real-time is a critical condition. The requirement of the rapidly evolving context puts models that need to adapt healthily to the new data within a very short duration of time, which requires not only a high predictive performance but also performance and adaptability [6]. This has made scholars explore ways that can be used to strike a balance between complexity of models and efficiency of runtime and still offer meaningful insights. The assessment of traffic prediction model and its analysis is enabled by the open datasets and transportation benchmarks [7]. Cities and research institutions are more and more sharing databases of traffic, determined by inductive loops, radar, and floating car data, to compare the performance of their models in different conditions. Non-homogeneity of data and privacy concerns however make the process of standardization of model training and evaluation challenging.

Figure 1 shows the multiple factors, which have influences on the forecast of traffic flow. The most important part of the discussion is the traffic flow data such as parameters such as the speed and density. This data is affected by time, such as the daily activities and seasonal changes whereas environment variables like climate and activities within the traffic like accidents and constructions are also taken into consideration [8-10]. All the mentioned characteristics define the current state of traffic. Furthermore, the external condition, like the presence of the public holidays and special events, adds to the unpredictability. All these influencing parameters are uploaded into the analysis layer that is mandated with predicting the most likely traffic trends to enable effective functioning of the traffic.

• To construct a proper traffic flow prediction model based on the real-time and past traffic data with the help of such significant input features as Average True Range (ATR), Exponential Moving Average (EMA), Relative Strength Indicator (RSI), and Rate of Change (ROC).

• To minimize the number of states and the performance of Hidden Markov Model (HMM) to achieve higher prediction accuracy through the integration of metaheuristic approach overcoming the drawback of fixed-state models.

• To compare the results of the optimized model with the traditional classifiers (namely, HMM, ANN, RNN, and SVM) in various traffic conditions, namely, weekdays, holidays, and both ways of the road.

Experimental environment the traffic flow prediction model was coded in MATLAB. Traffic variables were observed in real-time, where the following variables were recorded: date, day, time sessions, and the number of vehicles on both sides of the road. To pick up the differences in the traffic flow, each day was split into seven-time sessions between midnight and midnight. There were four different test cases considered, that is, left side weekdays, left side holidays, right side weekdays, and right-side holidays. The prediction accuracy and error analysis were used to compare the proposed model to existing classifiers, which include HMM, ANN, RNN and SVM. Also, the optimizing ability of the metaheuristic algorithm was tested through a series of iterations (0 to 100) to judge the convergence behaviour. The efficiency and soundness of the proposed solution were confirmed with the aid of different evaluation measures including the number of vehicles, waiting time, queue length, and computational time.

The suggested method focuses on the construction of a better predictive model of the crowd traffic in the city by fine-tuning the traditional HMM and adding an optimization process in the form of metaheuristic in Figure 2. With the increased urban population and traffic movement the necessity to have decent and reliable traffic flow prediction has increased.

Figure 2. Advanced process of the suggested MHMM system for smart traffic flow forecasting

Non-linearity, time varying nature and external dependencies of the traffic data demand an adaptive model of prediction that can dynamically moderate the mapping process between observed and latent states of the traffic. The proposed approach is aimed at adaptation of MHMM with a recently developed optimization algorithm the MF-DA that is specifically designed to optimize number of hidden states and the values of model parameters that are incorporated into the HMM model.

This traffic flow prediction model, which is created in the work, starts with processing of real-time traffic data. The variables gathered are number of vehicles, time, location of the road segment and direction of traffic. Using this information, four main characteristics are derived namely; ATR, EMA, RSI and ROC.

These are indicators which are calculated using time series statistical operations and they provide an informative picture on the traffic trends and anomalies. The chosen features are used as inputs into the main MHMM framework. The feature extraction mechanism is the initial step of the presented process. ATR can be used to measure variability or volatility in the traffic flow and the calculation is done based on the true range of the range of values series at a chosen interval. ATR mathematically is indicated as:

$A T R=\operatorname{Aver}(V S, m)$   (1)

Here, VS signifies the actual range for each interval, whereas m indicates the total number of periods utilized for the average movement computation, Aver signifies the mean value calculated over m successive periods.

The EMA is used to provide a smoothed averaged of flow of traffic across time, assigning more significance to recent results. The EMA is articulated by the recursion formula:

$E M A=\left(S-E M A_n\right) \cdot E+E M A_v$    (2)

S represents the current flow of traffic value, EMA_v denotes the preceding EMA value, and E signifies the smoothing effect.

In this Eq. (2), S represents the latest traffic reading, EMA_v is the preceding EMA value, and E is the smoothing parameter that is specified as:

$D=\frac{2}{t+1}$    (3)

where, t signifies the total amount of data points utilized for the ordinary moving average.

The Relative Strength Indicator (RSI) measures the extent of recent fluctuations in traffic to assess overbought or oversold states within the traffic system. The RSI is calculated as follows:

$R S I=100-\left(\frac{100}{1+S B}\right)$    (4)

SB denotes the smoothing average of the ratios of upward and downward movements in traffic data.

The ROC quantifies the percentage variation in traffic flow throughout a specific amount of time intervals. It serves to identify momentum changes and may be mathematically articulated as:

$R O C=\left(\frac{C V-P V}{P V}\right) \times 100$   (5)

CV denotes the current traffic flow, whereas PV refers to the traffic flow from a selected prior time interval.

All these characteristics form the observation set of the MHMM. These features are them subsequently processed in the MHMM to forecast the underlying traffic states. Standard HMMs are probabilistic models that are used to represent a system whereby, there is an assumption of a Markov process with a hidden state. But it is one of the primary shortcomings of classic HMMs that they have a strict definition of the hidden states amount and this is predetermined and is not customized depending on data. This limitation has the tendency of resulting to not-so-good modelling of intricate traffic patterns.

In an attempt to circumvent this shortcoming, the suggested approach is an adaptation of the standard HMM, through the incorporation of a state count optimization mechanism. The MHMM is built with the help of three major blocks including the state transition probability matrix Q, the observation probability matrix T, and the initial state probability distribution \rho. The formulations of the elements of each component are as shown below:

The transition probability matrix Q is given:

$P_{m n}=A\left(m_{v+1}=e_n \mid m_v=e_m\right), m, n=1,2, \ldots, G$   (6)

m_v and m_v+1 represent the current and subsequent hidden states, e_m and e_n denote particular state labels, and G signifies the overall number of hidden states.

The observed probabilities matrix T associates each hidden state with the seen characteristics and is denoted as:

$\begin{gathered}r_n(l)=B\left(V_v=t_l \mid n_v=e_m\right), \quad l=1,2, \ldots, J, \quad n =1,2, \ldots, G\end{gathered}$    (7)

Here, V is the traffic feature that was seen at time v, t_l denotes the lth feasible observations, n_v denotes the hidden state at time v, e_m denotes a particular hidden state, J stands for the total quantity of observations, and G reflects the overall quantity of hidden states.

The initial state distribution of probabilities ρ is as follows:

$\rho_m=B\left(m_1=e_m\right), \quad m=1,2, \ldots, G$   (8)

$\rho_m$ is the initial possibility of commencing in hidden state $e_m$, where $G$ denotes the total amount of hidden states. It must meet the following probabilistic requirements:

$\sum_{m=1}^G Q_{m n}=1, \quad \sum_{l=1}^J v_n(l)=1, \quad \sum_{m=1}^G \rho_m=1$  (9)

$Q_{m n}$ represents the probability of transition among hidden states, $v_n(l)$ denotes the observation probabilities of the 1 -th features from state $n$, and $\rho \mathrm{m}$ signifies the starting probabilities of state m; G indicates the total number of hidden states, whereas J refers to the total number of observer types.

This structure connects the observed sequence $\mathrm{V}=\left\{\mathrm{v}_1, \mathrm{v}_2\right.$, $\left.\mathrm{v}_{\mathrm{K}}\right\}$ and the hidden state sequencing $\mathrm{L}=\left\{1_1, 1_2, \ldots, 1_{\mathrm{K}}\right\}$ using probability inference, aiming to ascertain the most probable sequence of hidden states that produces the seen data. Establishing the correct amount of hidden states H is a complex problem that greatly influences the reliability of predictions.

In order to optimize the state count to select the best possible combination, and, to improve the learning capacity of the HMM, the MF-DA is suggested. The MF-DA is an optimization algorithm model that borrows its behaviour on the dragonflies in nature, e.g., separating, aligning, flocking, and leaving enemies to find food. The algorithm in this improved version is also fitted with a fitness-based adjustment mechanism that employs the evaluation and optimization of candidate solutions in algorithms within the predictive performances.

The MF-DA optimization procedure is driven by a fitness (objective) function and in this study, the fitness function is referred to as the maximization of the classification accuracy of the MHMM. The objective function PE is Formulated as:

$\mathrm{PE}=\max (A c c)$   (10)

whereas, PE denotes the effectiveness evaluations value, Acc signifies the accuracy of the predictive model.

The MF-DA proceeds by instantiating a population with dragonflies, each of which represents one potential solution that is characterized by a counting-of-states problem configuration. A set of behavioral rules is then repeatedly applied to the population re-creating the natural behavior of dragonflies.

The average velocity of the neighbors controls the alignment behavior of the swarm and mathematically this can be expressed as:

$C_m=\frac{1}{N-a} \sum_{J=1}^N P_k$ (11)

$C_m$ denotes the measure of alignment or cohesiveness, N signifies the quantity of surrounding people, $a$ indicates a modifications constant, and $P_k$ indicates the velocity or location of the k-th neighbor.

The separation element, which mitigates overpopulation, is characterized as:

$D_m=\sum_{k=1}^N\left(R-R_k\right) \cdot p$  (12)

$D_m$ is the separation significance, R is the positioning of the current person, $R_k$ is the positioning of the k -th neighbor, p is the separating weight, and N is the overall amount of neighbors.

The cohesive behaviour, which compels dragonflies to orient towards the swarm's centre, is articulated as follows:

$P_m=\frac{1}{N_c} \sum_{k=1}^{N_c} R_k-R$   (13)

$P_m$ denotes the cohesiveness value, $R_k$ signifies the position of the k -th nearby person, R represents the current member's position, and $N_c$ indicates the number of surrounding people taken into account for cohesion.

To figure out the movement regarding food sources, use:

$E_m=R^{+}-R$   (14)

$E_m$ is the draw to the food source, $R^{+}$is the food source's location, and R is the person's present position.

$E_m=R^{-}-R$ (15)

By including all behaviours, the final step vector $\Delta \mathrm{R}$ is calculated for updating the locations of the dragonflies:

$\begin{gathered}\Delta R(m v+1)=p D_m+a C_m+d P_m+e E_m+c F_m +z \Delta R(m v)\end{gathered}$    (16)

$R(\mathrm{mv}+1)=R(\mathrm{mv})+\Delta R(\mathrm{mv}+1)$  (17)

$\Delta R(m v+1)$ represents the revised velocity or movements vector, $D_m$ denotes the separation element, $C_m$ signifies the alignment element, $P_m$ indicates the cohesion element, Em reflects the attraction to food, Fm denotes the repulsive force component exerted by adversaries in the dragonfly optimizing framework., $\Delta R(m v)$ refers to the prior velocity, and $p, a, d, e$, $c, \mathrm{z}$ are the corresponding weight parameters.

Whenever nearby solutions are unavailable, then global exploration is guaranteed by using a Levy flight mechanism, which is defined as:

$R(\mathrm{mv}+1)=R(\mathrm{mv})+\operatorname{Levx}(w) \cdot R(\mathrm{mv}+1)$   (18)

$\operatorname{Levx}(b)=0.01 \cdot \frac{s_1-\delta}{\left|s_2\right|^{1 / \eta}}$ (19)

where, R(mv+1) denotes the revised location after a stochastic exploration step, Levx(w) signifies the Levy flight functions executed with dimension w, and R(mv) indicates the present state. Levx(b) is the Levy flight values in dimensions b, s₁ and s₂ are random parameters within the interval [0, 1], $\eta$ represents the stable index of the Levy distribution, and $\delta$ is a scaled constant derived from the Levy distributed formula.

The overall MF-DA optimizing procedure is delineated by the following algorithm:

The optimum configuration from MF-DA is then implemented in the MHMM for final trained and predictions. The training procedure involves calculating the HMM variables $\lambda$=(Q,T,ρ) by an estimation of maximum likelihood. The probability of observing a sequence given the model is optimized by iterative methods like the Expectation maximization algorithm, often used in Hidden Markov Model training. This technique yields a trained MHMM model proficient in predicting traffic flow by analysing observable traffic characteristics to infer traffic states computationally.

The second Algorithm demonstrates the comprehensive training and prediction process of the MHMM using the optimum state configurations derived from MF-DA.

Upon selecting the best state count using the MF-DA method, the MHMM becomes operational with the specified quantity of hidden states. The last stage is training the model to ascertain the probabilistic parameters—transition probability Q_mn, observable probability v_n (l), and starting state possibilities ρ_m—that characterize the stochastic framework of the system. The variables are evaluated to optimize the chance of witnessing the training patterns. The Baum-Welch method, a specific instance of the Expectation-Maximization (EM) technique, is often used for this operation.

Let S=(s₁,s₂,...,s_V) denote a series of observable derived from traffic data (i.e., attributes such as ATR, EMA, RSI, and ROC), and let P=(p₁,p₂,...,p_V) signify the associated hidden state pattern, where each p_t∈{R₁,R₂,...,R_G}. The objective is to identify the set of variables λ=(Q,T,ρ) that optimizes the probability ratio.

$\mathrm{Q}(S \mid \lambda)=\sum_P Q(\mathrm{~S}, Q \mid \lambda)$    (20)

The calculation of $\mathrm{Q}(S \mid \lambda)$ requires the determination of forward probabilities $\alpha \_\mathrm{v}(\mathrm{m})$, which are defined as the likelihood of being in state $R_v$ at time $v$ while observing the partial pattern $s_1, s_2, \ldots, s_v$. The calculation is performed recursively in the following manner:

Initialize:

$\alpha_1(m)=\rho_m \cdot v_m\left(s_1\right), \quad 1 \leq m \leq G$ (21)

$\alpha_1(\mathrm{m})$ represents the initial forwards possibility, $\rho_{\mathrm{m}}$ denotes the starting likelihood of observing state $\mathrm{m}, \mathrm{v}_{\mathrm{m}}\left(\mathrm{s}_1\right)$ indicates the observed possibility of seeing $s_1$ in state $m$, and $G$ signifies the overall amount of hidden states.

Induction:

$\begin{gathered}\alpha_v(m)=\left[\sum_{m=1}^G \alpha_{v-1}(m) \cdot Q_{m n}\right] \cdot v_n\left(s_v\right), \quad 2 \leq v \leq V, \quad 1 \leq m \leq G\end{gathered}$    (22)

Terminate:

$Q(S \mid \lambda)=\sum_{m=1}^G \alpha_V(m)$ (23)

$\alpha_v(m)$ denotes the forward possibility at time v for state m, $\alpha_{\mathrm{v}-1}(\mathrm{~m})$ represents the preceding forward possibility, $Q_{m n}$ indicates the state transitioning possibility, $v_n\left(s_v\right)$ signifies the observable possibility for observations $s_v$ in state n , and G refers to the overall number of hidden states. $Q(S / \lambda)$ denotes the general probability of the observed sequence S given the framework $\lambda, \alpha_V(m)$ represents the forward probabilities at the last time step $V$ for state m, and $G$ signifies the total count of hidden states.

Additionally, backward probability $\beta_v(m)$ denote the likelihood of detecting the subsequent sequence $\mathrm{s}_{(\mathrm{v}+1)}, \ldots, \mathrm{s}_{\mathrm{v}}$, conditional on the system being in state Rm at time v. These are calculated as:

Initial phase:

$\beta_V(m)=1, \quad 1 \leq m \leq G$     (24)

Induction:

$\begin{gathered}\beta_v(m)=\sum_{n=1}^G Q_{m n} \cdot v_n\left(s_{v+1}\right) \cdot \beta_{v+1}(m), \quad v= V-1, V-2, \ldots, 1\end{gathered}$  (25)

The forward and backward probability are utilized for estimating the projected amount of transitioning and emissions, which then inform the updates of $\mathrm{Q}_{\mathrm{mn}}, \mathrm{v}_{\mathrm{n}}(\mathrm{l})$, and $\rho_{\mathrm{m}}$.

The formulae for re-estimating the variables are as follows:

Distribution of initial states:

$\rho_m=\gamma_1(m)$ (26)

Transition probabilities:

$Q_{m n}=\frac{\sum_{v=1}^{V-1} \xi_v(m, n)}{\sum_{v=1}^{V-1} \gamma_v(m)}$  (27)

Observation probabilities:

$v_n(l)=\frac{\sum_{v=1, s_v=u_l}^V \gamma_v(m)}{\sum_{v=1}^V \gamma_v(m)}$ (28)

where, $\gamma_v(m)$ represents the likelihood of occupying state $R_m$ at time v , and $\xi_\nu(m, n)$ denotes the chance of transition from state ${R}_{{m}}$ to state $R_n$ at time $v$, conditioned on the observed sequences and the model.

The following quantities are computed as:

$\gamma_v(m)=\frac{\alpha_v(m) \cdot \beta_v(m)}{Q(S \mid \lambda)}$    (29)

$\xi_v(m, n)=\frac{\alpha_v(m) \cdot Q_{m n} \cdot v_m\left(s_{v+1}\right) \cdot \beta_{v+1}(m)}{Q(S \mid \lambda)}$  (30)

$\gamma_v(m)$ denotes the possibility of being in state $m$ at time $v$, $\xi_\nu(m, n)$ represents the probabilities of transforming from state $m$ to $n$ at time $\mathrm{v}, \alpha$ and $\beta$ signify the forward and backward possibilities, $Q_{m n}$ indicates the state transformation possibility, $\mathrm{v}_{\mathrm{m}}\left(\mathrm{s}_{\mathrm{v}+1}\right)$ refers to the observations probabilities for the subsequent symbol, and $Q(S / \lambda)$ denotes the total pattern probabilities.

Upon completion of training and estimation of variables, the framework is used to forecast the most likely pattern of traffic states correlating to fresh observing sequences. The Viterbi algorithm executes this deciphering process by determining the most probable pattern of hidden states that produces the observable sequence.

The Viterbi algorithm employs a recursively dynamical programming methodology. Let $\delta_\mathrm{v}(\mathrm{m})$ represent the greatest possible outcome along a singular route at time t concluding in state $R_m$, and let $\psi_{\mathrm{v}(\mathrm{m})}$ signify the state that optimizes this value. The algorithm operates in the following manner:

Initialize:

$\delta_1(m)=\rho_m \cdot v_m\left(s_1\right), \quad \psi_1(m)=0$   (31)

Recursion:

$\delta_v(m)=\max _{1 \leq m \leq G}\left[\delta_{v-1}(m) \cdot Q_{m n}\right] \cdot v_m\left(s_v\right)$ (32)

$\psi_v(n)=\arg \max _{1 \leq m \leq G}\left[\delta_{v-1}(m) \cdot Q_{m n}\right]$    (33)

Terminate:

$Q^*=\max _{1 \leq m \leq G} \delta_V(m), \quad p_V^*=\max _{1 \leq m \leq G} \delta_V(m)$  (34)

Backtrack:

$p_v^*=\psi_{v+1}\left(p_{v+1}^*\right), \quad v=V-1, V-2, \ldots, 1$       (35)

$\delta_v(m)$ denotes the maximum probabilities of any state sequence concluding in state $m$ at time v, while $\psi_v(n)$ serves as the back pointer suggesting the preceding state that optimized the probabilities for state $\mathrm{m}. \rho \mathrm{m}$ symbolizes the initial probabilities of commencing in state m , and $v_m(\mathrm{s} \mathrm{v})$ signifies the observations likelihood of encountering symbol $s_v$ in state m. Qmn indicates the transformation probabilities from state m to $\mathrm{n}, Q^*$ reflects the maximal possibility of the optimal state order, $p_V^*$ is the terminal state in that sequence, and $p_v^*$ retraces the most possible path backward utilizing the stored back pointer numbers.

In traffic simulation, each hidden state S_i represents a distinct quantitative traffic situation, including free flow, modest congestion, or high congestion. The states are not immediately visible but may be deduced from patterns in the observable characteristics. The analysis of data in space, including ATR, EMA, RSI, and ROC values, represents the dynamics of vehicle flow across time and functions as an input layer for the trained MHMM.

The adjustment of the hidden state count by MF-DA is crucial for enhancing the flexibility and accuracy of the MHMM. An insufficient number of states may lead to an oversimplified model that neglects critical variations in traffic conduct, while an excessive number of states may result in overfitting, hence diminishing generalizability. MF-DA automatically identifies the ideal quantity of hidden states, ensuring the model is appropriately instantiated without under- or over-parameterization.

The result space in MF-DA is represented by integer values denoting possibility state counts. Every candidate is assessed according to the predictive accuracy of the MHMM trained with the specified state count. The fitness landscapes is examined via swarm conduct, with convergence directed by the overall health of the individuals and their closeness to optimum solutions. The behavioural parameters (distinction p, alignment b, cohesiveness d, food attraction e, and adversary avoidance c) are adapted adjusted in every repetition, while random excursions using Lévx flights avert a rapid convergence.

The final product of the suggested methodology is a predicting paradigm that can assimilate real-time traffic characteristics, calculate the most likely hidden states, and anticipate future traffic circumstances. This model is designed to serve as a vital element in smart transit systems, which allows preventive transportation planning and congestion alleviation via timely and precise predictions.

The work described in the paper concerns a sophisticated method of forecasting the traffic flow based on the modified and optimized statistical model. The analysis adequately incorporates essential traffic oscillators including ATR, EMA, RSI, and ROC to visualize the implicit movement of the traffic patterns. Being analyzed and evaluated in a great variety of scenarios, including the various days, road directions, and time sessions, the model proves to have high prediction accuracy, narrow error margins, and enhanced responsiveness compared to the traditional classifiers, namely, HMM, ANN, RNN, and SVM. Experimental findings are clear regarding the capability of the model to follow closely real time vehicle counts data and give accurate estimations even at the busy hour traffic regime. Moreover, the optimized prediction framework has less computational time, higher accuracy of the queue length as well as minimal error in the waiting time. The efficiency and stability of the method is proven to be true statistically in all the test conditions. One of the strengths of the model is its stability concerning various traffic conditions, and it indicates that it can be applied to be used in the smart transportation systems in the reality. The research can be regarded as an improvement of the assortment of predictive traffic management systems, which will enable offering a market-tested solution to traffic congestion-related mitigation and more sophisticated traffic management. The enhancements created in to the process of prediction do not only embody the efficiency in computation but also the utility of the same.