I had refactored you code to meet my requirement 
#include <iostream>
#include <vector>
#include <queue>
#include <algorithm>
#include <string>
#include <thread>
#include <mutex>
#include <condition_variable>
#include <chrono>
#include <atomic>
using namespace std;

// Constant for load type. Can also create enum
const int LOW_LOAD = 1;
const int MEDIUM_LOAD = 2;
const int HIGH_LOAD = 3;

const int TIME_QUANTUM = 15; // in ms

struct Process {
    int id;
    int arrival_time;
    int total_execution_time;
    int remaining_time;
    int load;
    int priority;
    Process(int pid, int arrival, int execution_time, int lo, int pri = 0){
        id = pid; arrival_time = arrival; total_execution_time = execution_time; load = lo; priority = pri;
    }

    Process(){}
};

// Comparator for priority queue (higher priority first). Used when we implement "priority_queue".
struct ComparePriority {
    bool operator()(const Process& a, const Process& b) {
        return a.priority < b.priority;
    }
};

class Core {
public:
    // When we will be using this "mtx" to lock the std::lock_guard<std::mutex> lock(mtx); it will lock all the data of this class 
    // (so it is better to make this private. So, no random access is given by mistake).
    int id;
    queue<Process> process_queue;
    mutex mtx;
    int current_load; // See getCoreLoad()
    thread core_thread; // I will be using this to simulate a process running on Core.
    bool stop;

    Core(int core_id)
        : id(core_id), current_load(0), stop(false){}

    // Function executed by the core thread
    void run(){
        while(!stop) {
            Process current_process;
            bool has_process = false;

            // Fetch process from its own queue
            // Writing in Separate block so the "lock" will finish as soon as i leave this block
            {
                lock_guard<mutex> lock(mtx);
                if(!process_queue.empty()) {
                    current_process = process_queue.front();
                    process_queue.pop();
                    current_load -= current_process.load;
                    has_process = true;
                }
            }

            if(has_process) {
                // Simulate execution for TIME_QUANTUM or remaining_time, whichever is smaller
                int exec_time = std::min(TIME_QUANTUM, current_process.remaining_time);
                std::cout << "Core " << id << " executing Process P" << current_process.id 
                        << " for " << exec_time << "ms\n";
                std::this_thread::sleep_for(std::chrono::milliseconds(exec_time));

                current_process.remaining_time -= exec_time;

                if(current_process.remaining_time > 0) {
                    {
                        // Re-add the process to the ready queue
                        lock_guard<mutex> lock(mtx);
                        process_queue.push(current_process);
                    }
                } else {
                    cout << "Process P" << current_process.id << " completed on Core " << id << "\n";
                }
            } else {
                // No process to execute, wait for a while
                std::this_thread::sleep_for(std::chrono::milliseconds(10));
            }
        }
    }

    // Start the core thread
    void start(); // Starting from Scheduler class itself

    // Instead of this we can also update core_load when we are adding a process and when a process execution complete
    int getCoreLoad(){
        // So, how do we calculate a Load on a core. Note, that in Process structure we have a field name Load.
        // So, to get a core load what we do is sum all the Process load present in queue of this particular core.
        // This is somewhat the Research Paper Do (https://ieeexplore.ieee.org/document/9626411)
        return current_load;
    }

    // Stop the core thread
    void stop_core() {
        stop = true;
        // Notify in case the core is waiting
        {
            lock_guard<mutex> lock(mtx);
        }
    }
};


// Class to manage scheduling and load balancing
class Scheduler {
private:
    
public:
    vector<Core*> cores;
    // priority_queue<Process, vector<Process>, ComparePriority> ready_queue;  //No need Currently we will do round Robin i.e. when a process come we
    // we will allocate it to a core process_queue.
    mutex ready_queue_mtx;
    int which_core_turn = 0; // For allocating process to core in round robin manner.
    condition_variable cv;
    thread balancer_thread; // This is used to regularly balance the process
    bool stop = 0;
    int num_cores = 0;

    Scheduler(int cores_count){
        stop = false;
        num_cores = cores_count;
        for(int i = 0; i < cores_count; ++i) {
            cores.push_back(new Core(i));
        }
    }

    ~Scheduler() {
        // Stop all cores
        for(auto core : cores) {
            core->stop_core();
            if(core->core_thread.joinable())
                core->core_thread.join();
            delete core;
        }
        // Stop balancer thread
        stop = true;
        if(balancer_thread.joinable())
            balancer_thread.join();
    }

    // Assign process to a specific core
    void assign_process_to_core(const Process& proc) {
        Core* core = cores[which_core_turn];
        {
            lock_guard<mutex> lock(core->mtx);
            core->process_queue.push(proc);
            core->current_load += proc.load;

            // lock_guard<mutex> lock(ready_queue_mtx);
            which_core_turn = (which_core_turn + 1)%num_cores;
        }

        cout << "Assigned Process P" << proc.id << " to Core " << core->id << "\n";
    }

    // Start all core threads and the balancer thread
    void start() {
        // Start core threads
        for(auto core : cores) {
            core->core_thread = std::thread(&Core::run, core);
        }
        // Start balancer thread
        balancer_thread = std::thread(&Scheduler::balance_load, this);
    }

    // Dynamic Load Balancing Function
    void balance_load() {
        while(!stop) {
            this_thread::sleep_for(chrono::milliseconds(50)); // Balance every 50ms

            /* For calculating load on a core with respect to other cores
             The sum of the time-slice sizes (LOW,MEDIUM,HIGH) of all ready tasks on a single processor is regarded 
             as the processor load which is denoted by L. And T denotes the load proportion threshold. 
             In our design, the value of T is 20%. 'A' denotes the average processor load of all CPUs in 
             the current system. The value of L/A is referred 
             to as the degree of load on the core
             heavy : L > A*(1 + T)
             light : L < A 
            */
            // Calculate average load
            
            int total_load = 0;
            for(auto core : cores) {
                // lock_guard<mutex> lock1(core->mtx,adopt_lock);
                total_load += core->getCoreLoad();
            }
            double average_load = static_cast<double>(total_load) / cores.size();
            double threshold = average_load * 0.2; // 20% threshold

            // Find overloaded and underloaded cores
            Core* max_core = nullptr;
            Core* min_core = nullptr;
            int max_load = INT32_MIN;
            int min_load = INT32_MAX;

            for(auto core : cores) {
                // lock_guard<mutex> lock1(core->mtx,adopt_lock);
                int load = core->current_load;
                if(load > max_load) {
                    max_load = load;
                    max_core = core;
                }
                if(load < min_load) {
                    min_load = load;
                    min_core = core;
                }
            }

            if(max_core && min_core && (max_load - min_load > threshold)) {
                // taskMigration(max_core, min_core);
                // Move one process from max_core to min_core
                std::lock(max_core->mtx, min_core->mtx);
                std::lock_guard<std::mutex> lock1(max_core->mtx, std::adopt_lock);
                std::lock_guard<std::mutex> lock2(min_core->mtx, std::adopt_lock);

                if(!max_core->process_queue.empty()) {
                    Process proc = max_core->process_queue.front();
                    max_core->process_queue.pop();
                    max_core->current_load -= proc.load;

                    // Re-add remaining_time if not already updated
                    if(proc.remaining_time > 0) {
                        min_core->process_queue.push(proc);
                        min_core->current_load += proc.load;
                        std::cout << "Balancer: Moved Process P" << proc.id 
                                  << " from Core " << max_core->id 
                                  << " to Core " << min_core->id << std::endl;
                    }
                }
            }
        }
    }

    void taskMigration(Core* max_core, Core* min_core){
        lock(max_core->mtx, min_core->mtx);
        lock_guard<mutex> lock1(max_core->mtx,adopt_lock);
        lock_guard<mutex> lock2(min_core->mtx,adopt_lock);

        if (!max_core->process_queue.empty())
        {
            Process proc = max_core->process_queue.front();
            max_core->process_queue.pop();
            max_core->current_load -= proc.load;

            // Re-add remaining_time if not already updated
            if (proc.remaining_time > 0)
            {
                min_core->process_queue.push(proc);
                min_core->current_load += proc.load;
                std::cout << "Balancer: Moved Process P" << proc.id
                          << " from Core " << max_core->id
                          << " to Core " << min_core->id << std::endl;
            }
        }
    }

    // Display process assignment to cores
    void display_assignment() {
        std::cout << "\nProcess Assignment to Cores:\n";
        for(auto core : cores) {
            std::lock_guard<std::mutex> lock(core->mtx);
            std::queue<Process> temp = core->process_queue;
            std::cout << "Core " << core->id << " [Load: " << core->current_load << "]: ";
            while(!temp.empty()) {
                std::cout << "P" << temp.front().id << "(" 
                          << (temp.front().load == LOW_LOAD ? "Low" : "High") 
                          << ", Rem: " << temp.front().remaining_time << "ms) ";
                temp.pop();
            }
            std::cout << "\n";
        }
    }
};


int main(){
    int num_cores = 2;

    Scheduler scheduler(num_cores);

    // cout<<scheduler.cores.size()<<endl;
    // Example Input
    std::vector<Process> processes = {
        {1, 0, 125, LOW_LOAD, 1},
        {2, 5, 150, HIGH_LOAD, 3},
        {3, 10, 150, LOW_LOAD, 2},
        {4, 15, 100, HIGH_LOAD, 1}
        // {5, 20, 180, LOW_LOAD, 2},
        // {6, 25, 220, HIGH_LOAD, 3},
        // {7, 30, 170, LOW_LOAD, 1},
        // {8, 35, 120, HIGH_LOAD, 2},
        // {9, 40, 140, LOW_LOAD, 3},
        // {10, 45, 160, HIGH_LOAD, 1}
    };
    // Start the scheduler
    scheduler.start();

    auto start_time = std::chrono::steady_clock::now();
    for(auto& proc : processes) {
        // Wait until the process's arrival time
        auto now = std::chrono::steady_clock::now();
        auto elapsed = std::chrono::duration_cast<std::chrono::milliseconds>(now - start_time).count();
        if(proc.arrival_time > elapsed) {
            std::this_thread::sleep_for(std::chrono::milliseconds(proc.arrival_time - elapsed));
        }
        std::cout << "Process P" << proc.id << " arrived (Load: " 
                      << (proc.load == LOW_LOAD ? "Low" : "High") 
                      << ", Priority: " << proc.priority << ")\n";
            scheduler.assign_process_to_core(proc);
    }

    // Let the simulation run for a certain period
    std::this_thread::sleep_for(std::chrono::seconds(5));

    // Stop the scheduler
    scheduler.stop = true;

    // Notify all waiting threads
    scheduler.cv.notify_all();
    // Allow some time for cores to finish
    std::this_thread::sleep_for(std::chrono::milliseconds(100));

    // Display final assignment
    scheduler.display_assignment();

    return 0;

}


But i am getting stuck in an infinite loop can you pipoint the error

Core 0 executing Process P3 for 15ms
Core 1 executing Process P2 for 9ms
Process P2 completed on Core 1
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms
Core 0 executing Process P3 for 15ms