diff --git a/main_package/classes/priority_queue.py b/main_package/classes/priority_queue.py
new file mode 100644
index 0000000..db7df08
--- /dev/null
+++ b/main_package/classes/priority_queue.py
@@ -0,0 +1,19 @@
+
+
+class PriorityQueue():
+    """
+    Rappresenta una semplice coda con priorità FIFO
+    :queue: lista che contiene i valori della coda
+    """
+
+    def __init__(self):
+        self.queue = []
+
+    def enqueue(self, node):
+        self.queue.append(node)
+
+    def dequeue(self):
+        return self.queue.pop(0)
+
+    def is_empty(self):
+        return len(self.queue) == 0
diff --git a/main_package/classes/rate_matrix.py b/main_package/classes/rate_matrix.py
new file mode 100644
index 0000000..2012456
--- /dev/null
+++ b/main_package/classes/rate_matrix.py
@@ -0,0 +1,68 @@
+import numpy as np
+import dynamic_graph as dg
+import sample_path as sp
+import priority_queue as pq
+
+
+class RateMatrix():
+    """
+    Rappresenta la matrice Q di una generica CTMC costruita a partire dalle informazioni contenute nel grafo dinamico
+    """
+    def __init__(self, graph, dim):
+        self.graph = graph
+        self.matrix = np.zeros(shape=(dim,dim))
+        self.pr_queue = pq.PriorityQueue()
+
+    def build_matrix(self):
+        root = self.graph.get_root_node()
+        root.color = dg.node.Color.GRAY
+        self.pr_queue.enqueue(root)
+        
+
+        while not self.pr_queue.is_empty():
+            n = self.pr_queue.dequeue()
+            adjacency_list = self.graph.get_neighbours(n)
+            #print(adjacency_list)
+            time = self.graph.graph[n.state_id]["Time"]
+            sum_of_qs = 0.0
+            for nd, weight in adjacency_list.items():
+                sum_of_qs += self.calculate_off_diagonal_element_and_fill_matrix(n.node_id, nd.node_id, weight, time)
+                if self.graph.graph[nd.state_id]["Node"].color == dg.node.Color.WHITE:
+                    self.graph.graph[nd.state_id]["Node"].color = dg.node.Color.GRAY
+                    self.pr_queue.enqueue(nd)
+            n.color = dg.node.Color.BLACK
+            self.calculate_diagonal_element_and_fill_matrix(sum_of_qs, n.node_id)
+
+
+    def calculate_off_diagonal_element_and_fill_matrix(self, start_node, arrival_node, weight, time):
+        q = weight / time
+        self.matrix[start_node][arrival_node] = q
+        return q
+
+    def calculate_diagonal_element_and_fill_matrix(self, sum_of_qs, start_node):
+        self.matrix[start_node][start_node] = -sum_of_qs
+
+
+# A Simple Test #
+s1 = sp.SamplePath()
+s1.build_trajectories()
+print(s1.get_number_trajectories())
+
+g1 = dg.DynamicGraph(s1)
+g1.build_graph()
+print(g1.graph)
+#print(g1.states_number)
+
+Q = RateMatrix(g1, g1.states_number)
+#print(Q.matrix)
+Q.build_matrix()
+print(Q.matrix)
+
+non_zero_values = 0
+val = 0.0
+for coeff in Q.matrix[0][1:]:
+    if(coeff != 0):
+        non_zero_values += 1
+        val += coeff
+
+print(non_zero_values == len(Q.graph.graph["222"]["Arcs"].keys()))
\ No newline at end of file