example_sim_network.py

# Queueing network using matrices to define the transition rates between the stations
# The following modes consists of two process stations. The clients generated at the source are sent to one of the two process stations.
# From there the clients can go to the exit or again to one of the two process stations. The transition rates between the stations are defined by matrices.


# Importing modules

# Simulator
from queuesim import Simulator

# Station types
from queuesim.stations import Source, Process, Dispose

# Pseudo random number generators
from queuesim.random_dist import exp as dist_exp

# Model builder
from queuesim.models import build_network_model

# Plot model
from queuesim import build_graph
import networkx as nx
import matplotlib.pyplot as plt
import seaborn as sns

# Defining general plot style
sns.set()


# Model parameters

# Arrivals to be simulated
count = 100000

# Arrival process
mean_i = 100

# Service process
mean_s1 = 180
mean_s2 = 140

# Number of operators
c1 = 3
c2 = 2


# Define stations

simulator = Simulator()

source = Source(simulator, count, dist_exp(mean_i))
process1 = Process(simulator, dist_exp(mean_s1), c1)
process2 = Process(simulator, dist_exp(mean_s2), c2)
dispose = Dispose(simulator)


# Defining transition rates by matrices

connections1=[[0.8, 0.2]]  # Most clients go to process1, some to process2
connections2=[[0.0, 0.2, 0.8], [1, 0, 0]]  # Most clients leave system after process1, some go to process2; all clients from process2 go to process1


# Adding `Decide` stations and connection stations based on the transition matrices

build_network_model([source],[process1,process2],[dispose],connections1,connections2)


# Running the simulation

simulator.run()


# Output results

print("Arrival count at station 1:", process1.statistic.count)
print("Arrival count at station 2:", process2.statistic.count)

print("Mean waiting time at station 1: E[W,1]=", round(process1.statistic_station_waiting.mean))
print("Mean waiting time at station 1: E[W,2]=", round(process2.statistic_station_waiting.mean))


# Queueing network model

dg = build_graph([source])
fig, ax = plt.subplots(figsize=(19, 9))
nx.draw(dg, ax=ax, with_labels=True, node_color='#CCCCFF', node_size=2000, arrowsize=30, width=2)
plt.show()