README_networks.md

Queueing networks

Since the connection of the stations is completely user-defined (by using the set_next methods of the stations) any type of queueing network can be implemented. Retry or rework can be implemented easily.

For larger networks consisting only of sources, process stations and dispose stations there is a helper function build_network_model in queuesim.models that can build station networks based on transitions matrices. Lets assume we have a single source object named source, two process station objects process1 and process2 and a dispose object dispose. We want to send 80% of the clients from the source to process1 and 20% to process2. When leaving process2 all clients are to be sent to process1. When leaving process1 30% or the clients are sent to process2 and 70% well leave the system.

A model implementing this network can be created by:

from queuesim import Simulator
from queuesim.stations import Source, Process, Dispose

simulator = Simulator()

source = Source(simulator, ...)
process1 = Process(simulator, ...)
process2 = Process(simulator, ...)
dispose = Dispose()

connections1=[[0.8, 0.2]]  # 80% of the clients go to process1, 20% to process2
connections2=[[0.0, 0.3, 0.7], [1, 0, 0]]  # Most clients (70%) leave system after process1, some (30%) go to process2; all clients from process2 go to process1

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

simulator.run()

Assume we have m₁ sources, m₂ process stations and m₃ dispose stations, then the first transition rates matrix has the shape m₁ × m₂ and the second transition rates matrix has the shape m₂ × (m₂+m₃).

Displaying the queueing network

If you want to get a graphical representation of your queueing network, you can use queueim.build_graph(list_of_sources) to get a digraph which can be plotted using networkx:

from queuesim import Simulator
from queuesim.stations import Source, ...
from queuesim import build_graph

import matplotlib.pyplot as plt
import networkx as nx

simulator = Simulator()

simulator = Simulator()
source = Source(simulator, ...)

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)

Example files

See example_sim_network.ipynb or example_sim_network.py for a complete example of creating a queueing network using build_network_model.