A smart function scheduler for dynamic flow-based programming.

License: EUPL-1.1

Language: Python

schedula: A smart function scheduler for dynamic flow-based programming

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release: 1.2.0
date: 2020-04-08 17:50:00
keywords: flow-based programming, dataflow, parallel, async, scheduling, dispatch, functional programming, dataflow programming
license: EUPL 1.1+

About schedula

schedula is a dynamic flow-based programming environment for python, that handles automatically the control flow of the program. The control flow generally is represented by a Directed Acyclic Graph (DAG), where nodes are the operations/functions to be executed and edges are the dependencies between them.

The algorithm of schedula dates back to 2014, when a colleague asked for a method to automatically populate the missing data of a database. The imputation method chosen to complete the database was a system of interdependent physical formulas - i.e., the inputs of a formula are the outputs of other formulas. The current library has been developed in 2015 to support the design of the CO2MPAS tool - a CO2 vehicle simulator. During the developing phase, the physical formulas (more than 700) were known on the contrary of the software inputs and outputs.

Why schedula?

The design of flow-based programs begins with the definition of the control flow graph, and implicitly of its inputs and outputs. If the program accepts multiple combinations of inputs and outputs, you have to design and code all control flow graphs. With normal schedulers, it can be very demanding.

While with schedula, giving whatever set of inputs, it automatically calculates any of the desired computable outputs, choosing the most appropriate DAG from the dataflow execution model.


The DAG is determined at runtime and it is extracted using the shortest path from the provided inputs. The path is calculated based on a weighted directed graph (dataflow execution model) with a modified Dijkstra algorithm.

schedula makes the code easy to debug, to optimize, and to present it to a non-IT audience through its interactive graphs and charts. It provides the option to run a model asynchronously or in parallel managing automatically the Global Interpreter Lock (GIL), and to convert a model into a web API service.

Dataflow Execution Model

The :class:`~schedula.dispatcher.Dispatcher` is the main model of schedula and it represents the dataflow execution model of your code. It is defined by a weighted directed graph. The nodes are the operations to be executed. The arcs between the nodes represent their dependencies. The weights are used to determine the control flow of your model (i.e. operations' invocation order).

Conceptually, when the model is executed, input-data flows as tokens along the arcs. When the execution/:func:`~schedula.dispatcher.Dispatcher.dispatch` begins, a special node (:obj:`~schedula.utils.cst.START`) places the data onto key input arcs, triggering the computation of the control flow. The latter is represented by a Directed Acyclic Graph (DAG) and it is defined as the shortest path from the provided inputs. It is computed using the weighted directed graph and a modified Dijkstra algorithm. A node is executed when its inputs and domain are satisfied. After the node execution, new data are placed on some or all of its output arcs. In presence of cycles in the graph, to avoid undesired infinite loops, the nodes are computed only once. In case of an execution failure of a node, the algorithm searches automatically for an alternative path to compute the desired outputs. The nodes are differentiated according to their scope. schedula defines three node's types:

  • data node: stores the data into the solution. By default, it is executable when it receives one input arch.
  • function node: invokes the user defined function and place the results onto its output arcs. It is executable when all inputs are satisfied and it has at least one data output to be computed.
  • sub-dispatcher node: packages particular dataflow execution model as sub component of the parent dispatcher. Practically, it creates a bridge between two dispatchers (parent and child) linking some data nodes. It allows to simplify your model, reusing some functionality defined in other models.

The key advantage is that, by this method, the scheduling is not affected by the operations' execution times. Therefore, it is deterministic and reproducible. Moreover, since it is based on flow-based programming, it inherits the ability to execute more than one operation at the same time, making the program executable in parallel. The following video shows an example of a runtime dispatch.

Your browser does not support the video tag.


To install it use (with root privileges):

$ pip install schedula

or download the last git version and use (with root privileges):

$ python install

Install extras

Some additional functionality is enabled installing the following extras:

  • io: enables to read/write functions (see : ).
  • plot: enables the plot of the Dispatcher model and workflow (see :func:`~schedula.utils.base.Base.plot`).
  • web: enables to build a dispatcher Flask app (see :func:`~schedula.utils.base.Base.web`).
  • sphinx: enables the sphinx extension directives (i.e., autosummary and dispatcher).
  • parallel: enables the parallel execution of Dispatcher model.

To install schedula and all extras, do:

$ pip install schedula[all]


plot extra requires Graphviz. Make sure that the directory containing the dot executable is on your systems' path. If you have not you can install it from its download page.


Let's assume that we want develop a tool to automatically manage the symmetric cryptography. The base idea is to open a file, read its content, encrypt or decrypt the data and then write them out to a new file. This tutorial shows how to:

  1. define and execute a dataflow execution model,
  2. extract a sub-model, and
  3. deploy a web API service.


You can find more examples, on how to use the schedula library, into the folder examples.

Model definition

First of all we start defining an empty :class:`~schedula.dispatcher.Dispatcher` named symmetric_cryptography that defines the dataflow execution model:

>>> import schedula as sh
>>> dsp = sh.Dispatcher(name='symmetric_cryptography')

There are two main ways to get a key, we can either generate a new one or use one that has previously been generated. Hence, we can define three functions to simply generate, save, and load the key. To automatically populate the model inheriting the arguments names, we can use the decorator :func:`~schedula.utils.dsp.add_function` as follow:

>>> import os.path as osp
>>> from cryptography.fernet import Fernet
>>> @sh.add_function(dsp, outputs=['key'], weight=2)
... def generate_key():
...     return Fernet.generate_key().decode()
>>> @sh.add_function(dsp)
... def write_key(key_fpath, key):
...     with open(key_fpath, 'w') as f:
...         f.write(key)
>>> @sh.add_function(dsp, outputs=['key'], input_domain=osp.isfile)
... def read_key(key_fpath):
...     with open(key_fpath) as f:
...         return


Since Python does not come with anything that can encrypt/decrypt files, in this tutorial, we use a third party module named cryptography. To install it execute pip install cryptography.

To encrypt/decrypt a message, you will need a key as previously defined and your data encrypted or decrypted. Therefore, we can define two functions and add them, as before, to the model:

>>> @sh.add_function(dsp, outputs=['encrypted'])
... def encrypt_message(key, decrypted):
...     return Fernet(key.encode()).encrypt(decrypted.encode()).decode()
>>> @sh.add_function(dsp, outputs=['decrypted'])
... def decrypt_message(key, encrypted):
...     return Fernet(key.encode()).decrypt(encrypted.encode()).decode()

Finally, to read and write the encrypted or decrypted message, according to the functional programming philosophy, we can reuse the previously defined functions read_key and write_key changing the model mapping (i.e., function_id, inputs, and outputs). To add to the model, we can simply use the :class:`~schedula.dispatcher.Dispatcher.add_function` method as follow:

>>> dsp.add_function(
...     function_id='read_decrypted',
...     function=read_key,
...     inputs=['decrypted_fpath'],
...     outputs=['decrypted']
... )
>>> dsp.add_function(
...     'read_encrypted', read_key, ['encrypted_fpath'], ['encrypted'],
...     input_domain=osp.isfile
... )
>>> dsp.add_function(
...     'write_decrypted', write_key, ['decrypted_fpath', 'decrypted'],
...     input_domain=osp.isfile
... )
>>> dsp.add_function(
...     'write_encrypted', write_key, ['encrypted_fpath', 'encrypted']
... )

To inspect and visualize the dataflow execution model, you can simply plot the graph as follow:

>>> dsp.plot()  # doctest: +SKIP
.. dispatcher:: dsp
   :height: 915px

    >>> from examples.symmetric_cryptography.model import dsp
    >>> dsp = dsp.register()


You can explore the diagram by clicking on it.


.. testsetup::
    >>> import os.path as osp
    >>> import schedula as sh
    >>> from examples.symmetric_cryptography.model import dsp
    >>> dsp = dsp.register()
    >>> dsp.raises = ''

To see the dataflow execution model in action and its workflow to generate a key, to encrypt a message, and to write the encrypt data, you can simply invoke :func:`~schedula.dispatcher.Dispatcher.dispatch` or :func:`~schedula.dispatcher.Dispatcher.__call__` methods of the dsp:

.. dispatcher:: sol
   :opt: index=True

    >>> import tempfile
    >>> tempdir = tempfile.mkdtemp()
    >>> message = "secret message"
    >>> sol = dsp(inputs=dict(
    ...     decrypted=message,
    ...     encrypted_fpath=osp.join(tempdir, 'data.secret'),
    ...     key_fpath=osp.join(tempdir,'key.key')
    ... ))
    >>> sol.plot(index=True)  # doctest: +SKIP


As you can see from the workflow graph (orange nodes), when some function's inputs does not respect its domain, the Dispatcher automatically finds an alternative path to estimate all computable outputs. The same logic applies when there is a function failure.

Now to decrypt the data and verify the message without saving the decrypted message, you just need to execute again the dsp changing the inputs and setting the desired outputs. In this way, the dispatcher automatically selects and executes only a sub-part of the dataflow execution model.

>>> dsp(
...     inputs=sh.selector(('encrypted_fpath', 'key_fpath'), sol),
...     outputs=['decrypted']
... )['decrypted'] == message

If you want to visualize the latest workflow of the dispatcher, you can use the :func:`~schedula.utils.base.Base.plot` method with the keyword workflow=True:

.. dispatcher:: dsp
   :opt: index=True, workflow=True

    >>> dsp.plot(workflow=True, index=True)  # doctest: +SKIP

Sub-model extraction

.. testsetup::
    >>> import schedula as sh
    >>> from examples.symmetric_cryptography.model import dsp
    >>> dsp = dsp.register()

A good security practice, when design a light web API service, is to avoid the unregulated access to the system's reading and writing features. Since our current dataflow execution model exposes these functionality, we need to extract sub-model without read/write of key and message functions:

.. dispatcher:: api
   :opt: graph_attr={'ratio': '1'}

    >>> api = dsp.get_sub_dsp((
    ...     'decrypt_message', 'encrypt_message', 'key', 'encrypted',
    ...     'decrypted', 'generate_key', sh.START
    ... ))

API server

.. testsetup::
    >>> import schedula as sh
    >>> from examples.symmetric_cryptography.model import dsp
    >>> api = dsp.register().get_sub_dsp((
    ...     'decrypt_message', 'encrypt_message', 'key', 'encrypted',
    ...     'decrypted', 'generate_key', sh.START
    ... ))

Now that the api model is secure, we can deploy our web API service. schedula allows to convert automatically a :class:`~schedula.dispatcher.Dispatcher` to a web API service using the :func:`~schedula.dispatcher.Dispatcher.web` method. By default, it exposes the :func:`~schedula.dispatcher.Dispatcher.dispatch` method of the Dispatcher and maps all its functions and sub-dispatchers. Each of these APIs are commonly called endpoints. You can launch the server with the code below:

>>> server = api.web().site(host='', port=5000).run()
>>> url = server.url; url


When server object is garbage collected, the server shutdowns automatically. To force the server shutdown, use its method server.shutdown().

Once the server is running, you can try out the encryption functionality making a JSON POST request, specifying the args and kwargs of the :func:`~schedula.dispatcher.Dispatcher.dispatch` method, as follow:

>>> import requests
>>> res =
...     '', json={'args': [{'decrypted': 'message'}]}
... ).json()


By default, the server returns a JSON response containing the function results (i.e., 'return') or, in case of server code failure, it returns the 'error' message.

To validate the encrypted message, you can directly invoke the decryption function as follow:

>>> res =
...     '%s/symmetric_cryptography/decrypt_message?data=input,return' % url,
...     json={'kwargs': sh.selector(('key', 'encrypted'), res['return'])}
... ).json(); sorted(res)
['input', 'return']
>>> res['return'] == 'message'


The available endpoints are formatted like:

There is an optional query param data=input,return, to include the inputs into the server JSON response and exclude the possible error message.

.. testcleanup::
    >>> server.shutdown()

Asynchronous and Parallel dispatching

When there are heavy calculations which takes a significant amount of time, you want to run your model asynchronously or in parallel. Generally, this is difficult to achieve, because it requires an higher level of abstraction and a deeper knowledge of python programming and the Global Interpreter Lock (GIL). Schedula will simplify again your life. It has four default executors to dispatch asynchronously or in parallel:


Running functions asynchronously or in parallel has a cost. Schedula will spend time creating / deleting new threads / processes.

The code below shows an example of a time consuming code, that with the concurrent execution it requires at least 6 seconds to run. Note that the slow function return the process id.

.. dispatcher:: dsp
    :height: 350

    >>> import schedula as sh
    >>> dsp = sh.Dispatcher()
    >>> def slow():
    ...     import os, time
    ...     time.sleep(1)
    ...     return os.getpid()
    >>> for o in 'abcdef':
    ...     dsp.add_function(function=slow, outputs=[o])

while using the async executor, it lasts a bit more then 1 second:

>>> import time
>>> start = time.time()
>>> sol = dsp(executor='async').result()  # Asynchronous execution.
>>> (time.time() - start) < 2  # Faster then concurrent execution.

all functions have been executed asynchronously, but on the same process:

>>> import os
>>> pid = os.getpid()  # Current process id.
>>> {sol[k] for k in 'abcdef'} == {pid}  # Single process id.

if we use the parallel executor all functions are executed on different processes:

>>> sol = dsp(executor='parallel').result()  # Parallel execution.
>>> pids = {sol[k] for k in 'abcdef'}  # Process ids returned by ``slow``.
>>> len(pids) == 6  # Each function returns a different process id.
>>> pid not in pids  # The current process id is not in the returned pids.
>>> sorted(sh.shutdown_executors())
['async', 'parallel']

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