Chapter 3. Discrete Processes and Business Processes

A discrete event process, or simply discrete process (DP), consists of a partially ordered set of events such that each of them causes zero or more discrete state changes of affected objects. When two or more events within such a process have the same order rank, this means that they occur simultaneously. A discrete process may be an instance of a discrete process type defined by a discrete process model.

A business process (BP) is a discrete process that involves activities performed by organizational agents qua one of their organizational roles defined by their organizational position. Typically, a business process is an instance of a business process type defined by an organization or organizational unit (as the owner of the business process type) in the form of a business process model.

While there are DPs that do not have an organizational context (like, for instance, message exchange processes in digital communication networks or private conversations among human agents), a BP always happens in the context of an organization.

The performance of a resource-dependent activity is constrained by the availability of the required resources, which may include human resources or other resource objects (such as rooms or devices).

There are two kinds of business process models:

1. BPMN-style Activity Networks (ANs) consisting of event nodes and activity nodes (with task queues) connected by means of event scheduling arrows and resource-dependent activity scheduling (RDAS) arrows, such that event and activity nodes may be associated with objects representing their participants. In the case of an activity node, these participating objects include the resources required for performing an activity. Typically, an activity node is associated with a particular resource object representing the activity performer.

2. GPSS/Arena-style Processing Networks (PNs) consisting of entry nodes, processing nodes (with task queues and input buffers) and exit nodes connected by means of processing flow arrows, which overlay an RDAS arrow with an object flow arrow. The PN concept is a conservative extension of the AN concept, that is, a PN is a special type of AN.

In an AN, all activity nodes have a task queue filled with tasks (or planned activities) waiting for the availability of the required resources. An RDAS arrow from an AN node to a successor activity node expresses the fact that a corresponding activity end event (or plain event) triggers the conditional scheduling of a successor activity start event, corresponding to the creation of a new task in the task queue of the successor activity node.

A PN process is a business process that involves one or more processing objects and includes arrival events, processing activities and departure events. An arrival event for one or more processing objects happens at an entry station, from where they are routed to a processing station where processing activities are performed on them, before they are routed to another processing station or to an exit station where they leave the system via a departure event.

A PN process model defines a PN where each node represents a combination of a spatial object and an event or activity variable:

1. Defining an entry node means defining both an entry station object (e.g., a reception area or a factory entrance) and a variable representing arrival events for arriving processing objects (such as people or manufacturing parts).
2. Defining a processing node means defining both a processing station object (often used as a resource object, such as a workstation or a room) and a variable representing processing activities.
3. Defining an exit node means defining both an exit station object and a variable representing departure events.

In a PN, all processing nodes have a task queue and an input buffer filled with processing objects that wait to be processed. A PN where all processing activities have exactly one abstract resource (often called a "server") is also known as a Queuing Network in Operations Research where processing nodes are called "servers" and processing objects are called "entities" or "jobs".

For accommodating resource-constrained activities and Processing Networks, basic OEM and DPMN are extended in two steps. The first extension, OEM/DPMN-A, comprises four new information modeling categories (activity types, resource roles, resource pools, and parallel participation) and one new process modeling element (RDAS arrows), while the second extension, OEM/DPMN-PN, comprises a set of four pre-defined object type categories (processing objects, entry stations, processing stations, exit stations), two pre-defined event type categories (arrival events, departure events), one activity type category (processing activities), three node type categories (entry nodes, processing nodes, exit nodes) and one new process modeling element (object flow arrows).