6.2 Discrete-Event Dynamic Systems

Nelson (1995) states that the event-view “defines system events by describing what happens to the system as it encounters entities.” In addition, Nelson (1995) states that the process view “implies system events by describing what happens to an entity as it encounters the system.” One can consider the event-view as taking the perspective of the system and the process-view as taking the perspective of the entity. The process-view describes the life cycles of objects within the system. Because of the way in which the process-view has been implemented through a network transaction flow approach within many simulation packages, the term entity has taken on the connotation of objects that flow or move within the system. To avoid confusion, the more general term, object, will be used to encompass non-flowing objects as well as flowing objects within the system.

To understand the event-view, the concepts of event, activity, state, and process must be clearly defined. Rumbaugh et al. (1991) defines state and its relationship to events and activities as “an abstraction of the attribute values and links of an object. Sets of values are grouped together into a state according to properties that affect the gross behavior of the object. A state corresponds to the interval between two events. A state has duration; it occupies an interval of time. A state is often associated with an activity that takes time to complete or with the value of an object satisfying some condition. In defining states, we ignore those attributes that do not affect the behavior of the object and we lump together in a single state all combinations of attribute values and links that have the same response to events.” Thus, the state of an object should entail only those aspects that are required for the modeling.

An event is something that happens at an instant in time that corresponds to a change in object state. An event is a one-way transmission of information from one object to another that causes an action resulting in a change in state. An event is said to be a scheduled event (or timed, determined, bounded) if its occurrence can be expressed as a function of system time and can thus be scheduled in time. For example, suppose you have a doctor’s appointment at 11 am. The beginning of the appointment represents a scheduled event. An event is said to be a conditional event if it is dependent upon the outcome of certain conditions that cannot be predicted with certainty in advance (e.g. the availability of a server). Conditional events are sometimes called unbounded or contingent. If a scheduled event ends an activity, then the activity is said to be a scheduled or timed activity; otherwise, it is said to be a conditional activity.

Associated with an event is an action that is an instantaneous operation, i.e. it takes zero simulated time to complete. In contrast, an activity is an operation that takes simulated time to complete. An activity can be associated with the state of an object over an interval. Activities are defined by the occurrence of two events that represent the activity’s beginning time and ending time and mark the entrance and exit of the state associated with the activity. In the simulation literature, it is common to refer to activities that take a specified duration of time as simply activities. To be more specific, it is useful to classify activities of a specified duration as timed activities. Getting your haircut is an example of a timed activity. There is a clear beginning and a clear ending for the activity. An activity that encompasses an interval of time that is unspecified or of indefinite length is called a conditional activity. An example of a conditional activity is a customer waiting in a queue for the barber to become available. The length of the activity depends on when the barber becomes available.

In the next section, we begin our exploration of simulation where time is an integral component in driving the behavior of the system. In addition, we will see that time will not necessarily advance at regular intervals (e.g. hour 1, hour 2, etc.). As discussed, an event occurs at a specific point in time, thus we need to understand how the simulation time clock works.