Activity Cycle Diagram
The oldest simulation modeling methodology
1. Introduction
Activity Cycle Diagram (ACD), aka., flow diagram, or activity diagram describes the target world in activity cycles of resources and entities, which are either in a passive or active state. This modeling paradigm was firstly introduced by K.D. Tocher, 1960. At that time, it was called as flow diagram, but later, researchers refer it as to activity cycle diagram.
The ACD is composed of activity cycles of resources and entities. Each activity cycle describes the active and passive states of a resource or entity in the system. Usually, active state of a resource or entity is represented by a rectangle, called as “activity”, a passive state of a resource or entity is represented by a circle, called as “queue” as shown in Figure 1. The arc is used to connect the activity and queue.
The activity represents the interaction between an entity and resource(s), which usually takes a time delay to finish it. The token is used to represent the state of the queue and activity. All activity cycles are closed on itself (Crookes 1986).
2. Activity Cycle Diagram (ACD)
An ACD model for a single machine system with a setup operator is shown in Figure 2. This model consists of four activity cycles: three for resources of “generator”, “machine” and “operator” and one for an entity of “jobs”. A job is generated at the interval of ta time unit by the generator and stored in a queue “B” waiting its processing on a machine. A ready-to-process machine serves a job for tp time unit if a queue “B” has at least one job and it holds for a moment until the operator is available. The operator sets up the machine for ts time unit as soon as it is available. Other resources also perform one or more different activities in any sequence or are idle. Here, all activity cycles are closed.
3. Activity Transition Table (ATT)
The three-phase rule is also proposed by Tocher (Tocher 1963) to handle the flow of time in the discrete event simulation:
Phase A: Advance the clock to the time of the next (bound-to-occur) event.
Phase B: Terminate any activity bound to end at this time.
Phase C: Initiate any activity whose condition now permits.
The ACD represents the state flow of an entity or resource in a system, while the three-phase rule is based on the event that denotes the change in the state of the model. In phase B, the activities bound to occur at a time are terminated with the release of resources and entities (into output queues), which is called bound or bound-to-occur (BTO) event. In phase C, the conditional events, which satisfies the beginning condition of the availability of entities and resources, are initiated by acquiring of them (Crookes 1986).
The three-phase rule has the atomistic structure of advancing time and executing BTO and conditional events. In the simulation execution, the BTO event is handled by the event routine and the conditional event is executed by the activity routine.
The activity routine firstly checks the at-begin condition of an activity, whether all input queues of that activity has at least one token or not. If it is true, the at-begin action is fulfilled, which takes one token out of each input queue. Then it schedules a BTO event to occur in a time delay or time duration. The event routine executes the at-end action, which adds one token to each output queue.
The phase C of the three-phase rule has an inefficiency of scanning all activity in the ACD model, even though the BTO event has an effect only on the succeeding activities.
The activity transition table (ATT) as a model specification for the simulation execution of the ACD models is a set of activity transitions. Each activity transition has at-begin condition, at-begin action, BTO event with the time delay, at-end conditon, at-end action and influenced activities.
Table 1 shows the ATT model for the single machine system with a setup operator in Figure 2. The queue “Jobs” does not show up in the ATT model, because it is a dummy node used for making the activity cycle closed.
4. Simulation of Activity Cycle Diagram
The core of the simulation of activity cycle diagram is the three-phase rule. In order to reduce the time to scan all the activities at Phase C, the influenced activities can be defined from the activity cycle diagram, which are the activities that are directly influenced by the the terminated activity in Phase B. In Table 1, the column, named Influenced Activities, is located in the last of the columns. For example, the activity Process has one influenced activity, Setup, because the queue Hold is the input queue of the activity Setup while it is the output queue of the activity Process.
The three-phase rule is elaborated into the activity scanning algorithm to simulate the activity cycle diagrams. For more details on the activity scanning algorithm, please refer to the paper, titled “How to Develop Your Own Simulators for Discrete-Event Systems”, Proceeding of the 2014 Winter Simulation Conference.
Also, you can try our own simulator for the activity cycle diagram, named Activity Cycle Executor (ACE).
