What is a discrete process

     Here are common definitions of terms "process" and "discrete process", taken from the Wikipedia (open Internet encyclopaedia).

Definition 1. Process (from the Latin processus — promotion) — is a successive change of states in time for some object of arbitrary nature. Distinguish discrete and continuous processes. In discrete processes the states are clearly separated from each other, and for every state you can specify the adjacent (previous and subsequent, or only one of them). In continuous processes between any two states you can always select an intermediate one, which implies that the concept of neighboring states is not applicable to such process (you can only talk about the subsequent states and their proximity in time to each other). An example of a discrete process is the work of a cashier at a store (you can select states of getting money from a buyer, returning him odd money, issuing checks, etc.). Examples of continuous processes are: boiling water, motion of planets around the Sun, etc. .

     From the above formulation follows that the distinctive feature of a discrete process is the existence of successively changeable discrete (i.e. precisely expressed) states. Based on this formulation, we will try to find out the characteristic properties of a discrete process. First, we note the following its feature. The presence in a discrete process of successively changeable discrete states does not mean that it can not have the smoothly changed states (call them analog states). Rather, such states more often are present in a discrete process.

     Indeed, if we go back to the previous example with the cashier, then each of its discrete state (for example, getting money from a buyer) can be detailed as an analog state, that lasts a certain time and is characterized by a smooth hand movements of the cashier, performing specific action. Strictly speaking, in this case, there are not the purely discrete states, but the discrete-analog ones.

     Let's consider another simple example of a discrete process that describes the processing of a batch of details on a machine. Discreteness here is expressed in an enlarged state of each detail (unprocessed, processed or at the stage of processing), and continuity — in a detailed state of a currently being processed detail or in a curent state of the mashine during its changeover.

     We now give an example of a discrete process without analog states. This — the so-called process of selecting choices, for which the time factor is absent. A typical example of such process is the filling of a truck body by cargo that must be transported. In this case, we are interested not in the time required for loading the truck, but in the set of samples of the cargo, which have been selected for sending to their recipient. At the same time we do not matter in what order these samples were loaded onto the truck body.

     This simple example shows that for a discrete process of selecting choices is important not the order of changing discrete states and the required time for this, but the result thus obtained. It follows that the process of selecting choices can be considered as an instant process.

     Here we came to the point to find out about the categories of controlled and non-controlled discrete processes. To the first relate such processes, in which an order of changing discrete states is fixed and can't be changed with this or that purpose, depending on the current situation. For controlled discrete processes such change is permissible.

     A typical example of a non-controlled discrete process is the servicing by a seller of buyers in the order of their staying in a queue. A more complex example is, when a machine processes details of various types, for which are given priorities, that determine the order of their processing.

     Regardless of whether a discrete process is controlled or not, it almost always has controlling influences on its objects (further — controls). In particular, this control when servicing by a seller of a queue of buyers is the choice of a next buyer after releasing a previous one.

     Controls used in discrete processes have the following two properties:

  • they are applied to objects of the process in discrete moments of time, separated from each other by a finite time interval;
  • every control can be either instant or non-instant, i.e. extended in time until the application of a next control.

   The following is the expanded definition of a discrete process, in which formulation we took into account the above material of the current subsection of this website section.

Definition 2. Discrete process is called a process of successive changes of discrete and analog states for the whole totality of the process objects under the influence of consistently applying to them at discrete time moments of instant and non-instant controls.

     On the possibility of changing a process control strategy, discrete processes are divided into controlled and non-controlled (a sign of controllability), on the predictability of the process flowing — into random (probabilistic) and deterministic (a sign of behavior) and on its flow time — into infinite, time-limited and instant (a sign of duration).

Definition 3. Technological process a sequence of technological operations, required to perform a certain kind of works. A technological process consists of working operations, which in turn consist of working movements (techniques). Information process — a process of obtaining, creating, collecting, processing, storage, storing, search, distribution and use of information.

     If, for example, a discrete process describes the sequential execution of operations in construction of a building or in manufacture of a product, or in servicing buyers by a seller, then such process is actually the technological one. If we are talking about the exchange of discrete messages in a communication network or the solving some task of selecting choices, then it is the information process.

     In cases when it is required to emphasize the reality of a discrete process in question, as well as the possibility of its effective control via Technology (IT AC DTIP), we will use in relation to it the term "discrete technological or information process (in short — DTIP)".