Fixed, Jittered, And Sporadic Release Times

Fixed, Jittered, and Sporadic Release Times

In many systems, we do not know exactly when each job will be released. In other words, we do not know the actual release time ri of each job Ji ; only that ri is in a range can be as early as the earliest release time ri⁻ and as late as the latest release time ri . Indeed, some models assume that only the range of ri is known and call this range the jitter in ri, or release-time jitter. Sometimes, the jitter is negligibly small compared with the values of other temporal parameters. If, for all practical purposes, we can approximate the actual release time of each job by its earliest or latest release time, then we say that the job has a fixed release time.

Almost every real-time system is required to respond to external events which occur at random instants of time. When such an event occurs, the system executes a set of jobs in response. The release times of these jobs are not known until the event triggering them occurs. These jobs are called sporadic jobs or aperiodic jobs because they are released at random time instants. (We will return shortly to discuss the difference between these two types of jobs.) For example, the pilot may disengage the autopilot system at any time. When this occurs, the autopilot system changes from cruise mode to standby mode. The jobs that execute to accomplish this mode change are sporadic jobs.

The release times of sporadic and aperiodic jobs are random variables. The model of the system gives the probability distribution A(x) of the release time of such a job, or when there is a stream of similar sporadic or aperiodic jobs, the probability distribution of interrelease time (i.e., the length of the time interval between the release times of two consecutive jobs in the stream). A(x) gives us the probability that the release time of the job is at or earlier than x (or the interrelease time of the stream of jobs is equal to or less than x) for all valid values of x. Rather than speaking of release times of aperiodic jobs, we sometimes use the term arrival times (or interarrival time) which is commonly used in queueing theory. An aperiodic job arrives when it is released. A(x) is the arrival time distribution (or interarrival time distribution).