An Operating Systems Vade Mecum

Policies 31α =3Probability ofk arrivalsin 1 time unitα =5α =10510kFigure 2.2 Probability of k arrivals under the exponential distributionWe will often combine α and β to form ρ (‘‘rho’’), the saturation level, whichrepresents how busy the computer is on the average. We define ρ to be α / β. If ρ is 0,new processes never arrive, so the machine is completely idle. If ρ is 1, processes arriveon the average just exactly at the same rate as they can be finished. If ρ is greater than 1,processes are coming faster than they can be served. In this last case, we would expectthe ready list to get longer and longer. In fact, even if ρ is just 1, the expected length ofthe ready list is unbounded. The value of ρ affects the response measures differently fordifferent scheduling policies. We will therefore express these measures in terms of ρ.As you can see, the formal study of time management involves a certain amount ofmathematics. It is important to realize that any comparison of policies requires that therebe a way of describing their behavior (such as R ) and a way to characterize the situationin which the policies are measured (such as the distribution of service times). We willexpress the behavior of various policies using the notation just presented but will omit allthe derivations. We will discuss formal analysis later in the Perspective section.2 POLICIESAs we have seen, short-term scheduling refers to allocating time to processes that are inthe ready list. Every time a process arrives at the ready list, we will treat it as a new process.It may truly be a new process, but more often it is an old one that has been broughtback to the ready list from outside the short-term scheduler. It may have returnedbecause the transput it was waiting for has completed, some resource it was requestinghas been granted, or the medium-term scheduler has decided to favor it. Every time itleaves the ready list, either because it has terminated or because it must wait for somethinglike transput, we will forget about the process. We will say that the process hasdeparted when we do not need to state why it has left. This narrow view will allow us toconcentrate on the fundamentals of short-term scheduling.