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The question of which task to schedule for execution at any moment has been the subject of much research and considerable design effort The answer depends in part on the type of operating system If the system is a batch system, the scheduling plan should optimize throughput (the number of jobs completed per hour), CPU utilization, and/or turnaround time (the average elapsed time between the submission of a job and its completion) If the system is an interactive system, the scheduler should provide responsiveness and the impression of fairness to all users Interactive systems often have less well-defined boundaries of jobs, so the criteria mentioned for batch systems are not as relevant A more important criterion is response time to the user, the time delay between input from the user and some response back from the process.

The Fibonacci function (Example 9.6) is more heavily recursive than the factorial function (Example 9.2) because it includes two recursive calls. The consequences can be seen from the trace of the call

fib(5), shown in Figure 9.2 on page 168. The call originates in the main() function, passing 5 to the fib() function. There, the value of the parameter n is 5, so it calls fib(4) and fib(3), passing 4 and 3,

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If the system is a real-time system, with important constraints on execution time, the scheduler will be judged by the consistency with which applications meet their deadlines, and the predictability of performance Some real-time systems are hard real-time systems, meaning that important absolute limits bound performance requirements (imagine a system that coordinates process equipment in a chemical plant) Other real-time systems are soft real-time systems, meaning the highest priority processes should execute as fast as possible, but absolute limits on processing time do not exist An important way in which schedulers differ is in whether or not the scheduler is preemptive A preemptive scheduler can interrupt an executing process and switch to a different one Such a change is called a context switch, and entails a substantial amount of system overhead in changing the contents of registers, memory maps, and cache memory.

respectively. Each of these calls then makes two more recursive calls, continuing down to the basis calls f(1) and f(0). Each of these basis calls returns 1. The recursive calls then return the sum of the two values returned to them, ultimately resulting in the value 8 being returned to main().

THE RECURSIVE BINARY SEARCH The nonrecursive binary search algorithm is given on page 31. It uses the divide-and-conquer strategy, each time splitting the sequence in half and continuing the search on one half. This is naturally recursive. EXAMPLE 9.9 The Recursive Binary Search

First come first served (FCFS) Early batch systems used a simple FCFS (FCFS also called FIFO, for first in first out) scheduling system With FCFS, the first process to the system is scheduled, and it runs to completion or until it is blocked.

Here is the recursive binary search algorithm: (Precondition: s = {s0, s1, . . ., sn 1} is a sorted sequence of n ordinal values of the same type as x.) (Postcondition: either the index i is returned where si = x, or 1 is returned.) 1. If the sequence is empty, return 1. 2. Let si be the middle element of the sequence. 3. If si = x, return its index i . 4. If si < x, apply the algorithm on the subsequence that lies above si . 5. Apply the algorithm on the subsequence of s that lies below si . It is implemented in Example 9.10.

The recursive binary search runs in O(lgn) time. The running time is proportional to the number of recursive calls made. Each call processes a subsequence that is half as long as the previous one. So the number of recursive calls is the same as the number of times that n can be divided in two, namely lg n.

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(eg, for I/O) When a job completes or blocks, the next process on the waiting queue of processes is allowed to execute As a process becomes unblocked, it goes to the end of the FCFS queue as if it had just arrived While simple to implement, FCFS does not perform as well as other algorithms on the measures of turnaround time and throughput, particularly when some processes are much more compute-bound (need extended time with the CPU for computation) and others are more I/O-bound (use less CPU time, but require many interruptions for I/O) Shortest job first (SJF) With SJF, the operating system always chooses the shortest job to execute first The merit of this plan is that such a scheme will insure the minimum average turnaround time and the maximum average throughput (in terms of jobs per hour).

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