Question

Suppose a multiprogramming operating system is allotting time slices of 50 milliseconds. If it normally takes 8 milliseconds to position a disk's read/ write head over the desired track and another 17 milliseconds for the desired data to rotate around to the read/write head, how much of a program's time slice can be spent waiting for a read operation from a disk to take place? If the machine is capable of executing ten instructions each nanosecond, how many instructions can be executed during this waiting period? (This is why when a process performs an operation with a peripheral device, a multiprogramming system terminates that process's time slice and allows another process to run while the first process is waiting for the services of the peripheral device.)

Short answer

A program spends 25 ms waiting for a read, executing 250 million instructions.

Step-by-step solution

Calculate Total Waiting Time

First, determine the total time required to complete the disk read operation. This involves two tasks: positioning the disk's read/write head, which takes 8 milliseconds, and waiting for the desired data to rotate to the head, which takes another 17 milliseconds. Therefore, the total time spent waiting is the sum of these two durations: \[ \text{Total Waiting Time} = 8 \text{ ms} + 17 \text{ ms} = 25 \text{ ms} \]

Determine Time Spent Waiting in Time Slice

Next, find out how much of the program's 50 millisecond time slice is used for waiting. As calculated earlier, the total waiting time for the read operation is 25 milliseconds. Since this time is within the given time slice, the program spends 25 milliseconds of its 50 millisecond time slice waiting.

Execute Power of the Machine

The problem states that the machine can execute 10 instructions each nanosecond. Since 1 millisecond equals 1,000,000 nanoseconds, we can calculate how many instructions can be executed in one millisecond by multiplying: \[ \text{Instructions per millisecond} = 10 \times 1,000,000 \text{ = 10,000,000 instructions/ms} \]

Calculate Total Executable Instructions

Now calculate the total number of instructions executable during the 25 millisecond waiting period. Use the instructions per millisecond determined in the previous step, and multiply by the 25 milliseconds of wait time: \[ \text{Total Instructions} = 10,000,000 \text{ instructions/ms} \times 25 \text{ ms} \] This results in \( 250,000,000 \) instructions that can be executed during the waiting period.

Key concepts

Multiprogramming

Multiprogramming is a technique used by operating systems to improve the efficiency of CPU utilization. It involves running multiple programs concurrently by sharing system resources like CPU time, memory, and I/O devices. By doing so, the operating system can ensure that the CPU is never idle, as there is always another process ready to execute while one process waits for a resource such as a disk or network operation.

In the context of the exercise, the multiprogramming system allows a process to use a time slice of CPU time. When a program requests a peripheral operation, such as reading from a disk, it might need to wait. To make use of this waiting time, another process can be scheduled, making sure the CPU is always busy executing instructions. This approach keeps all parts of the computer operating efficiently, preventing idleness and boosting overall system performance.

Time Slices

An essential concept of modern operating systems is the time slice, which is the duration a process is allowed to run on the CPU before being preempted to let another process use the CPU. This is part of a technique called "time-sharing," where multiple processes appear to be running simultaneously by switching between them rapidly.

In this particular exercise, each process is allocated a time slice of 50 milliseconds. During this slice, the process holds control of the CPU and can perform calculations and other operations. The operating system is responsible for managing these allocations and ensuring all processes receive fair chances to utilize the CPU.

Time slicing allows for effective multiprogramming as it ensures that no single process can monopolize the CPU, thereby maximizing the overall throughput and responsiveness of the system.

Disk Scheduling

Disk scheduling is a crucial function in operating systems that manages the order and timing of disk access requests. This becomes particularly important in multiprogramming environments where multiple processes may have pending disk operations. The goal of disk scheduling is to optimize access times and data retrieval efficiency.

In the exercise scenario, a disk read operation involves positioning the disk's read/write head and waiting for the data to align with it, a process that takes a total of 25 milliseconds. Effective disk scheduling might involve reordering disk requests to minimize the delay experienced by processes to access their data.

This optimizes the use of disk bandwidth and reduces wait times for processes, improving the system's overall throughput.

Instruction Execution Rate

The instruction execution rate refers to the speed at which a CPU can process instructions. It is often measured in instructions per second, million instructions per second (MIPS), or similar metrics.

In the exercise, the CPU can execute 10 instructions per nanosecond, which translates into being able to perform 10,000,000 instructions in just one millisecond. This ability is utilized when the CPU is idle from waiting for I/O operations, such as disk reads; the system can execute a tremendous number of instructions during what might otherwise be dead time.

By calculating the total instructions possible during a disk wait time of 25 milliseconds, you see how important it is to understanding the instruction execution rate. Here, a total of 250,000,000 instructions can be executed while the CPU patiently waits. This highlights the operating system's role in optimizing these moments to keep the system working efficiently.