Conversation with Merlin [email protected] · Thu Nov 16 2023

Can you please tell me how to calculate the cpu efficency of round robin scheduling when total processing time is given as 't', context switching time is given as 's' , time slice/quantum is 'q' and number of processes are 'n'.

To calculate the CPU efficiency of round robin scheduling, you can use the following formula:

CPU Efficiency = (Total Processing Time) / ((Total Processing Time) + (Number of Context Switches * Context Switching Time))

Where:

  • Total Processing Time (T) is the total time taken to complete all processes.
  • Number of Context Switches is calculated as (Total Processing Time) / (Time Slice/Quantum).
  • Context Switching Time (S) is the time it takes to save the state of one process and load the state of another.
  • Time Slice/Quantum (Q) is the maximum amount of time a process is allowed to run in a preemptive multitasking system before being put back in the ready queue.
  • The Number of Processes (N) is the total number of processes in the system.

Here's the step-by-step process for calculating CPU efficiency:

  1. Calculate the total processing time (T) by summing up the processing times of all the processes. T = t1 + t2 + ... + tn

  2. Calculate the number of context switches: Number of Context Switches = Total Processing Time / Time Slice/Quantum

  3. Calculate the CPU Efficiency using the formula: CPU Efficiency = T / (T + (Number of Context Switches * S))

By plugging in the values of T, S, Q, and N, you can calculate the CPU efficiency of the round robin scheduling algorithm.

Now using the above formula can you sovle this question. Measurements of a certain system have shown that a process runs, on the average, for time T before blocking for Input/Output. Process switch requires time S which is overhead. For round robin scheduling with quantum Q, give a formula for the cpu efficiency in each of the following cases:

(a) Q=infinity (b) Q>T (c) S<Q<T (d) Q=S (e) Q nearly 0

The CPU efficiency is influenced by the time quantum (Q). In round robin scheduling, different values of the time quantum will produce different CPU efficiencies. It's important to remember that, in the provided formula, a context switch is essentially a switch from one to another during execution due to the expiration of the quantum time. Below, I've outlined how to find CPU efficiency for each specified case:

(a) Q = ∞ This means that the scheduling is essentially non-preemptive as the task will not be context-switched until it requires IO, or in other words, until it completes its job. The CPU efficiency in this case will be 100%, as there won't be any context switches and no time is wasted for process.

(b) Q > T When the time quantum is greater than the process run time, it behaves in a way that is very similar to the scenario where Q = ∞. Even though we have a finite time quantum here, as long as it is greater than T, the process will likely complete before Q expires, making the system essentially non-preemptive.

(c) S < Q < T When the time quantum is less than the process run time but greater than the context switching time, context switches will occur. In this case, you should use the provided formula, which should look like this:

CPU Efficiency = T / (T + (T/Q)*S)

Here (T/Q) is the number of context switches.

(d) Q = S In this case, the time quantum equals the context switching time. Using the same formula as above, we see that the CPU Efficiency will be T / (T + (T/S)*S) or T / (2T), which is equal to 50%.

(e) Q nearly 0 When the quantum time is very small, the CPU is frequently switched between the tasks, leading to a very high number of context switches and very low CPU efficiency due to the overhead of context switch operations. The efficiency approaches 0% as Q approaches 0.