Scheduling criteria (turnaround time, waiting time, throughput) in Operating Systems - Time & Space Complexity

Time Complexity: Scheduling criteria (turnaround time, waiting time, throughput)

O(n)

Understanding Time Complexity

When we analyze scheduling criteria like turnaround time, waiting time, and throughput, we want to understand how the time taken by the system changes as the number of processes grows.

We ask: How does the system's work increase when more tasks need scheduling?

Scenario Under Consideration

Analyze the time complexity of calculating scheduling criteria for a list of processes.

for each process in process_list:
    calculate turnaround_time = completion_time - arrival_time
    calculate waiting_time = turnaround_time - burst_time
calculate throughput = total_processes / total_time
    

This code calculates turnaround time and waiting time for each process, then computes throughput for all processes.

Identify Repeating Operations

Look for repeated steps that take most time.

• Primary operation: Looping through each process to calculate turnaround and waiting times.
• How many times: Once for every process in the list.

How Execution Grows With Input

As the number of processes increases, the calculations grow in a simple way.

Input Size (n)	Approx. Operations
10	About 10 calculations for turnaround and waiting times
100	About 100 calculations
1000	About 1000 calculations

Pattern observation: The work grows directly with the number of processes, doubling the processes doubles the work.

Final Time Complexity

Time Complexity: O(n)

This means the time to calculate scheduling criteria grows in a straight line with the number of processes.

Common Mistake

[X] Wrong: "Calculating turnaround and waiting times takes the same time no matter how many processes there are."

[OK] Correct: Each process needs its own calculation, so more processes mean more work and more time.

Interview Connect

Understanding how scheduling calculations scale helps you explain system performance clearly and shows you grasp how operating systems handle many tasks efficiently.

Self-Check

"What if we had to recalculate waiting times every time a new process arrives? How would that affect the time complexity?"

Practice

1. Which scheduling criterion measures the total time taken from the arrival of a process to its completion?

easy

A. Turnaround time

B. Waiting time

C. Throughput

D. Response time

Solution

1. Step 1: Understand the definition of turnaround time

   Turnaround time is the total time from when a process arrives until it finishes execution.

2. Step 2: Compare with other criteria

   Waiting time is only the time a process waits before starting, throughput is number of processes completed per time, and response time is time until first response.

3. Final Answer:

   Turnaround time -> Option A

4. Quick Check:

   Turnaround time = total process duration [OK]

Hint: Turnaround = arrival to finish total time [OK]

Common Mistakes:

• Confusing waiting time with turnaround time
• Mixing throughput with time durations
• Thinking response time equals turnaround time

2. Which of the following correctly defines waiting time in process scheduling?

easy

A. Number of processes completed per unit time

B. Time from process arrival to completion

C. Time a process spends in the ready queue before execution

D. Time taken by CPU to execute the process

Solution

1. Step 1: Define waiting time

   Waiting time is the time a process spends waiting in the ready queue before it starts running on the CPU.

2. Step 2: Eliminate other options

   Time from process arrival to completion describes turnaround time, C describes throughput, and D is CPU burst time, not waiting time.

3. Final Answer:

   Time a process spends in the ready queue before execution -> Option C

4. Quick Check:

   Waiting time = time before execution [OK]

Hint: Waiting time = time before process runs [OK]

Common Mistakes:

• Confusing waiting time with turnaround time
• Thinking waiting time includes execution time
• Mixing throughput with waiting time

3. Consider three processes with the following completion times (in seconds): P1=10, P2=15, P3=20. If all arrived at time 0, what is the throughput if the total time observed is 20 seconds?

medium

A. 0.20 processes per second

B. 0.15 processes per second

C. 0.10 processes per second

D. 0.25 processes per second

Solution

1. Step 1: Calculate total processes completed

   All three processes (P1, P2, P3) completed within 20 seconds, so total completed = 3.

2. Step 2: Calculate throughput

   Throughput = number of processes completed / total time = 3 / 20 = 0.15 processes per second.

3. Final Answer:

   0.15 processes per second -> Option B

4. Quick Check:

   Throughput = 3/20 = 0.15 [OK]

Hint: Throughput = completed tasks ÷ total time [OK]

Common Mistakes:

• Dividing total time by number of processes instead of reverse
• Counting incomplete processes
• Using average completion time instead of total time

4. A scheduler reports the following for a process: Arrival time = 0, Start time = 5, Completion time = 12. The waiting time is incorrectly calculated as 7 seconds. What is the correct waiting time?

medium

A. 5 seconds

B. 7 seconds

C. 12 seconds

D. 0 seconds

Solution

1. Step 1: Understand waiting time formula

   Waiting time = Start time - Arrival time = 5 - 0 = 5 seconds.

2. Step 2: Identify error in reported waiting time

   The reported waiting time of 7 seconds is incorrect because it does not match the formula.

3. Final Answer:

   5 seconds -> Option A

4. Quick Check:

   Waiting time = start - arrival = 5 [OK]

Hint: Waiting time = start time minus arrival time [OK]

Common Mistakes:

• Using completion time instead of start time
• Adding instead of subtracting times
• Confusing waiting time with turnaround time

5. A system runs 4 processes with arrival times and burst times as follows:
P1: arrival=0, burst=4
P2: arrival=1, burst=3
P3: arrival=2, burst=1
P4: arrival=3, burst=3
If the scheduler uses First-Come-First-Serve (FCFS), what is the average turnaround time?

hard

A. 3.5 seconds

B. 4.5 seconds

C. 5.0 seconds

D. 6.0 seconds

Solution

1. Step 1: Calculate completion times using FCFS

   Process order by arrival: P1(0), P2(1), P3(2), P4(3).
   P1 completes at 0+4=4,
   P2 starts at 4, completes at 4+3=7,
   P3 starts at 7, completes at 7+1=8,
   P4 starts at 8, completes at 8+3=11.

2. Step 2: Calculate turnaround times

   Turnaround = completion - arrival:
   P1: 4-0=4,
   P2: 7-1=6,
   P3: 8-2=6,
   P4: 11-3=8.
   Average turnaround = (4+6+6+8)/4 = 24/4 = 6.0 seconds.

3. Final Answer:

   6.0 seconds -> Option D

4. Quick Check:

   Average turnaround = 24/4 = 6.0 [OK]

Hint: Turnaround = completion - arrival; average = sum/number [OK]

Common Mistakes:

• Calculating turnaround as burst time only
• Ignoring arrival times in scheduling order
• Mixing waiting time with turnaround time