Understanding the Problem: Average Waiting Time Calculation

The question asks us to find the average waiting time for each process based on the rate at which processes arrive and the average number of processes currently waiting in the queue. This is a classic problem that can be solved using principles from queueing theory, specifically Little's Law.

Applying Little's Law

Little's Law is a fundamental theorem in queueing theory that provides a relationship between the average number of items in a stable system ($L$), the average arrival rate ($λ$), and the average time an item spends in the system ($W$). The formula is:

$ L = \lambda \times W $

In the context of this problem:

• $L_q$ represents the average number of processes waiting in the queue. From the question, we know $L_q = 20$ processes.
• $λ$ represents the average arrival rate of processes. The question states that $λ = 10$ processes/second.
• $W_q$ represents the average time a process spends waiting in the queue (average waiting time). This is what we need to calculate.

We can adapt Little's Law to calculate the average waiting time in the queue ($W_q$):

$ L_q = \lambda \times W_q $

Step-by-Step Calculation

1. Identify the given values:
   • Average number of processes in the queue ($L_q$): 20
   • Average arrival rate ($λ$): 10 processes per second
2. Rearrange Little's Law to solve for $W_q$:

   $ W_q = \frac{L_q}{\lambda} $

3. Substitute the given values into the formula:

   $ W_q = \frac{20 \text{ processes}}{10 \text{ processes/second}} $

4. Calculate the result:

   $ W_q = 2 \text{ seconds} $

Conclusion

Therefore, the average waiting time per process in the queue is 2 seconds. This means, on average, a process arriving will have to wait for 2 seconds before it starts executing.