Question

Requests From A Database Server Arrive At Mean Arrival Rate For 500 Per Second. The DB Server Responds In About 1 Ms. Assuming That We Can Replicate The Data Using Data Mirroring Technology Which Will Slow Down The Response Rate By 10%. A. Analyze This Queue Under Both Assumptions. B. Assuming A Finite Queue Of 20 Buffers, What Is The Probability Of

Answer 1

The average arrival rate is 500 requests per second, and the average response time is 1.1 milliseconds after data mirroring technology is applied. Assuming a finite queue of 20 buffers, the probability of the system being full is 2.75%.

Step-by-step explanation:

a. Since we expect 500 requests per second, on average, one request will arrive every 1/500 seconds (or 2 milliseconds). After data mirroring technology is applied, the response rate will slow down by 10%, so the response time will be approximately 1.1 milliseconds.

b. Assuming a finite queue of 20 buffers, we can use Little's Law to calculate the probability of the system being full. Little's Law states that the average number of customers in a system is equal to the average arrival rate multiplied by the average time spent in the system.

In this case, the average arrival rate is 500 requests per second and the average time spent in the system is the response time, which is 1.1 milliseconds. So, the average number of requests in the system is 500 * 0.0011 = 0.55 requests. Since the number of buffers is 20, the probability of the system being full is 0.55/20 = 0.0275, or 2.75%.