COMP9334 Revision Questions Week 2A
The following question is Question 10 from Chapter 3 of Mensace et al. ¡°Performance by Design¡±. It has been reproduced below for your convenience.
It is then followed two questions on Poisson process on Page 2.
Questions on the arrival process.
Question 1. If the inter-arrival time of requests at a server is exponentially distributed with a mean rate of 20 requests per second, answer the following questions.
a) What is the mean inter-arrival time?
b) Over a duration of 1 minute, what is the mean number of
requests arriving at the server?
c) Over a duration of 1 minute, what is the probability of
having no arrivals at the server?
d) Over a duration of 1 minute, what is the probability of
having 10 arrivals at the server?
Question 2. This question is about Poisson Process. A server receives requests from two arrival processes. Both arrival processes are Poisson. The rates of these two processes are r1 and r2 respectively. Assuming these two processes are independent, prove that the aggregation of these two arrival processes is also Poisson. What is the aggregated arrival rate?