Question

A cloud computing provider has 475 customers and a farm of 250 compute servers each having 4 cores. The company statistics indicate that at the peak hour the workload requirements of its customers are such that each requires {0,1,2,3,4} cores with uniform probability. Use the approximation based on Central Limit Theorem to answer the following questions.

1. Compute the outage probability, i.e., the probability that there are not a sufficient number of cores to meet customers demands.

2. The company decides to offer its customers a new super fast service which would speed up their quality of service by automatically doubling the number of cores allocated to each customer. Each customer would thus be allocated {0,2,4,6,8} cores with uniform probability. How many extra (4 core) machines should you need to buy in order support new service while maintaining the same outage probability ?

3. The server vendor is quite happy to sell you the number of 4 core servers determined in the previous question, but offers you a great deal on the same number of 8 core servers. If you purchased the same number of servers but now with 8 cores, how many super fast customers could you support same outage probability?

Answer 1

The number of cores required by the customers is the random variable , where with probability . The mean of

The variance

So the mean of is

So the variance of is

1) According to CLT,, The outage probability is found as

The probability that there are not a sufficient number of cores to meet customers demands is

2) Now . The mean is

As in part (1)

Let be the number of cores required. Then

So the number of cores required is 2002. Number of machines required is .The number of extra (4 core) machines requrted is

3) Let you can support same outage probability. Then

He can support customers.