Data center with an infinite number of servers.

Consider a data center with an infinite number of servers. Each server has 1 unit of CPU available. Three types of VMs (virtual machines) arrive to this system. VMs of type 1 request 1/2 unit of CPU each, VMs of type 2 request 1(4 unit of CPU each, and VMs of type 3 request 1/8 unit of CPU each. In each time slot, the number of VMs which arrive into the system is binomially distributed with parameters N and A. and each VM is of type 1. 2. or 3, with probability 113 each. Consider the following two assignment policies. • FirstFit policy: assign the VM to the lowest indexed server which can accommodate it. Update the available space in the server, once a VM is assigned to it. • BestFit policy: assign the VM to the server with the least amount of space available (among all servers which have enough space to accommodate the VM). Update the available space in the server, once a VM is assigned to it. VMs of type 1 stay in the system for a geometrically distributed amount of time with mean 10, VMs of type 2 stay in the system for a geometrically distributed amount of time with mean 8, VMs of type 3 stay in the system for a geometrically distributed amount of time with mean 30. Assume the following sequence of events in each time slot: departures occur first, then arrivals occur, followed by assignment of VMs to servers. • Assume A = 0.9. For different values of N, N = 10, N = 100, and N = 1000, compute the average number of servers used by simulating FirstFit policy for 106 time slots. • Assume A = 0.9. For different values of N. N = 10, N = 100, and N = 1000, compute the average number of servers used by simulating BestFit policy for 106 time slots. • Plot the average number of servers versus N under two policies, respectively. (in one plot) Note: 1. Choose one programming language to do the simulation from C/C••. Matlab, Python, Java, and R. 2. Report should include the plot, simulation code, and annotations. 3. Upload one single PDF file to Moodie for submission.