Optimal provision of multiple service types

Services of different types are provided to paying customers on servers hired from a cloud. Different virtual machines can share a server, subject to one or more resource constraints. Incoming jobs whose resource requirements cannot be satisfied are lost. The objective is to maximize the long-term average profit per unit time. A single-server model is analyzed exactly and the results provide approximations for the system with n servers. The latter is also solved exactly when the servers are dedicated and when the VMs can migrate instantaneously. Numerical examples and comparisons with simulations are presented.