Optimal provision of multiple service types

Services of different types are provided to payingcustomers on servers hired from a cloud. Different virtualmachines can share a server, subject to one or more resourceconstraints. Incoming jobs whose resource requirements cannotbe satisfied are lost. The objective is to maximize the long-termaverage profit per unit time. A single-server model is analyzedexactly and the results provide approximations for the systemwith n servers. The latter is also solved exactly when the serversare dedicated and when the VMs can migrate instantaneously.Numerical examples and comparisons with simulations are presented