An infinite server system with customer-to-server packing constraints

We consider a model which is motivated primarily by the problem of efficient “packing” of virtual machines into physical host machines in a network cloud. There is infinite number of servers and multiple flows of arriving customers of different types. Each server can simultaneously serve several customers, subject to some packing constraints. Service times of different customers are independent - even if customers share a server. Customers leave after their service is complete. A key underlying objective is to minimize the number of occupied servers. In this paper we consider the problem with approximate (“convexified”) objective, which can be arbitrarily close to the original one. We show that some versions of a greedy strategy are asymptotically optimal as the system scale (the total customer arrival rate) goes to infinity.