1. A system for managing requests for an additional virtual machine, the system comprising: a memory; a processor communicatively coupled to the memory, where the processor is configured to perform operating at least one virtual machine accessing at least one computer resource associated with at least one physical machine within a computing cluster; receiving at least one non-deterministic virtual machine request for the computer resource; determining a maximum number of allowed concurrent computer resource requests in a policy for the physical machine is given by a minimum of a supreme subset of independent computational resource requests and a probability of a utilization of the computer resource, wherein the maximum number of allowed concurrent computer resource requests N max in a policy is given by N ma ⁢ ⁢ x = min k ∈ K ⁢ { sup ⁢ { n | F Z k n ⁡ ( U k * ) ≥ ( 1 - ɛ k ) } } , where sup is a supremum subset and n is a sum of independent k th computer resource request; and based on the probability of the utilization of the computer resource being less than a probabilistic bound on an over-utilization of the computer resource, allowing admission of an additional virtual machine on the physical machine associated with the computer resource, otherwise, rejecting the request for the computer resource.