At a load sharing network consumers of different types arrive according to independent Poisson processes. They can be served at certain locations within the network depending on their type, and they are assigned to suitable locations using an allocation policy. The holding times of the demands are i.i.d. exponentially distributed. Three different allocation policies are compared by evaluating the associated overflow exponents of the network: optimal repacking (AR), least load routing (LLR), and Bernoulli splitting (BS). At first the evaluation is performed for simple and basic networks and then in case of AR and BS generalized for networks with arbitrary topologies. For the LLR-policy in the general case a conjecture is formulated. The proofs heavily depend on large deviations theory.