Sharing within limits: Partial resource pooling in loss systems

Fragmentation of expensive resources, e.g., the spectrum for wireless services, between providers can introduce inefficiencies in resource utilization and worsen overall system performance. In such cases, resource pooling between independent service providers can be used to improve performance. However, for providers to agree to pool their resources, the arrangement has to be mutually beneficial. The traditional notion of resource pooling, which implies complete sharing, need not have this property. For example, under full pooling, one of the providers may be worse off and hence has no incentive to participate. In this paper, we propose partial resource sharing models as a generalization of full pooling, which can be configured to be beneficial to all participants. We formally define and analyze two partial sharing models between two service providers, each of which is an Erlang-B loss system with the blocking probabilities as the performance measure. We show that there always exist partial sharing configurations that are beneficial to both providers, irrespective of the load and the number of circuits of each of the providers. A key result is that the Pareto frontier has at least one of the providers sharing all its resources with the other. Furthermore, full pooling may not lie inside this Pareto set. The choice of the sharing configurations within the Pareto set is formalized based on the bargaining theory. Finally, large system approximations of the blocking probabilities in the quality-efficiency-driven regime are presented.