Pooia's law: Estimation of the emergent value of service oriented environments

In this paper we are to estimate the emergent value of service oriented environments considering number of system services and service usage. Although there are some previously proposed formulas to deal with networked environments such as Metcalfe's law, Sarnoff's law, Reed's law, and Zipf's law, they are not applicable for service oriented environments because of their dynamic ever-changing nature and also the capability of integration and composition. Focusing on service composition, either through orchestration or choreography, we propose a formula to calculate the emergent externalities by considering the usage probability of each service from atomic services to coarse grained ones, and treated these probabilities according to Zipf's distribution to present the final relation which is named as Pooia's law.