Formulating the influence of peer-to-peer systems scale up on access transparency

Distributed systems concepts have been presented since 1960 and there are many more attempts to develop these concepts to reach a real distributed system. But none of them able to implement all distributed systems goals and have some limitation. The major part of these limitations is related to no clear quantity relation are defined for distributed systems concepts. These limitations cause the developments were very special purpose like P2P system. P2P systems were developed on internet that is a dynamically scalable and heterogeneous system. Therefore scalability is one of the important challenges in P2P systems. On the other hand P2P systems have tried to provide transparent sharing in the Internet, especially transparent access to resources. Access transparency is more important to P2P systems because it affects more the system configuration, dynamicity and performance therefore the other important challenge in P2P systems is access transparency. However in distributed systems there isn't any clear mathematic relation between these two concepts, scalability and access transparency. Although we know that any increase in the scalability of a P2P systems cause complexity in access transparency establishing because the frequency of data exchanges as well as the system's process communication time increases exponentially. It is thus important for a P2P system to decide dynamically how far to allow the scale up, given the additional overheads it has to suffer from establishing data access transparency. This tradeoff decision in the statically or dynamically created P2P system can be made either quite centrally by a single manager, completely distributed by independent machines, or in a hybrid way. In this paper we first define scalability concept base on set theories and then adapted concept of access transparency to P2P systems and define some metrics for it. Finally formulates the relation between scalability and access transparency in P2P systems. The relation helps to calculate the overhead of establishing data access transparency when a P2P system is scaled up.