Optimal use of Virtual Paths for connection setup reduction: The single link problem

One of the major problems faced by large networks is the enormous amount of processing required for setting up and tearing down the large number of connections maintained by the network. ATM aims at solving these problems via the Virtual Path (VP) mechanism which is used to group together the Virtual Connections (VC's). When a need for setting up a VC rises the request and its resource allocation are processed by the VP authority and not by the network, thus reducing the processing cost significantly. An important question in the design of these networks is the amount of network resources to be allocated to and held by the VP authorities; too high allocation will result with resource waste, while too low allocation will result with heavy connection set-up and tear-down processing load. In this paper we deal with this problem, aiming at deriving simple operational rules to determine the amount of bandwidth resources to be held by the various VP authorities. We formulate the resource allocation problem by accounting both for bandwidth utilization and for connection processing constraints. For a single link network we realize that the pure problem is too complex and thus formulate an approximate modal and derive the optimal allocation for it. The optimal rule is expressed as a closed-form square-root allocation. Extensive numerical examination shows that the algorithms proposed yield very efficient allocations. The single link model is then generalized to a general network model and an algorithm based on the single link allocation is proposed; that analysis is however beyond the scope of this paper and is reported in [2].