Modelling window flow control mechanisms

We present an approximation technique for solving open queueing networks consisting of several su~networks.Each subnetwork models a set of shared resources managed by a semaphore. The 9~euelng n~tworks analyzed have features that are commonly used in Petri Nets, such as, fork and JOIn operations and semaphore queues. This type of queueing network arises naturally when modelling multiple window flow control mechanisms. The approximation procedure is easy to implement and it can be included in a software package. Using this procedure, we present a case study involving the modelling and analysis of the ISO X25 flow control mechanism. 1INTRODUcnON In this paper, we describe and analyze the sharing of a resource depicted by a queueing network. The resource sharing is managed by a semaphore operation. Semaphore operations have traditionally been described using Petri nets. The Petri Net approach, however, relies on the numerical solution of an underlying rate matrix. The size of this matrix grows rapidly as the problem under study becomes more complex. In view of this, we model such systems as queueing networks, which we then analyze approximately using a hierarchical decomposition algorithm. The sharing of several resources is a common phenomenon in computer systems. This problem has been studied by several authors. In particular, Jacobson and Lazowska [Jaco 82] developed an iterative approximation method for analyZ0~ a sy~tem involyi!1~ the sharing of a set of reso~ces. This set of resources is assumed to be partitioned Into two disjointed groups, namely, the pnmary and the secondary resource group. A customer, after it accesses a primary resource, is allowed to access secondary resources in sequence. The primary resource elements are kept by the customer, as long as the customer utilizes elements of the secondary resource group. Freund and Bexfield [preu 83] developed an approximation method based on decomposition, to analyze the sharing of resources modelled as a closed queueing network. Sauer [Saue 81a] exten~ed an approximation method to the case where heterogeneous customers share a resource. The solution