Mission critical publish-subscribe performance modeling using linear algebraic and classical methods

Modeling Service Oriented Architecture (SOA) PublishSubscribe (Pub/Sub) message patterns using queueing models is challenging for several reasons. Due to the single source to multiple destination nature of Pub-Sub message distribution. Most queueing models assume a work conserving approach where a pass-thru server does not create jobs. However in the Pub-Sub message pattern, a message can be duplicated at any message node along the route to be routed to a different destinations, forming a tree type distribution. Also, most analytic performance models of large networks make simplifying assumptions for the arrival and service processes to keep the models tractable. This may affect the accuracy of the model significantly. In this work, we construct analytic and simulation performance models for Pub/Sub messaging systems. In this work, we construct an analytic performance model of a Pub/Sub system using Linear Algebraic Queueing Theory (LAQT) that is both scalable and accurate. Matrix-Exponential distributions are used to model general arrival and service processes (Gi/G/1). A second analytic model is constructed that is a variation of the popular classical model Queueing Network Analyzer (QNA). In QNA, we use the customer creation feature of QNA to create messages at interior nodes where message duplication may occur. Finally, we use a simulation model both to validate the QNA and LAQT models as well as to gain insight to the problem of modeling Pub/Sub message patterns. We test all of these models on a network of 9 nodes and 12 products distributed to users.