Stochastic analysis and comparison of self-stabilizing routing algorithms for publish/subscribe systems

Publish/subscribe is becoming increasingly popular as it provides means for decoupled communication. One important issue for increasing the success of publish/subscribe middleware is to make them fault tolerant. Classical fault-tolerance mechanisms apply redundancy to mask certain faults. However, if a fault cannot be masked, it is not guaranteed that the system ever returns to normal operation. In contrast to that, self-stabilizing systems recover from arbitrary transient faults provided that faults do not continue to occur until the system is stable again. However, while the system stabilizes, it may not exhibit the desired behavior. In this paper, we present the first comprehensive analysis of publish/subscribe systems including self-stabilization, giving an alternative to extensive simulations. The analysis is based on continuous time birth-death Markov Chains and investigates the characteristics of publish/subscribe systems in equilibrium. We give closed analytical solutions for the sizes of routing tables, for the overhead required to keep the routing tables up-to-date, and for the leasing overhead required for self-stabilization. To judge the efficiency of self-stabilizing routing, we compare it to flooding which is the naive implementation of a self-stabilizing publish/subscribe system.