On a unified framework for the evaluation of distributed quorum attainment protocols

Quorum attainment protocols are an important part of many mutual exclusion algorithms. Assessing the performance of such protocols in terms of number of messages, as is usually done, may be less significant than being able to compute the delay in attaining the quorum. Some protocols achieve higher reliability at the expense of increased message cost or delay. A unified analytical model which takes into account the network delay and its effect on the time needed to obtain a quorum is presented. A combined performability metric, which takes into account both availability and delay, is defined, and expressions to calculate its value are derived for two different reliable quorum attainment protocols: D. Agrawal and A. El Abbadi´s (1991) and Majority Consensus algorithms (R.H. Thomas, 1979). Expressions for the primary site approach are also given as upper bound on performability and lower bound on delay. A parallel version of the Agrawal and El Abbadi protocol is introduced and evaluated. This new algorithm is shown to exhibit lower delay at the expense of a negligible increase in the number of messages exchanged. Numerical results derived from the model are discussed