1 Quorum System

• replicated databases,
• mutual exclusion,
• read/write storage, and
• group communication.
We’ll cover classical quorum systems in the class and evaluate the quorum systems using
various measures. Specifically, we’ll look into following two applications of quorum systems:
1. distributed read/write storage (Lamport’s register) and
2. consensus.
1.2.1 Replicated Databases
A major goal of the Replicated databases is to ensure consistency in the context of failures,
and Quorum system was first used to implement them by [Thomas, 1979]. He proposed a
majority approach to achieve the consensus in order to maintain the concurrency control
over multiple copies of a replicated database. The majority approach works as follows. To
write data into database, the writer would timestamp the data (Lamport timestamp) and
write it to a majority of servers. Then to read data from the database, the reader would
contact a majority (possibly different) and return the data with the highest timestamp.
Later, arbitrary quorum sizes (not just majority) were also allowed, but all of them required
the non-empty pairwise intersections between quorums (the main reason behind consistency
of Quorum system). In fact, separate read and write quorums are also studied where only
quorum of different classes need to intersect (for example, among read and write quorums,
but not among read quorums).
1.3 System Model
Let S = {s 1 , s 2 , . . . , s n } be the set of n processes that constitute the distributed system.
Each process is running its own protocol. For now, we assume a fixed set of processes, but
this model can be extended to deal with system with dynamic process membership, where
processes join or leave the system (and hence S is not fixed).
Definition 2 A process is a state machine (or I/O automaton), which can be in various
states following the various process actions (called transitions), as defined below. Every
process has input, internal, and output actions, defined by in(s), int(s), out(s) respectively,
for a given process s. External actions to a process are either the input to it (recv) or output
to other process (send). More formally,
2