Suppose there are five sites, each with a copy of a database element X. One of these sites P is the dominant site for X and will be used as X’s primary site in a primary-copy distributed-lock system. The statistics regarding accesses to X are:
i. 50% of all accesses are read-only accesses originating at P.
ii. Each of the other four sites originates 10% of the accesses, and these are read-only.
iii. The remaining 10% of acceses require exclusive access and may originate at any of the five sites with equal probability (i.e., 2% originate at each).
For each of the lock methods below, give the average number of messages needed to obtain a lock. Assume that all requests are granted, so no denial messages are needed.
a) Read-locks-one; write-locks-all.
b) Majority locking.
c) Primary-copy locking, with the primary copy at P.