Fair and efficient mutual exclusion algorithms

Abstract

Peterson’s n-process mutual exclusion algorithm [P81] has been widely touted for elegance and simplicity. It has been analyzed extensively, and yet certain properties have eluded the researchers. This paper illustrates, and expands on, several properties of Peterson’s algorithm: (1) We reiterate that the number of processes that can overtake a process, called unfairness index, is unbounded in Peterson’s algorithm; (2) With a slight modification of the algorithm, we obtain the unfairness index of n(n – 1)/2; (3) We identify an inherent characteristic of that algorithm that sets the lower bound of n(n – 1)/2 for the unfairness index; (4) By modifying the characteristic, we obtain algorithms with unfairness index (n –− 1); (5) We show that the new algorithms are amenable to reducing shared space requirement, and to improving time efficiency (where the number of steps executed is proportional to the current contention); and (6) We also extend the algorithms to solve lexclusion problem in a simple and straightforward way.