## Computer Science Technical Reports

Technical Report

12-1-2007

TR2007-608

#### Abstract

This paper concerns two fundamental problems in distributed computing---mutual exclusion and mobile object tracking. For a variant of the mutual exclusion problem where the network topology is taken into account, all existing distributed solutions make use of tokens. It turns out that these token-based solutions for mutual exclusion can also be adapted for object tracking, as the token behaves very much like a mobile object. To handle objects with replication, we go further to consider the more general $k$-exclusion problem which has not been as well studied in a network setting. A strong fairness property for $k$-exclusion requires that a process trying to enter the critical section will eventually succeed even if \emph{up to} $k-1$ processes stay in the critical section indefinitely. We present a comparative survey of existing token-based mutual exclusion algorithms, which have provided much inspiration for later $k$-exclusion algorithms. We then propose two solutions to the $k$-exclusion problem, the second of which meets the strong fairness requirement. Fault-tolerance issues are also discussed along with the suggestion of a third algorithm that is also strongly fair. Performances of the three algorithms are compared by simulation. Finally, we show how the various exclusion algorithms can be adapted for tracking mobile objects.

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