I&C Journal 1994 Journal Article
Time Bounds for Real-Time Process Control in the Presence of Timing Uncertainty
- H. Attiya
- N.A. Lynch
A timing-based variant of the mutual exclusion problem is considered. In this variant, only an upper bound, m, on the time it takes to release the resource is known, and no explicit signal is sent when the resource is released; furthermore, the only mechanism to measure real time is an inaccurate clock, whose tick intervals take time between two constants, c 1 ≤ c 2. When control is centralized it is proved that n[c2(⌊(m+l)/c1⌋+1)]+l is an exact bound on the worst case response time for any such algorithm, where n is the number of contenders for the resource and l is an upper bound on process step time. On the other hand, when control is distributed among processes connected via communication lines with an upper bound, d, for message delivery time, it is proved that n[c2(⌊(m+l)/c1⌋+1)+d+c2+2l] is an upper bound. A new technique involving shifting and shrinking executions is combined with a careful analysis of the best allocation policy to prove a corresponding lower bound of n·c2(m/c1)+(n−1)d. These combinatorial results shed some light on modeling and verification issues related to real-time systems.