An example of deriving performance properties from a visual representation of program execution

Abstract

Through geometry, program visualization can yield performance properties. We derive all possible synchronization sequences and durations of blocking and concurrent execution for two process programs from a visualization mapping processes, synchronization, and program execution to Cartesian graph axes, line segments, and paths, respectively. Relationships to Petri nets are drawn.

Geometric Performance Analysis of Periodic Behavior

“…5b. Point G ϭ (0, 0) lies off a constraint line and follows Rule II, case (1). Thus the TET is ray [(0, 0), (1, 1)) followed by the TETs rooted at (1, 1).…”

“…Thus a point within an interval represents partial execution of a code segment. We could draw a similar diagram for philosopher 1: the intervals for each location would be [0, 1), [1,2), and [2,3); the cycle time would be 1 ϩ 1 ϩ 1 ϭ 3. applies to the horizontal lines. The TET is constructed as follows: A TET cannot cross a constraint line.…”

“…Any infinite length path through the graph, starting with initial state (Ϫ1, Ϫ1), represents a possible TES; one was listed in Section 1.2. All possible TESs contain the LCES (1, 0), (2,1), and (0, 2) for 3, 1, and 1 time units, respectively.…”

“…Furthermore, they conclude, an exponential task time assumption could actually lead to more severe errors than a constant-time assumption. Because we develop our solution method by starting with a program as a transition system, we lay the foundation for relaxing the remaining assumptions to study other parallel program classes, such as those in [1], with geometry.…”

“…The TES represents a program that starts in state (Ϫ1, Ϫ1), instantly moves to state (0, 0), remains in state (0, 0) for 1 time unit, then moves to state (1, 0) for 3 time units, and so on. The repeated sequence (i.e., (1, 0), (2,1), and (0, 2) for 3, 1, and 1 time units, respectively) is termed the limit cycle execution sequence (LCES). In general, for a given program there may exist an infinite number of possible TESs.…”