Analyzing Event-Based Scheduling in Concurrent Reactive Systems

Abstract

The traditional research on scheduling focuses on task scheduling and schedulability analysis in concurrent reactive systems. In this article, we dedicate ourselves to event-based scheduling. We first formally define an event-based scheduling policy and propose the notion of the correctness of a scheduling policy in terms of weak termination. Then we investigate the correctness of the decomposition of scheduling controls and finally obtain a decentralized scheduling method. The method can automatically decompose the scheduling policies of a concurrent reactive system into atomic scheduling policies. Every atomic scheduling policy corresponds to one subsystem. Each of the subsystems is a completely independent system, which may be developed and deployed independently. An experiment demonstrates these results that may help engineers to design correct and efficient schedule policies for a concurrent reactive system.

Decomposition of UML activity diagrams

“…The detailed explanation refers the reader to the literature. 28 Definition 3. A dependency structure () is a tuple ⟨, I, T, S, C, P, F⟩ with…”

“…It has been used to analyze service adaptation, 30 business process configuration, 27 service configuration, 37 and decomposition of scheduling. 28 …”

“…Based on the previous discussion, the picture of the activity diagram of Figure 6 is drawn in the DStool tool. The tool will translate the picture into the activity diagram  = ⟨A, AO, Dn, Mn, Fn, Jn, R, Ia, Fa⟩ (see Definition 1) as the input of the decomposition algorithm, where A = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, i, f 1, f 2, f 3, f 4, f 5, dn1, dn2, dn3, dn4, dn5, dn6, dn7, fn1, fn2, fn3, fn4, fn5, jn1, jn2, jn3, mn1, mn2, mn3, mn4}, AO = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39}, Dn = {dn1, dn2, dn3, dn4, dn5, dn6, dn7}, Mn = {mn1, mn2, mn3, mn4}, Fn = {fn1, fn2, fn3 (7, jn1), (8, jn1), (dn2, 6), (6, f 1), (dn2, 9), (9, 10), (10, mn2), ( jn1, 11), (11,12), (12, dn3), (dn3, 13), (13, f 2), (dn3, 14), (14,15), (15, dn4), (dn4, 16), (dn4, 17), (16, fn2), ( fn2, 18), ( fn2, mn1), (18, f 3), (17, 19), (19, mn2), (mn2, 20), (20, fn3), ( fn3, 21), ( fn3, 22), (21, jn2), (22, jn2), ( jn2, 23), (23,24), (24,27), (27,29), (29, fn4), ( fn4, 30), ( fn4, 31), (30, dn5), (dn5, 28), (dn5, mn3), (28,26), (26, mn3), (mn3, 25), (25, f 4), (31, dn6), (dn6, 32), (dn6, mn2), (32, dn7), (dn7, 33), (dn7, 36), (33, fn5), ( fn5, 34), ( fn5, 35), (35, jn3), (34, jn3), ( jn3, 37), (36, mn4), (37,38), (38, mn4), (mn4, 39), (39, f 5)}, Ia = {i}, and…”

“…According to the translation rule in Definition 7, the activity diagram  is first translated into the dependency structure td() = ⟨, I, T, S, C, P, F⟩ where  = {0, 1, 2, 3, 4, 5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39, i, f 1, f 2, f 3, f 4, f 5}, I = {{i}}, T = {({i}, {0}), ({0}, {3}), ({0}, {1}), ({1}, {2}), ({2}, {4}), ({2}, {8}), ({4}, {7}), ({7, 8}, {11}), ({3}, {5}), ({5}, {6}), ({6}, {f 1}), ({5}, {9}), ({9}, {10}), ({11}, {12}), ({12}, {13}), ({13}, {f 2}), ({12}, {14}), ({14}, {15}), ({15}, {16}), ({16}, {18}), ({18}, {f 3}), ({16}, {2}), ({15}, {17}), ({17}, {19}), ({10}, {20}), ({19}, {20}), ({20}, {21}), ({20}, {22}), ({21, 22}, {23}), ({23}, {24}), ({24}, {27}), ({27}, {29}),({29}, {30}),({29}, {31}),({30}, {28}),({30}, {25}),({28}, {26}),({26}, {25}), ({25}, {f 4}), ({31}, {20}), ({31}, {32}), ({32}, {33}), ({32}, {36}), ({33}, {34}), ({33}, {35}), ({34, 35}, {37}), ({37}, {38}), ({36}, {39}), ({38}, {39}), ({39}, {f 5})}, S = {{7, 8}, {21, 22}, {34, 35}}, C = {{1, 3}, {6, 9}, {13, 14}, {16, 17}, {25, 28}, {20, 32}, {33, 36}}, P = ∅, and F = {{f 1}, {f 2}, {f 3}, {f 4}, {f 5}}.…”

“…Such semantics is actually the transition system-based structural operational semantics. 26 We choose an event-based model called a dependency structure 27,28 (formerly called a protocol structure 29,30 ) as the semantical model of activity diagram. Dependency structures are an extended version of the event-based models, such as the event structures, 31 the configuration structures, 32,33 and the Rapide approach.…”