Liveness Enforcing Supervision of Video Streaming Systems Using Nonsequential Petri Nets

Abstract

The Internet motivated video streaming systems are largely complicated by issues such as a high degree of network resource sharing amongst many flows, which potentially leads to deadlocks. Using concepts of siphons along with their corresponding dangerous markings, we derive an algebraically necessary and sufficient characterization for such a much undesirable situation. The target system is assumed to be described in a Petri net formalism, whose markings provide the information on the current interactions among related network operations and resources. The theoretic materials allow us to introduce the control laws iteratively. At each iteration step, we produce a generalized mutual exclusion constraint which contains only markings for which liveness can be enforced. Since the explicit enumeration of all siphons is avoided, the proposed method can greatly reduce the complexity of off-line computation for the on-line restriction policy. Furthermore, a generalized elementary siphon control investigation is involved such that the final supervisor can be structurally simplified. Examples are demonstrated in this paper to validate the effectiveness and efficiency of the proposed approach.

Modelling and Control of Resource Allocation Systems within Discrete Event Systems by Means of Petri Nets -- Part 1: Invariants, Siphons and Traps in Deadlock Avoidance

“…There exist many papers where siphons and traps are defined -see e.g. [72,84,58,60,61,92,93,54] and many newer ones mostly written by Chinese authors [63,8,25,55,56,57,59,62,64,28,29,30,31,32,33,34,35,36,37,38,39,40]. Siphons and traps are basic net structures of PN [84] which allow important views on the behaviour of the modelled system as well as on some implications on this behaviour.…”

“…Of course, since that time the deadlock theory, and especially the deadlock avoidance one, has been intensively developed -see e.g. [46,78,79,80,81,75,74,73,82,86,87] and especially [63,8,25,55,56,57,59,62,64,28,29,30,31,32,33,34,35,36,37,38,39,40,92,93,94,91,88,89,65,66,67,68,69,58,60,61,47,48,49,50,51,…”

“…Then, the properties of found siphons are utilized at the control synthesis. Although this topic was opened long ago [72,1,2] it is still very live -see recent contributions [7,24,25,51,9,10,63,8,25,55,56,57,59,62,64,28,29,30,31,32,33,34,35,36,37,38,39,40]. The basis of such an approach to control consists in avoiding of emptying (unmarking) of places creating the siphons.…”

“…More details can be found e.g. in [47,48,49,50,51] as well as in [63,8,25,55,56,57,59,62,64,28,29,30,31,32,33,34,35,36,37,38,39,40]. More details can be seen e.g.…”

“…More details can be seen e.g. in [47,48,49,50,51] as well as in a great deal of applications in [63,8,25,55,56,57,59,62,64,28,29,30,31,32,33,34,35,36,37,38,39,40], where also newest approaches to the siphon-based control of AMS/FMS and RAS are presented as follows.…”