Starvation-Based Instability of Distributed Scheduling Policies in Non-Acyclic Fluid and Queuing Networks
We review the stability condition of a class of guided distributed scheduling policies in queuing systems and show that the same stability condition also holds for fluid systems. This condition is interpreted as requiring a contraction of machine starvation delays in the cycles of material flow in the system. Machine starvation is the cause of instability and arises naturally in queuing systems due to the discrete nature of operations (it can also be caused by the scheduling policy). In fluid systems, however, machine starvation can only be caused by the scheduling policy. Although the cause of machine starvation can be different in queuing and fluid systems, our results show that this is inconsequential to the condition for stability.
Noting that instability is caused by machine starvation which leads to slow down (or stoppage) of machines, we show that the condition for stability of a system studied by Kumar and Seidman can be expressed as an ordinary capacity condition for the corresponding slowed down system.
KeywordsFluid System Reference Trajectory Part Type Part Release Fluid Network
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