# Cyclo-Static DPN's

+1 vote

Hello,

my question relates to the exam on April 3, 2018: Problem 4b)

Why is the vector p multiplied by the lengths of the extended cycles?

Is there a difference between a bounded and a balanced DPN?

+1 vote

In a cyclo-static DPN, each node fires periodically a sequence of actions where each one has a fixed consumption/production rate. To determine a balanced schedule, we reduce the cycle-static DPN to a simple static DPN in that we consider an entire period of actions of a node as its single (period) action. We then solve the balance equations for the obtained static DPN, and in the example, we find out that in a balanced schedule, the nodes a,b,c,d have to fire 1,1,2,3 periods. To obtain the firing rate of atomic actions of each node, we multiply this vector by the lengths of the periods of each node that gives us then the number of actions that each node has to fire in a balanced schedule.

A balanced DPN satisfies the balance equations, thus, there EXISTS a schedule that keeps the DPN buffers in balance, i.e., non-empty and without buffer overflow. A bounded DPN is more restricted and has the property that ALL schedules are balanced. In a bounded DPN, we don't have to enforce a particular schedule, all nodes may fire as they like, and there will never be a buffer over-/underflow.
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