Note on `distributed scheduling based on due dates and buffer priorities´ by S.H. Lu and P.R. Kumar

In the above-titled paper by Lu and Kumar (ibid., vol.36. no.12, pp.1406-1416, Dec 91), the issue of stability of a scheduling policy for a system with reentrant structure is studied. It has been shown that whenever the arrival rate, allowing for some burstiness, is less than the system capacity, the following four scheduling policies are stable: first buffer first serve, last buffer first serve, earliest due date, and least slack policies. To verify that the problem is not trivial, a counterexample of instability, yet satisfying the usual stability condition, is provided. However, the counter-example calls for zero processing times. It is shown that counter-examples with nonzero processing times do exist, and understanding of the stability issue of general discrete-event dynamic systems is promoted