The BAR approach for multiclass queueing networks with SBP service policies

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Abstract: We extend the BAR-approach to prove heavy traffic steady-state convergence of multiclass queueing networks operating under static-buffer-priority service disciplines. Previously, a restrictive version of the BAR-approach was introduced to study generalized Jackson networks in which each service station has a single job class. The extension makes a connection with Palm distributions that allow one to attack a difficulty arising from queue length truncation. The convergence occurs under three additional conditions: stability, state space collapse, and a certain matrix being "tight". These three conditions are shown to hold in reentrant lines operating under first-buffer-first-serve and last-buffer-first-serve disciplines. In a two-station, five-class reentrant line, under the heavy traffic condition, the tight-matrix condition implies both the stability and SSC conditions. It is an open problem whether such a relationship holds generally. The extension is expected to be needed for studying heavy traffic steady-state convergence of stochastic processing networks.

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