ASYMPTOTIC BUFFER OVERFLOW PROBABILITIES IN MULTICLASS MULTIPLEXERS -AN OPTIMAL-CONTROL APPROACH

We consider a multiclass multiplexer with support for multiple service classes and dedicated buffers for each service class, Under specific scheduling policies for sharing bandwidth among these classes, we seek the asymptotic (as the buffer size goes to infinity) tail of the buff er overflow probability for each dedicated buffer, We assume dependent arrival and ser,ice processes as is usually the case in models of bur sty traffic, In the standard large deviations methodology, we provide a lower and a matching (up to first degree in the exponent) upper boun d on the buffer overflow probabilities. We introduce a novel optimal c ontrol approach to address these problems. In particular, we relate th e lower bound derivation to a deterministic optimal control problem, w hich we explicitly solve, Optimal state trajectories of the control pr oblem correspond to typical congestion scenarios, We explicitly and in detail characterize the most likely modes of overflow, We specialize our results to the generalized processor sharing policy (GPS) and the generalized longest queue first policy (GLQF). The performance of stri ct priority policies is obtained as a corollary, We compare the GPS an d GLQF policies and conclude that GLQF achieves smaller overflow proba bilities than GPS for all arrival and service processes for which our analysis holds, Our results have important implications for traffic ma nagement of high-speed networks and can be used as a basis for an admi ssion control mechanism which guarantees a different loss probability for each class.