Many-Sources Large Deviations for Max-Weight Scheduling

In this paper, a many-sources large deviations principle (LDP) for the transient workload of a multi-queue single-server system is established where the service rates are chosen from a compact, convex and coordinate-convex rate region and where the service discipline is the max-weight policy. Under the assumption that the arrival processes satisfy a many-sources LDP, this is accomplished by employing Garcia's extended contraction principle that is applicable to quasi-continuous mappings. For the simplex rate-region, an LDP for the stationary workload is also established under the additional requirements that the scheduling policy be work-conserving and that the arrival processes satisfy certain mixing conditions. The LDP results can be used to calculate asymptotic buffer overflow probabilities accounting for the multiplexing gain, when the arrival process is an average of \emph{i.i.d.} processes. The rate function for the stationary workload is expressed in term of the rate functions of the finite-horizon workloads when the arrival processes have \emph{i.i.d.} increments.Comment: 44 page

GPS queues with heterogeneous traffic classes

We consider a queue fed by a mixture of light-tailed and heavy-tailed traffic. The two traffic classes are served in accordance with the generalized processor sharing (GPS) discipline. GPS-based scheduling algorithms, such as weighted fair queueing (WFQ), have emerged as an important mechanism for achieving service differentiation in integrated networks. We derive the asymptotic workload behavior of the light-tailed class for the situation where its GPS weight is larger than its traffic intensity. The GPS mechanism ensures that the workload is bounded above by that in an isolated system with the light-tailed class served in isolation at a constant rate equal to its GPS weight. We show that the workload distribution is in fact asymptotically equivalent to that in the isolated system, multiplied with a certain pre-factor, which accounts for the interaction with the heavy-tailed class. Specifically, the pre-factor represents the probability that the heavy-tailed class is backlogged long enough for the light-tailed class to reach overflow. The results provide crucial qualitative insight in the typical overflow scenario

A methodological approach to BISDN signalling performance

Sophisticated signalling protocols are required to properly handle the complex multimedia, multiparty services supported by the forthcoming BISDN. The implementation feasibility of these protocols should be evaluated during their design phase, so that possible performance bottlenecks are identified and removed. In this paper we present a methodology for evaluating the performance of BISDN signalling systems under design. New performance parameters are introduced and their network-dependent values are extracted through a message flow model which has the capability to describe the impact of call and bearer control separation on the signalling performance. Signalling protocols are modelled through a modular decomposition of the seven OSI layers including the service user to three submodels. The workload model is user descriptive in the sense that it does not approximate the direct input traffic required for evaluating the performance of a layer protocol; instead, through a multi-level approach, it describes the actual implications of user signalling activity for the general signalling traffic. The signalling protocol model is derived from the global functional model of the signalling protocols and information flows using a network of queues incorporating synchronization and dependency functions. The same queueing approach is followed for the signalling transfer network which is used to define processing speed and signalling bandwidth requirements and to identify possible performance bottlenecks stemming from the realization of the related protocols