On the Stability of Isolated and Interconnected Input-Queued Switches under Multiclass Traffic

In this correspondence, we discuss the stability of scheduling algorithms for input-queueing (IQ) and combined input/output queueing (CIOQ) packet switches. First, we show that a wide class of IQ schedulers operating on multiple traffic classes can achieve 100 % throughput. Then, we address the problem of the maximum throughput achievable in a network of interconnected IQ switches and CIOQ switches loaded by multiclass traffic, and we devise some simple scheduling policies that guarantee 100 % throughput. Both the Lyapunov function methodology and the fluid modeling approach are used to obtain our results

Decomposing the queue length distribution of processor-sharing models into queue lengths of permanent customer queues

We obtain a decomposition result for the steady state queue length distribution in egalitarian processor-sharing (PS) models. In particular, for an egalitarian PS queue with $K$ customer classes, we show that the marginal queue length distribution for class $k$ factorizes over the number of other customer types. The factorizing coefficients equal the queue length probabilities of a PS queue for type $k$ in isolation, in which the customers of the other types reside \textit{ permanently} in the system. Similarly, the (conditional) mean sojourn time for class $k$ can be obtained by conditioning on the number of permanent customers of the other types. The decomposition result implies linear relations between the marginal queue length probabilities, which also hold for other PS models such as the egalitarian processor-sharing models with state-dependent system capacity that only depends on the total number of customers in the system. Based on the exact decomposition result for egalitarian PS queues, we propose a similar decomposition for discriminatory processor-sharing (DPS) models, and numerically show that the approximation is accurate for moderate differences in service weights. \u

A Fixed-Point Algorithm for Closed Queueing Networks

In this paper we propose a new efficient iterative scheme for solving closed queueing networks with phase-type service time distributions. The method is especially efficient and accurate in case of large numbers of nodes and large customer populations. We present the method, put it in perspective, and validate it through a large number of test scenarios. In most cases, the method provides accuracies within 5% relative error (in comparison to discrete-event simulation)

Heart-like fair queuing algorithms (HLFQA)

We propose a new family of fair, work conserving traffic scheduling mechanisms that imitate the behavior of the human heart in the cardiovascular system. The algorithms have MAX (where MAX is the maximum packet size) fairness and O(log N) complexity and thus compare favorably with existing algorithms. The algorithms are simple enough to be implemented in hardwar