Sample path large deviations for multiclass feedforward queueing networks in critical loading

We consider multiclass feedforward queueing networks with first in first out and priority service disciplines at the nodes, and class dependent deterministic routing between nodes. The random behavior of the network is constructed from cumulative arrival and service time processes which are assumed to satisfy an appropriate sample path large deviation principle. We establish logarithmic asymptotics of large deviations for waiting time, idle time, queue length, departure and sojourn-time processes in critical loading. This transfers similar results from Puhalskii about single class queueing networks with feedback to multiclass feedforward queueing networks, and complements diffusion approximation results from Peterson. An example with renewal inter arrival and service time processes yields the rate function of a reflected Brownian motion. The model directly captures stationary situations.Comment: Published at http://dx.doi.org/10.1214/105051606000000439 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

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

Product-form solutions for integrated services packet networks and cloud computing systems

We iteratively derive the product-form solutions of stationary distributions of priority multiclass queueing networks with multi-sever stations. The networks are Markovian with exponential interarrival and service time distributions. These solutions can be used to conduct performance analysis or as comparison criteria for approximation and simulation studies of large scale networks with multi-processor shared-memory switches and cloud computing systems with parallel-server stations. Numerical comparisons with existing Brownian approximating model are provided to indicate the effectiveness of our algorithm.Comment: 26 pages, 3 figures, short conference version is reported at MICAI 200

A Numerical Approach to Stability of Multiclass Queueing Networks

The Multi-class Queueing Network (McQN) arises as a natural multi-class extension of the traditional (single-class) Jackson network. In a single-class network subcriticality (i.e. subunitary nominal workload at every station) entails stability, but this is no longer sufficient when jobs/customers of different classes (i.e. with different service requirements and/or routing scheme) visit the same server; therefore, analytical conditions for stability of McQNs are lacking, in general. In this note we design a numerical (simulation-based) method for determining the stability region of a McQN, in terms of arrival rate(s). Our method exploits certain (stochastic) monotonicity properties enjoyed by the associated Markovian queue-configuration process. Stochastic monotonicity is a quite common feature of queueing models and can be easily established in the single-class framework (Jackson networks); recently, also for a wide class of McQNs, including first-come-first-serve (FCFS) networks, monotonicity properties have been established. Here, we provide a minimal set of conditions under which the method performs correctly. Eventually, we illustrate the use of our numerical method by presenting a set of numerical experiments, covering both single and multi-class networks