Redundancy Scheduling with Locally Stable Compatibility Graphs

Redundancy scheduling is a popular concept to improve performance in parallel-server systems. In the baseline scenario any job can be handled equally well by any server, and is replicated to a fixed number of servers selected uniformly at random. Quite often however, there may be heterogeneity in job characteristics or server capabilities, and jobs can only be replicated to specific servers because of affinity relations or compatibility constraints. In order to capture such situations, we consider a scenario where jobs of various types are replicated to different subsets of servers as prescribed by a general compatibility graph. We exploit a product-form stationary distribution and weak local stability conditions to establish a state space collapse in heavy traffic. In this limiting regime, the parallel-server system with graph-based redundancy scheduling operates as a multi-class single-server system, achieving full resource pooling and exhibiting strong insensitivity to the underlying compatibility constraints.Comment: 28 pages, 4 figure

Transient bayesian inference for short and long-tailed GI/G/1 queueing systems

In this paper, we describe how to make Bayesian inference for the transient behaviour and busy period in a single server system with general and unknown distribution for the service and interarrival time. The dense family of Coxian distributions is used for the service and arrival process to the system. This distribution model is reparametrized such that it is possible to define a non-informative prior which allows for the approximation of heavytailed distributions. Reversible jump Markov chain Monte Carlo methods are used to estimate the predictive distribution of the interarrival and service time. Our procedure for estimating the system measures is based in recent results for known parameters which are frequently implemented by using symbolical packages. Alternatively, we propose a simple numerical technique that can be performed for every MCMC iteration so that we can estimate interesting measures, such as the transient queue length distribution. We illustrate our approach with simulated and real queues

Queueing models for cable access networks

abstract in thesi

TRANSIENT BAYESIAN INFERENCE FOR SHORT AND LONG-TAILED GI/G/1 QUEUEING SYSTEMS

In this paper, we describe how to make Bayesian inference for the transient behaviour and busy period in a single server system with general and unknown distribution for the service and interarrival time. The dense family of Coxian distributions is used for the service and arrival process to the system. This distribution model is reparametrized such that it is possible to define a non-informative prior which allows for the approximation of heavytailed distributions. Reversible jump Markov chain Monte Carlo methods are used to estimate the predictive distribution of the interarrival and service time. Our procedure for estimating the system measures is based in recent results for known parameters which are frequently implemented by using symbolical packages. Alternatively, we propose a simple numerical technique that can be performed for every MCMC iteration so that we can estimate interesting measures, such as the transient queue length distribution. We illustrate our approach with simulated and real queues.

A Lightweight, Non-intrusive Approach for Orchestrating Autonomously-managed Network Elements

Software-Defined Networking enables the centralized orchestration of data traffic within a network. However, proposed solutions require a high degree of architectural penetration. The present study targets the orchestration of network elements that do not wish to yield much of their internal operations to an external controller. Backpressure routing principles are used for deriving flow routing rules that optimally stabilize a network, while maximizing its throughput. The elements can then accept in full, partially or reject the proposed routing rule-set. The proposed scheme requires minimal, relatively infrequent interaction with a controller, limiting its imposed workload, promoting scalability. The proposed scheme exhibits attracting network performance gains, as demonstrated by extensive simulations and proven via mathematical analysis.Comment: 6 pages 7, figures, IEEE ISCC'1