Robust Queueing Theory

We propose an alternative approach for studying queues based on robust optimization. We model the uncertainty in the arrivals and services via polyhedral uncertainty sets, which are inspired from the limit laws of probability. Using the generalized central limit theorem, this framework allows us to model heavy-tailed behavior characterized by bursts of rapidly occurring arrivals and long service times. We take a worst-case approach and obtain closed-form upper bounds on the system time in a multi-server queue. These expressions provide qualitative insights that mirror the conclusions obtained in the probabilistic setting for light-tailed arrivals and services and generalize them to the case of heavy-tailed behavior. We also develop a calculus for analyzing a network of queues based on the following key principles: (a) the departure from a queue, (b) the superposition, and (c) the thinning of arrival processes have the same uncertainty set representation as the original arrival processes. The proposed approach (a) yields results with error percentages in single digits relative to simulation, and (b) is to a large extent insensitive to the number of servers per queue, network size, degree of feedback, and traffic intensity; it is somewhat sensitive to the degree of diversity of external arrival distributions in the network

Analysis of Multiserver Retrial Queueing System: A Martingale Approach and an Algorithm of Solution

The paper studies a multiserver retrial queueing system with $m$ servers. Arrival process is a point process with strictly stationary and ergodic increments. A customer arriving to the system occupies one of the free servers. If upon arrival all servers are busy, then the customer goes to the secondary queue, orbit, and after some random time retries more and more to occupy a server. A service time of each customer is exponentially distributed random variable with parameter $\mu_1$. A time between retrials is exponentially distributed with parameter $\mu_2$ for each customer. Using a martingale approach the paper provides an analysis of this system. The paper establishes the stability condition and studies a behavior of the limiting queue-length distributions as $\mu_2$ increases to infinity. As $\mu_2\to\infty$, the paper also proves the convergence of appropriate queue-length distributions to those of the associated `usual' multiserver queueing system without retrials. An algorithm for numerical solution of the equations, associated with the limiting queue-length distribution of retrial systems, is provided.Comment: To appear in "Annals of Operations Research" 141 (2006) 19-52. Replacement corrects a small number of misprint

Stochastic performance analysis of Network Function Virtualisation in future internet

This is the author accepted manuscript. The final version is available from the publisher via the DOI in this recordIEEE Network Function Virtualisation (NFV) has been considered as a promising technology for future Internet to increase network flexibility, accelerate service innovation and reduce the Capital Expenditures (CAPEX) and Operational Expenditures (OPEX) costs, through migrating network functions from dedicated network devices to commodity hardware. Recent studies reveal that although this migration of network function brings the network operation unprecedented flexibility and controllability, NFV-based architecture suffers from serious performance degradation compared with traditional service provisioning on dedicated devices. In order to achieve a comprehensive understanding of the service provisioning capability of NFV, this paper proposes a novel analytical model based on Stochastic Network Calculus (SNC) to quantitatively investigate the end-to-end performance bound of NFV networks. To capture the dynamic and on-demand NFV features, both the non-bursty traffic, e.g. Poisson process, and the bursty traffic, e.g. Markov Modulated Poisson Process (MMPP), are jointly considered in the developed model to characterise the arriving traffic. To address the challenges of resource competition and end-to-end NFV chaining, the property of convolution associativity and leftover service technologies of SNC are exploited to calculate the available resources of Virtual Network Function (VNF) nodes in the presence of multiple competing traffic, and transfer the complex NFV chain into an equivalent system for performance derivation and analysis. Both the numerical analysis and extensive simulation experiments are conducted to validate the accuracy of the proposed analytical model. Results demonstrate that the analytical performance metrics match well with those obtained from the simulation experiments and numerical analysis. In addition, the developed model is used as a practical and cost-effective tool to investigate the strategies of the service chain design and resource allocations in NFV networks.Engineering and Physical Sciences Research Council (EPSRC

Fully Unleashing the Power of Paying Multiplexing Only Once in Stochastic Network Calculus

The stochastic network calculus (SNC) holds promise as a versatile and uniform framework to calculate probabilistic performance bounds in networks of queues. A great challenge to accurate bounds and efficient calculations are stochastic dependencies between flows due to resource sharing inside the network. However, by carefully utilizing the basic SNC concepts in the network analysis the necessity of taking these dependencies into account can be minimized. To that end, we fully unleash the power of the pay multiplexing only once principle (PMOO, known from the deterministic network calculus) in the SNC analysis. We choose an analytic combinatorics presentation of the results in order to ease complex calculations. In tree-reducible networks, a subclass of general feedforward networks, we obtain a perfect analysis in terms of avoiding the need to take internal flow dependencies into account. In a comprehensive numerical evaluation, we demonstrate how this unleashed PMOO analysis can reduce the known gap between simulations and SNC calculations significantly, and how it favourably compares to state-of-the art SNC calculations in terms of accuracy and computational effort. Motivated by these promising results, we also consider general feedforward networks, when some flow dependencies have to be taken into account. To that end, the unleashed PMOO analysis is extended to the partially dependent case and a case study of a canonical example topology, known as the diamond network, is provided, again displaying favourable results over the state of the art

Delay Bound: Fractal Traffic Passes through Network Servers

Delay analysis plays a role in real-time systems in computer communication networks. This paper gives our results in the aspect of delay analysis of fractal traffic passing through servers. There are three contributions presented in this paper. First, we will explain the reasons why conventional theory of queuing systems ceases in the general sense when arrival traffic is fractal. Then, we will propose a concise method of delay computation for hard real-time systems as shown in this paper. Finally, the delay computation of fractal traffic passing through severs is presented