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

Branching processes, the max-plus algebra and network calculus

Branching processes can describe the dynamics of various queueing systems, peer-to-peer systems, delay tolerant networks, etc. In this paper we study the basic stochastic recursion of multitype branching processes, but in two non-standard contexts. First, we consider this recursion in the max-plus algebra where branching corresponds to finding the maximal offspring of the current generation. Secondly, we consider network-calculus-type deterministic bounds as introduced by Cruz, which we extend to handle branching-type processes. The paper provides both qualitative and quantitative results and introduces various applications of (max-plus) branching processes in queueing theory

Sharp Bounds in Stochastic Network Calculus

The practicality of the stochastic network calculus (SNC) is often questioned on grounds of potential looseness of its performance bounds. In this paper it is uncovered that for bursty arrival processes (specifically Markov-Modulated On-Off (MMOO)), whose amenability to \textit{per-flow} analysis is typically proclaimed as a highlight of SNC, the bounds can unfortunately indeed be very loose (e.g., by several orders of magnitude off). In response to this uncovered weakness of SNC, the (Standard) per-flow bounds are herein improved by deriving a general sample-path bound, using martingale based techniques, which accommodates FIFO, SP, EDF, and GPS scheduling. The obtained (Martingale) bounds gain an exponential decay factor of ${\mathcal{O}}(e^{-\alpha n})$ in the number of flows $n$. Moreover, numerical comparisons against simulations show that the Martingale bounds are remarkably accurate for FIFO, SP, and EDF scheduling; for GPS scheduling, although the Martingale bounds substantially improve the Standard bounds, they are numerically loose, demanding for improvements in the core SNC analysis of GPS

Performance Modelling and Resource Allocation of the Emerging Network Architectures for Future Internet

With the rapid development of information and communications technologies, the traditional network architecture has approached to its performance limit, and thus is unable to meet the requirements of various resource-hungry applications. Significant infrastructure improvements to the network domain are urgently needed to guarantee the continuous network evolution and innovation. To address this important challenge, tremendous research efforts have been made to foster the evolution to Future Internet. Long-term Evolution Advanced (LTE-A), Software Defined Networking (SDN) and Network Function Virtualisation (NFV) have been proposed as the key promising network architectures for Future Internet and attract significant attentions in the network and telecom community. This research mainly focuses on the performance modelling and resource allocations of these three architectures. The major contributions are three-fold: 1) LTE-A has been proposed by the 3rd Generation Partnership Project (3GPP) as a promising candidate for the evolution of LTE wireless communication. One of the major features of LTE-A is the concept of Carrier Aggregation (CA). CA enables the network operators to exploit the fragmented spectrum and increase the peak transmission data rate, however, this technical innovation introduces serious unbalanced loads among in the radio resource allocation of LTE-A. To alleviate this problem, a novel QoS-aware resource allocation scheme, termed as Cross-CC User Migration (CUM) scheme, is proposed in this research to support real-time services, taking into consideration the system throughput, user fairness and QoS constraints. 2) SDN is an emerging technology towards next-generation Internet. In order to improve the performance of the SDN network, a preemption-based packet-scheduling scheme is firstly proposed in this research to improve the global fairness and reduce the packet loss rate in SDN data plane. Furthermore, in order to achieve a comprehensive and deeper understanding of the performance behaviour of SDN network, this work develops two analytical models to investigate the performance of SDN in the presence of Poisson Process and Markov Modulated Poisson Process (MMPP) respectively. 3) NFV is regarded as a disruptive technology for telecommunication service providers to reduce the Capital Expenditure (CAPEX) and Operational Expenditure (OPEX) through decoupling individual network functions from the underlying hardware devices. While NFV faces a significant challenging problem of Service-Level-Agreement (SLA) guarantee during service provisioning. In order to bridge this gap, a novel comprehensive analytical model based on stochastic network calculus is proposed in this research to investigate end-to-end performance of NFV network. The resource allocation strategies proposed in this study significantly improve the network performance in terms of packet loss probability, global allocation fairness and throughput per user in LTE-A and SDN networks; the analytical models designed in this study can accurately predict the network performances of SDN and NFV networks. Both theoretical analysis and simulation experiments are conducted to demonstrate the effectiveness of the proposed algorithms and the accuracy of the designed models. In addition, the models are used as practical and cost-effective tools to pinpoint the performance bottlenecks of SDN and NFV networks under various network conditions

Stochastic Service Curve and Delay Bound Analysis: A Single Node Case

A packet-switched network node with constant capacity (in bps) is considered, where packets within each flow are served in the first in first out (FIFO) manner. While this single node system is perhaps the simplest computer communication system, its stochastic service curve characterization and independent case analysis in the context of stochastic network calculus (snetcal) are still basic and many crucial questions surprisingly remain open. Specifically, when the input is a single flow, what stochastic service curve and delay bound does the node provide? When the considered flow shares the node with another flow, what stochastic service curve and delay bound does the node provide to the considered flow, and if the two flows are independent, can this independence be made use of and how? The aim of this paper is to provide answers to these fundamental questions