Traffic-Driven Spectrum Allocation in Heterogeneous Networks

Next generation cellular networks will be heterogeneous with dense deployment of small cells in order to deliver high data rate per unit area. Traffic variations are more pronounced in a small cell, which in turn lead to more dynamic interference to other cells. It is crucial to adapt radio resource management to traffic conditions in such a heterogeneous network (HetNet). This paper studies the optimization of spectrum allocation in HetNets on a relatively slow timescale based on average traffic and channel conditions (typically over seconds or minutes). Specifically, in a cluster with $n$ base transceiver stations (BTSs), the optimal partition of the spectrum into $2^n$ segments is determined, corresponding to all possible spectrum reuse patterns in the downlink. Each BTS's traffic is modeled using a queue with Poisson arrivals, the service rate of which is a linear function of the combined bandwidth of all assigned spectrum segments. With the system average packet sojourn time as the objective, a convex optimization problem is first formulated, where it is shown that the optimal allocation divides the spectrum into at most $n$ segments. A second, refined model is then proposed to address queue interactions due to interference, where the corresponding optimal allocation problem admits an efficient suboptimal solution. Both allocation schemes attain the entire throughput region of a given network. Simulation results show the two schemes perform similarly in the heavy-traffic regime, in which case they significantly outperform both the orthogonal allocation and the full-frequency-reuse allocation. The refined allocation shows the best performance under all traffic conditions.Comment: 13 pages, 11 figures, accepted for publication by JSAC-HC

Series expansions for finite-state Markov chains

This article provides series expansions of the stationary distribution of a finite Markov chain. This leads to an efficient numerical algorithm for computing the stationary distribution of a finite Markov chain. Numerical examples are given to illustrate the performance of the algorithm. © 2007 Cambridge University Press

Series Expansions for Finite-State Markov Chains

This paper provides series expansions of the stationary distribution of a finite Markov chain. This leads to an efficient numerical algorithm for computing the stationary distribution of a finite Markov chain. Numerical examples are given to illustrate the performance of the algorithm

Interacting queues in heavy traffic

We consider a system of parallel queues with Poisson arrivals and exponentially distributed service requirements. The various queues are coupled through their service rates, causing a complex dynamic interaction. Specifically, the system consists of one primary queue and several secondary queues whose service rates depend on whether the primary queue is empty or not. Conversely, the service rate of the primary queue depends on which of the secondary queues are empty. An important special case arises when the service rates satisfy a specific relationship so that the various queues form a work-conserving system. This case is, in fact, equivalent to a so-called Generalized Processor Sharing (GPS) system. GPS-based scheduling algorithms have emerged as popular mechanisms for achieving service differentiation while providing statistical multiplexing gains. We consider a heavy-traffic scenario, and assume that each of the secondary queues is underloaded when the primary queue is busy. Using a perturbation procedure, we derive the lowest-order asymptotic approximation to the joint stationary distribution of the queue lengths, in terms of a small positive parameter measuring the closeness of the system to instability. Heuristic derivations of these results are presented. We also pursue two extensions: (i) the more general work-conserving case where the service rate of a secondary queue may depend on its own length, and is a slowly varying function of the length of the primary queue; and (ii) the non-work-conserving case where the service rate of a secondary queue may depend on its own length, but not on the length of the primary queue

Characterization of stationary distributions of reflected diffusions

Given a domain G, a reflection vector field d(.) on the boundary of G, and drift and dispersion coefficients b(.) and \sigma(.), let L be the usual second-order elliptic operator associated with b(.) and \sigma(.). Under suitable assumptions that, in particular, ensure that the associated submartingale problem is well posed, it is shown that a probability measure $\pi$ on \bar{G} is a stationary distribution for the corresponding reflected diffusion if and only if $\pi (\partial G) = 0$ and $\int_{\bar{G}} L f (x) \pi (dx) \leq 0$ for every f in a certain class of test functions. Moreover, the assumptions are shown to be satisfied by a large class of reflected diffusions in piecewise smooth multi-dimensional domains with possibly oblique reflection.Comment: 48 page

Delay analysis for wireless applications using a multiservice multiqueue processor sharing model

The ongoing development of wireless networks supporting multimedia applications requires service providers to efficiently deliver complex Quality of Service (QoS) requirements. The wide range of new applications in these networks significantly increases the difficulty of network design and dimensioning to meet QoS requirements. Medium Access Control (MAC) protocols affect QoS achieved by wireless networks. Research on analysis and performance evaluation is important for the efficient protocol design. As wireless networks feature scarce resources that are simultaneously shared by all users, processor sharing (PS) models were proposed for modelling resource sharing mechanisms in such systems. In this thesis, multi-priority MAC protocols are proposed for handling the various service traffic types. Then, an investigation of multiservice multiqueue PS models is undertaken to analyse the delay for some recently proposed wireless applications. We start with an introduction to MAC protocols for wireless networks which are specified in IEEE standards and then review scheduling algorithms which were proposed to work with the underlying MAC protocols to cooperatively achieve QoS goals. An overview of the relevant literature is given on PS models for performance analysis and evaluation of scheduling algorithms. We propose a multiservice multiqueue PS model using a scheduling scheme in multimedia wireless networks with a comprehensive description of the analytical solution. Firstly, we describe the existing multiqueue processor sharing (MPS) model, which uses a fixed service quantum at each queue, and correct a subtle incongruity in previous solutions presented in the literature. Secondly, a new scheduling framework is proposed to extend the previous MPS model to a general case. This newly proposed analytical approach is based on the idea that the service quantum arranged by a MAC scheduling controller to service data units can be priority-based. We obtain a closed-form expression for the mean delay of each service class in this model. In summary, our new approach simplifies MAC protocols for multimedia applications into an analytical model that includes more complex and realistic traffic models without compromising details of the protocol and significantly reduces the number of MAC headers, thus the overall average delay will be decreased. In response to using the studied multiservice multiqueue PS models, we apply the MPS model to two wireless applications: Push to Talk (PTT) service over GPRS/GSM networks and the Worldwide Interoperability for Microwave Access (WiMAX) networks. We investigate the uplink delay of PTT over traditional GPRS/GSM networks and the uplink delay for WiMAX Subscriber Station scheduler under a priority-based fair scheduling. MAC structures capable of supporting dynamically varying traffic are studied for the networks, especially, with the consideration of implementation issues. The model provides useful insights into the dynamic performance behaviours of GPRS/GSM and WiMAX networks with respect to various system parameters and comprehensive traffic conditions. We then evaluate the model under some different practical traffic scenarios. Through modelling of the operation of wireless access systems, under a variety of multimedia traffic, our analytical approaches provide practical analysis guidelines for wireless network dimensioning