Kenneth Mitchell

An analysis of the effects of mobility on bandwidth allocation strategies in multi-class cellular wireless networks

In this paper we present a multi-cell analytic model for multi-class cellular networks. We investigate the effects subscriber mobility has on bandwidth control strategies when the network supports multiple classes of subscribers having different bandwidth requirements. We introduce control strategies from non-mobile networks and examine them in a mobile environment. The expressions for call blocking using these control strategies have product form solutions. This allows us to develop a multi-cell, multi-class, model by generalizing on the Erlang fixed point approximation using generalized multi-rate, multi-class, Erlang loss formulas for each class of traffic. We produce expressions for originating calls lost, hand-off calls lost, forced-termination, and mean channel occupancy for each class of traffic in each cell for different control strategies. The multicell analytic model allows us to investigate the effects of asymmetric loads and mobility patterns in the network. The analytic results are supported by simulation.

Analytical models for understanding space, backoff, and flow correlation in CSMA wireless networks

In wireless networks employing carrier-sense multiple-access with collision avoidance (CSMA/CA), correlations between the service processes of different nodes arise as a result of competition for common wireless channels and the dependencies between upstream and downstream traffic flows. These dependencies make the development of tractable performance models extremely difficult. To address this purpose, we present a new continuous-time model for CSMA wireless networks where we combine a node model and a channel model in order to capture correlation. Simplification methods are presented that make our models computationally tractable for large networks with minimal loss of accuracy. The model can be used for both single and multi-hop wireless networks and takes into account non-saturated queues, backoff-stage dependence of collision probabilities, and the correlation between departure processes and arrival processes of adjacent nodes. The model can be used to compute probabilistic quality of service guarantees to optimize end-to-end throughput and end-to-end delay by adjusting arrival and backoff rates along various paths.

Correlation bounds for second-order MAPs with application to queueing network decomposition

Tools for performance evaluation often require techniques to match moments to continuous distributions or moments and correlation data to correlated processes. With respect to efficiency in applications, one is interested in low-dimensional (matrix) representations. For phase-type distributions (or matrix exponentials) of second order, analytic bounds could be derived earlier, which specify the space of permissible moments. In this paper, we add a correlation parameter to the first three moments of the marginal distribution to construct a Markovian arrival process of second order (MAP(2)). Exploiting the equivalence of correlated matrix-exponential sequences and MAPs in two dimensions, we present an algorithm that decides whether the correlation parameter is permissible with respect to the three moments and - if so - delivers a valid MAP(2) which matches the four parameters.We also investigate the restrictions imposed on the correlation structure of MAP(2)s with hyperexponential marginals. Analytic bounds for the envelope correlation region (i.e., for arbitrary third moment) and for the specific correlation region (i.e., for fixed third moment) are given.When there is no need for a MAP(2) representation (as in linear-algebraic queueing theory), the proposed procedure serves to check the validity of the constructed correlated matrix-exponential sequence.Numerical examples indicate how these results can be used to efficiently decompose queueing networks.

Approximation models of feed-forward G/G/1/N queueing networks with correlated arrivals

In this paper we develop approximation models for feed-forward networks of G/G/1/N queues. We use Linear Algebra Queueing Theory (LAQT) techniques to create reduced state space representations for the queue departure processes. Reduced state space departure processes are presented where the first three moments and the correlation decay are mapped to a two state process. A three state process is also presented matching the first five moments and the first three lag autocorrelations. Numerical examples of end-to-end performance for high-speed communications networks with correlated arrival traffic are presented. The results are compared with simulation models and other approximation methods.

A scalable delay based analytical framework for CSMA/CA wireless mesh networks

We present an analytical framework for the performance analysis of CSMA/CA based wireless mesh networks. This framework can provide an accurate throughput-delay evaluation for both saturated and unsaturated cases. An efficient algorithm that determines the collision domain for each node based on both the interference range and routing in the network is presented. As another important application of this framework, we develop an analytic model that enables us to obtain closed form expressions for delay in terms of multipath routing variables. A flow-deviation algorithm is used to derive the optimal flow over a given set of routes for any number of classes. The model takes into account the effects of neighbor interference and hidden terminals, and tools are provided to make it feasible for the performance analysis and optimization of large-scale networks. Numerical results are presented for different network topologies and compared with simulation studies.

Approximation models of wireless cellular networks using moment matching

In this paper we present an analytical model for micro- and pico-cell wireless networks for any arbitrary topology in a high mobility feedforward environment. We introduce an approximation technique which uses a single-cell decomposition analysis which incorporates moment matching of handoff processes into the cell. The approximation technique can provide close approximations for non-Poisson arrival traffic and it is easily parallelized. Performance measures such as new calls blocked, handoff calls lost, and forced termination are derived for any general independent call arrival distribution in a heterogeneous traffic environment. We produce some numerical examples for some simple topologies with varying mobility for several call arrival distributions and compare our results to those from simulation studies.

Correlation properties of the token leaky bucket departure process

In this paper we focus on the behavior of the leaky bucket mechanism with respect to second-order statistics of the departure process under various correlated cell arrival and deterministic token arrival distributions. We derive expressions for the lag-k auto-correlation of the inter-departure times for the leaky bucket cell departure stream and we produce numerical examples for the lag-k auto-correlation of the leaky bucket inter-departure times for several different cell arrival distributions exhibiting both positive and negative auto-correlations.

Flow-level upstream traffic behavior in broadband access networks: DSL versus broadband fixed wireless

We present flow-level upstream traffic behavior based on data collected from broadband fixed wireless (BFW) and digital subscriber line (DSL) access services. The study involves data collected using Ciscos NetFlow tools on both access networks. The observations indicate that a number of applications based on peer-to-peer (P2P) concepts create most of the upstream traffic. The flows observed are mostly short-lived for both BFW and DSL access, with DSL being the lesser of the two. The inter-arrival time displays near-range correlation for the DSL flows. There is a significant periodicity observed in the interarrival time distribution for flows on BFW access, which is indicative of the influence of the underlying medium access control (MAC) protocol on traffic behavior. These analysis of upstream traffic characteristics form the first step towards constructing a generalized parametric model for broadband access networks.

A Single Node Decomposition Based Analytic Model for Multiclass Route Optimization in Wireless Mesh Networks

In this paper we present a single node decomposition based model for the analysis of wireless mesh networks. With knowledge of the network topology and routing strategy, the performance of each node, including throughput, delay, etc., can be analyzed using a simple M/G/1 model that takes into account the interference due to neighbor transmissions. With this basic analytic framework, closed form expressions for delay in terms of multipath routing variables are presented. A flow deviation optimization algorithm is used to derive the optimal flow over a given set of routes for both single and multiple classes of traffic. Numerical results are presented for different network topologies and compared with simulation studies.

A delay based multipath optimal route analysis for multi-hop CSMA/CA wireless mesh networks

In this paper we present a method for determining optimal routes along selected paths in a wireless mesh network based on an interference aware delay analysis. We develop an analytic model that enables us to obtain closed form expressions for delay in terms of multipath routing variables. A flow deviation algorithm is used to derive the optimal flow over a given set of routes. The model takes into account the effects of neighbor interference and hidden terminals, and tools are provided to make it feasible for the performance analysis and optimization of large-scale networks. Numerical results are presented for different network topologies and compared with simulation studies.