15871709
Optimization of Location Management for PCS Networks with CTRW Mobility Model
This paper considers the design of the optimal locationupdate area (LA) of the distance-based scheme for personal communication service (PCS) networks. We focus on the optimization of two design parameters associated with the LA: 1) initial position upon LA update; 2) distance threshold for triggering of LA update. Based on the popular continuous-time random walk (CTRW) mobility model, we propose a novel analytical framework that uses a diffusion equation to minimize the location management cost. In this framework, a number of measurable physical parameters, such as length of road section, angle between road sections, and road section crossing time, can be integrated into the system design. This framework allows us to easily evaluate the total cost under general call arrival distributions and LA of different shapes. For the particular case of circular LA and small Poisson call-arrival rate, we prove the following: (1) When the drift is weak, the optimal initial position approaches the center of the LA; when the drift is strong, it approaches the boundary of the LA. (2) Comparing the optimal initial-position and center-initial-position solutions (which is assumed in most prior work), when the drift is weak, the optimal distance threshold and the minimum total cost are roughly equal; when the drift is strong, the optimal distance threshold in the later is about 1.260 times that in the former, and the minimum total cost in the later is about 1.587 times that in the former. That is, optimizing on initial position, which previous work did not consider, has the potential of reducing the cost measure by 37%.
62241965
Wireless and Mobile Network Architectures
From the Publisher: 
This book gives network engineers and managers a window on the world of wireless and mobile networks, from the enabling technologies and protocols to creating and managing mobile services." "Lin and Chlamtac use a unique sustained example approach to teach you how PCS concepts apply to real network operation. For example, they use location update to illustrate concepts in chapters on network signaling, mobility, security/handoff, and mobile prepaid services.
1402158
Movement-based location update and selective paging for PCS networks
This paper introduces a mobility tracking mechanism that combines a movement-based location update policy with a selective paging scheme. Movement-based location update is selected for its simplicity. It does not require each mobile terminal to store information about the arrangement and the distance relationship of all cells. In fact, each mobile terminal only keeps a counter of the number of cells visited. A location update is performed when this counter exceeds a predefined threshold value. This scheme allows the dynamic selection of the movement threshold on a per-user basis. This is desirable as different users may have very different mobility patterns. Selective paging reduces the cost for locating a mobile terminal in the expense of an increase in the paging delay. We propose a selective paging scheme which significantly decreases the location tracking cost under a small increase in the allowable paging delay. We introduce an analytical model for the proposed location tracking mechanism which captures the mobility and the incoming call arrival patterns of each mobile terminal. Analytical results are provided to demonstrate the cost-effectiveness of the proposed scheme under various parameters.
17848932
Minimizing the average cost of paging and registration: A timer-based method
Methods of balancing call registration and paging are developed in this paper. Given that the probability distribution on the user location as a function of time is either known or can be calculated, previous work shows the existence of lower bounds on the average cost of paging. Here these bounds are used in conjunction with a Poisson incoming-call arrival model to formulate the paging/registration optimization problem in terms oftimeout parameters, τm; the maximum amount of time to wait before registering given the last known location wasm. Timer-based methods, as opposed to location-based methods, do not require the user to record and process location information during the time between location updates. This feature might be desirable for minimizing mobile transceiver use during idle periods. We then consider uniform motion processes where a spatial translation of starting location produces an identical spatial translation of the associated time-varying probability distribution. This leads to a universal timeout parameter τ which may be readily calculated. We study τ and the minimum cost of paging/registration for a simple model of user motion and compare our results to an earlier method of location-based paging/registration cost minimization.
7292170
To Update or Not to Update?
Tracking strategies for mobile users in wireless networks are studied. In order to save the cost of using the wireless links mobile users should not update their location whenever they cross boundaries of adjacent cells. This paper focuses on three natural strategies in which the mobile users make the decisions when and where to update: the time-based strategy, the number of movements-based strategy, and the distance-based strategy. We consider both memoryless movement patterns and movements with Markovian memory along a topology of cells arranged as a ring. We analyze the performance of each one of the three strategies under such movements, and show the performance diierences between the strategies.
121258691
Aspects and Applications of the Random Walk
Introductory comments the ubiquitous characteristic function asymptotic properties and the diffusion limit lattice walks boundaries and constraints multistate random walks selected applications.
2805042
A new random walk model for PCS networks
This paper proposes a new approach to simplify the two-dimensional random walk models capturing the movement of mobile users in personal communications services (PCS) networks. Analytical models are proposed for the new random walks. For a PCS network with hexagonal configuration, our approach reduces the states of the two-dimensional random walk from (3n/sup 2/+3n-5) to n(n+1)/2, where n is the layers of a cluster. For a mesh configuration, our approach reduces the states from (2n2-2n+1) to (n/sup 2/+2n+4)/4 if n is even and to (n/sup 2/+2n+5)/4 if n is odd. Simulation experiments are conducted to validate the analytical models. The results indicate that the errors between the analytical and simulation models are within 1%. Three applications (i.e., microcell/macrocell configuration, distance-based location update, and GPRS mobility management for data routing) are used to show how our new model can be used to investigate the performance of PCS networks.
15414578
Performance evaluation of location management in UMTS
The universal mobile telecommunications system utilizes a three-level location-management strategy to reduce the net costs of location update and paging in the packet-switched service domain. Within a communication session, a mobile station (MS) is tracked at the cell level during packet transmission. In the idle period of an ongoing session, the MS is tracked at the UTRAN registration area (URA) level to avoid frequent cell updates while still keeping the radio connection. If the MS is not in any communication session, the MS is tracked at the routing-area (RA) level. The inactivity counter mechanism was proposed in 3GPP 25.331 to determine when to switch between the three location-tracking modes. In this mechanism, two inactivity counters are used to count the numbers of cell and URA updates in an idle period between two packet transmissions. If the number of cell updates reaches a threshold K/sub 1/, the MS is switched from cell tracking to URA tracking. After that, if the number of URA updates reaches a threshold K/sub 2/, the MS is tracked at the RA level. The paper proposes analytical and simulation models to investigate the performance of the inactivity counter mechanism. Our study provides guidelines for K/sub 1/ and K/sub 2/ selection to achieve lower net costs of location update and paging.
18127209
Wireless subscriber mobility management using adaptive individual location areas for PCS systems
We consider a new mobility management scheme-the adaptive location area tracking scheme-in which each mobile performs a location registration as it crosses the boundary of its current personal location area and is assigned a new location area. The size and shape of the new location area depend on the mobile's mobility and call characteristics in its previous location area. The objective is to minimize the combined average signaling cost of both paging and registration activities for each individual mobile user. We model the mobility and incoming call traffic of an individual mobile user using Brownian motion with the drift process and Poisson arrival process. Under the assumption of a one-dimensional cellular network environment, we investigate the effects of user mobility parameters such as average movement speed, location uncertainty and mean call arrival rate on the size and shape of individual location areas. This study reveals that, besides size, the shape of the location areas also plays an important role in signaling cost reduction. Performance analysis shows that this scheme offers a cost reduction up to 50% as compared to a previously proposed scheme.
3387170
FBM mobility modeling for nomadic subscribers
The performance in mobile systems is in many aspects dependent on mobility patterns. For instance the number of hand-of and signaling load is likely to increase as the subscriber mobility raises. Most performance analysis in the literature are based on constant motion models which is considered to be unrealistic. In this paper a fractional Brownian motion (FBM) model for mobile subscribers is presented providing a more realistic phenomena description.
14959238
An adaptive distance-based location update algorithm for next-generation PCS networks
In this paper, we propose a stochastic model to compute the optimal update boundary for the distance-based location update algorithm. The proposed model is flexible and captures some of the real characteristics in the wireless cellular environment. The model can adapt to arbitrary cell topologies in which the number of neighboring base stations at different locations may vary. The cell residence time can follow general distributions which captures the fact that the mobile user may spend more time at certain locations than others. The model also incorporates the concept of a trip in which the mobile user may follow a particular path to a destination. For implementation, the decision of location update can be made by a simple table lookup. Numerical results indicate that the proposed model provides a more accurate update boundary in real environment than that derived from a hexagonal cell configuration with a random walk movement pattern. The proposed model allows the network to maintain a better balance between the processing incurred due to location update and the radio bandwidth utilized for paging between call arrivals.
14696774
The Fundamental Capacity-Delay Tradeoff in Large Mobile Ad Hoc Networks
There has been recent interest within the networking research community to understand how mobility can improve the capacity of mobile ad hoc networks. Of particular interest is the achievable capacity under delay constraints. In this paper, we establish the following upper bound on the optimal capacity-delay tradeoff in mobile ad hoc networks for an i.i.d. mobility model. For a mobile ad hoc network with n nodes, if the per-bit-averaged mean delay is bounded by D̄, then the per-node capacity λ is upper bounded by λ ≤ O( D̄n log 3 n). By studying the condition under which the upper bound is tight, we are able to identify the optimal values of several key scheduling parameters. We then develop a new scheme that can achieve a capacity-delay tradeoff close to the upper bound up to a logarithmic factor. Our new scheme achieves a larger per-node capacity than the schemes reported in previous works. In particular, when the delay is bounded by a constant, our scheme achieves a per-node capacity of Θ(n/ logn). This indicates that, for the i.i.d. mobility model, mobility results in a larger capacity than that of static networks even with constant delays. Finally, the insight drawn from the upper bound allows us to identify limiting factors in existing schemes. These results present a relatively complete picture of the achievable capacity-delay tradeoffs under different settings.
1482754
Mobility model of vehicle-borne terminals in urban cellular systems
This paper presents a new model describing the mobility of vehicle-borne terminals under realistic urban traffic conditions. The model accounts for arbitrary urban street patterns and realistic terminal movements by a limited number of parameters that can be easily measured or derived from a city map. It introduces distribution functions of street length, direction changes at crossroads, and terminal velocity to find an analytical formulation. For validation, we show by simulation that the model yields cell sojourn time and remaining sojourn time distributions in agreement with previous results. Further independent validation by measurements and by a street pattern tracing software tool prove the model's accuracy.
3126654
Large wireless networks under fading, mobility, and delay constraints
We study wireless ad hoc networks with a large number of nodes. We first focus on a network of n immobile nodes, each with a destination node chosen in random. We develop a scheme under which, in the absence of fading, the network can provide each node with a traffic rate /spl lambda//sub 1/(n)=K/sub 1/(nlog n)/sup -1/ 2/. This result was first shown in J. Hightower and G. Borriello (2001) under a similar setting, however the proof presented here is shorter and uses only basic probability tools. We then proceed to show that, under a general model of fading, each node can send data to its destination with a rate /spl lambda//sub 2/(n)=K/sub 2/n/sup -1// /sup 2/(log n)/sup -3/2/. Next, we extend our formulation to study the effects of node mobility. We first develop a simple scheme under which each of the a mobile nodes can send data to a randomly chosen destination node with a rate /spl lambda//sub 3/(n)=K/sub 3/n/sup -1/2/(log n)/sup -3/2/, and with a fixed upper bound on the packet delay d/sub max/ that does not depend on n. We subsequently develop a scheme under which each of the nodes can send data to its destination with a rate /spl lambda//sub 4/(n)=K/sub 4/n/sup (d-1)/ 2/(log n)/sup -5/ 2 /provided that nodes are willing to tolerate packet delays smaller than d/sub max/(n)<K/sub 5/n/sup d/, where 0<d<1. With both schemes, a general model of fading is assumed. In addition, nodes require no global topology or routing information, and only need to coordinate locally. The above results hold for an appropriate choice of values for the constants K/sub i/, and with probability approaching 1 as the number of nodes n approaches infinity.
61534465
Capacity and delay tradeoffs for ad hoc mobile networks
We consider the throughput/delay tradeoffs for scheduling data transmissions in a mobile ad hoc network. To reduce delays in the network, each user sends redundant packets along multiple paths to the destination. Assuming the network has a cell partitioned structure and users move according to a simplified independent and identically distributed (i.i.d.) mobility model, we compute the exact network capacity and the exact end-to-end queueing delay when no redundancy is used. The capacity-achieving algorithm is a modified version of the Grossglauser-Tse two-hop relay algorithm and provides O(N) delay (where N is the number of users). We then show that redundancy cannot increase capacity, but can significantly improve delay. The following necessary tradeoff is established: delay/rate/spl ges/O(N). Two protocols that use redundancy and operate near the boundary of this curve are developed, with delays of O(/spl radic/N) and O(log(N)), respectively. Networks with non-i.i.d. mobility are also considered and shown through simulation to closely match the performance of i.i.d. systems in the O(/spl radic/N) delay regime.
203122873
Handbook of Linear Partial Differential Equations for Engineers and Scientists
INTRODUCTION: SOME DEFINITIONS, FORMULAS, METHODS, AND SOLUTIONS Classification of Second Order Partial Differential Equations Basic Problems of Mathematical Physics Properties and Particular Solutions of Linear Equations Separation of Variables Method Integral Transforms Method Representation of the Solution of the Cauchy Problem via the Fundamental Solution Nonhomogeneous Boundary Value Problems with One Space Variable Nonhomogeneous Boundary Value Problems with Many Space Variables Construction of the Green's Functions: General Formulas and Relations Duhamel's Principles in Nonstationary Problems Transformation Simplifying Initial and boundary Conditions EQUATIONS OF PARABOLIC TYPE WITH ONE SPACE VARIABLE Constant Coefficient Equations Heat Equation with Axial or Central Symmetry and Related Equations Equations Containing Power Functions and Arbitrary Parameters Equations Containing Exponential Functions and Arbitrary Parameters Equations Containing Hyperbolic Functions and Arbitrary Parameters Equations Containing Logarithmic Functions and Arbitrary Parameters Equations Containing Trigonometric Functions and Arbitrary Parameters Equations Containing Arbitrary Functions Equations of Special Form PARABOLIC EQUATIONS WITH TWO SPACE VARIABLES Heat Equation Heat Equation with a Source Other Equations PARABOLIC EQUATIONS WITH THREE OR MORE SPACE VARIABLES Heat Equation Heat Equation with a Source Other Equations with Three Space Variables Equations with n Space Variables HYPERBOLIC EQUATIONS WITH ONE SPACE VARIABLE Constant Coefficient Equations Wave Equation with Axial or Central Symmetry Equations Containing Power Functions and Arbitrary Parameters Equations Containing the First Time Derivative Equations Containing Arbitrary Functions HYPERBOLIC EQUATIONS WITH TWO SPACE VARIABLES Wave Equation Nonhomogeneous Wave Equation Telegraph Equation Other Equation with Two Space Variables HYPERBOLIC EQUATIONS WITH THREE OR MORE SPACE VARIABLES Wave Equation Nonhomogeneous Wave Equation Telegraph Equation Other Equations with Three Space Variables Equations with n Space Variables ELLIPTIC EQUATIONS WITH TWO SPACE VARIABLES Laplace Equation Poisson Equation Helmholtz Equation Other Equations ELLIPTIC EQUATIONS WITH THREE OR MORE SPACE VARIABLES Laplace Equation Poisson Equation Helmholtz Equation Other Equations Equations with n Space Variables HIGHER ORDER PARTIAL DIFFERENTIAL EQUATIONS Third Order Partial Differential Equations Fourth Order One-Dimensional Nonstationary Equations Two-Dimensional Nonstationary Fourth Order Equations Fourth Order Stationary Equations Higher Order Linear Equations with Constant Coefficients Higher Order Linear Equations with Variable Coefficients SUPPLEMENT A: Special Functions and Their Properties SUPPLEMENT B: Methods of Generalized and Functional Separation of Variables in Nonlinear Equations of Mathematical Physics REFERENCES INDEX
14915718
A mobility-based framework for adaptive clustering in wireless ad hoc networks
This paper presents a novel framework for dynamically organizing mobile nodes in wireless ad hoc networks into clusters in which the probability of path availability can be bounded. The purpose of the (/spl alpha/, t) cluster is to help minimize the far-reaching effects of topological changes while balancing the need to support more optimal routing. A mobility model for ad hoc networks is developed and is used to derive expressions for the probability of path availability as a function of time. It is shown how this model provides the basis for dynamically grouping nodes into clusters using an efficient distributed clustering algorithm. Since the criteria for cluster organization depends directly upon path availability, the structure of the cluster topology is adaptive with respect to node mobility. Consequently, this framework supports an adaptive hybrid routing architecture that can be more responsive and effective when mobility rates are low and more efficient when mobility rates are high.
56295019
Estimating position and velocity of mobiles in a cellular radio network
Determining the position and velocity of mobiles is an important issue for hierarchical cellular networks since the efficient allocation of mobiles to large or microcells depends on its present velocity. We suggest a method of tracing a mobile by evaluating subsequent signal-strength measurements to different base stations. The required data are available in the Global System for Mobile (GSM) system. The basic idea resembles multidimensional scaling (MDS), a well-recognized method in statistical data analysis. Furthermore, the raw data are smoothed by a linear regression setup that simultaneously yields an elegant, smoothed estimator of the mobile's speed. The method is extensively tested for data generated by the simulation tool GOOSE.
9332281
Predictive distance-based mobility management for multidimensional PCS networks
This paper presents a mobile tracking scheme that exploits the predictability of user mobility patterns in wireless PCS networks. In this scheme, a mobile's future location is predicted by the network, based on the information gathered from the mobile's recent report of location and velocity. When a call is made, the network pages the destination mobile around the predicted location. A mobile makes the same location prediction as the network does; it inspects its own location periodically and reports the new location when the distance between the predicted and the actual locations exceeds a threshold. To more realistically represent the various degrees of velocity correlation in time, a Gauss-Markov mobility model is used. For practical systems where the mobility pattern varies over time, we propose a dynamic Gauss-Markov parameter estimator that provides the mobility parameters to the prediction algorithm.Based on the Gauss-Markov model, we describe an analytical framework to evaluate the cost of mobility management for the proposed scheme. We also present an approximation method that reduces the computational complexity of the cost evaluation for multidimensional systems. We then compare the cost of predictive mobility management against that of the regular, nonpredictive distance-based scheme, for both the case with ideal Gauss-Markov mobility pattern and the case with time-varying mobility pattern.The performance advantage of the proposed scheme is demonstrated under various mobility patterns, call patterns, location inspection cost, location updating cost, mobile paging cost, and frequencies of mobile location inspections. As a point of reference, prediction can reduce the mobility management cost by more than 50% for all systems, where a the mobile users have moderate mean velocity and where performing a single location update is as least as expensive as paging a mobile in one cell.