We consider an opportunistic content sharing system designed to store and distribute local spatio-temporal “floating” information in uncoordinated P2P fashion relying solely on the mobile nodes passing through the area of interest, referred to as the anchor zone. Nodes within the anchor zone exchange the information in opportunistic manner, i.e., whenever two nodes come within each others' transmission range. Outside the anchor zone, the nodes are free to delete the information, since it is deemed relevant only for the nodes residing inside the anchor zone. Due to the random nature of the operation, there are no guarantees, e.g., for the information availability. By means of analytical models, we show that such a system, without any supporting infrastructure, can be a viable and surprisingly reliable option for content sharing as long as a certain criterion, referred to as the criticality condition, is met. The important quantity is the average number of encounters a randomly chosen node experiences during its sojourn time in the anchor zone, which again depends on the communication range and the mobility pattern. The theoretical studies are complemented with simulation experiments with various mobility models showing good agreement with the analytical results.

We consider the problem of finding the maximum directed packet flow that can be sustained in an infinite wireless multihop network. This ability of the network to relay traffic is called the forwarding capacity, and the problem appears when the spatial scales corresponding to the end-to-end paths (routing) and the neighboring nodes (forwarding) are strongly separated in a massively dense network. We assume a Boolean interference model. The infinite network is approximated with a finite but large network where the node locations form a spatial Poisson process. We study two constructive approaches to tighten the lower bound for the forwarding capacity by a significant amount. In path scheduling the packets traverse the network using predefined paths that do not interfere with each other, and coordination is thus required only between the nodes of a path. In greedy maximum weight scheduling, the transmissions are scheduled greedily according to queue-length based weights of the links. In addition to a fixed transmission radius, we consider greedy maximum weight scheduling with a transmission radius adjustable up to a given maximum. We are able to produce numerical results that characterize the achievable forwarding capacity under global coordination of the transmissions, providing, e.g., concrete points of reference for practical distributed implementations.

We study the maximal forwarding capacity of a massively dense wireless multi-hop network where a typical path consists of a vast number of hops. In such a network, the macroscopic level, corresponding to the scale of an end-to-end path, and the microscopic level, corresponding to the scale of a single hop, can be separated. At the macroscopic level the task is that of routing, while at the microscopic level the packets are forwarded based on the information received from the macroscopic level. We give a formulation for the forwarding problem and devise simulation algorithms based on an augmentation of the max-flow min-cut theorem for obtaining upper bounds for the maximal forwarding capacity. We compare the upper bounds with feasible forwarding methods and find out that the tightest bound is about three times the highest achieved performance.

The random linear fountain (RLF) is an efficient form of fountain coding with an expected overhead of only 1.6 packets. Because of increasing computational complexity, however, it cannot be directly used for large message sizes. In this paper, we study the performance penalty of dividing the data into k parts which are coded using the RLF. To ease the performance problem, we propose the use of macropackets which are generated by using LT-coding over the different parts of divided RLF. We calculate the decoding probabilities for k = 2 and 3 and compare the results to the overhead obtained using the combination of divided RLF and data carousel. The results indicate that while the use of macropackets improves the performance over the divided RLF, still better performance is obtained by data carousel in the case of low channel loss rate.

Fountain codes provide an efficient way to transfer information over erasure channels. We give an exact performance analysis of a specific type of fountain codes, called LT codes, when the message length N is small. Two different approaches are developed. In a Markov chain approach the state space explosion, even with reduction based on permutation isomorphism, limits the analysis to very short messages, N < 4. An alternative combinatorial method allows recursive calculation of the probability of decoding after N received packets. The recursion can be solved symbolically for values of N < 10 and numerically up to N ap30. Examples of optimization results give insight into the nature of the problem. In particular, we argue that a few conditions are sufficient to define an almost optimal LT encoding.

We consider dimensioning of data networks. The network is modeled in a dynamic setting where elastic flows (file transfers) arrive randomly and share the bandwidth according to balanced fairness. Simple methods are derived for determining the link capacities so that given flow-level throughput requirements are satisfied. We consider two different approaches to define the throughput requirements: single constraint on average throughput in the network and separate constraint for every route. The results enable a simple characterization of the order- of-magnitude of the required capacities, which can be utilized in practical network planning and dimensioning.

We consider the load balancing problem in large wireless multi-hop networks, often referred to as massively dense wireless multi-hop networks. A network is considered to be massively dense if there are nodes practically everywhere and a typical distance between two nodes is much larger than the transmission range necessitating communication over a large number of hops. The task is to choose the routes in such a way that the maximum relayed traffic load in the network is minimized. In fixed networks the multi-path routes generally yield a lower congestion and thus allow higher throughput. In contrast, we show that in the case of massively dense wireless multi-hop networks the optimal load balancing can be achieved by single-path routing. In particular, we show how any given multi-path routing can be transformed to a single-path routing with at least the same level of performance. The concepts are illustrated by numerical examples where the network nodes are assumed to reside inside a unit disk with uniform traffic demands. The shortest path routes, corresponding to straight line segments, yield a maximum traffic load of 0.637, whereas the single-path routes obtained by numerical optimization yield 0.343, corresponding to 46% reduction in the traffic load.

We study a time slotted random access network carrying elastic data traffic. We assume that the link access probabilities can be controlled on time scales comparable to network flow state changes but remain constant on shorter time scales and in particular do not react to slot-level backlogs. Capacity sets of such networks are defined, i.e. the effective link capacities which can be achievedby tuning the transmission probabilities. We revisit the problem of finding the capacity set and give an analytical characterization for the case of a single resource, which was derived already by Kleinrock. For the multihop case we provide a general algorithm to determine the boundary of the capacity set. The main contribution of the paper is to combine the capacity set results with the concept of balanced fairness to analyze the file transfer throughputs in a dynamic setting where a stochastically evolving number of file transfers adapt their rates to share the network resources among each other. Our numerical analysis shows that for light loads and short routes the throughput under flow-optimized random access is close to optimal that of slot-by-slot link scheduling, even though the control time scale required by the random access is much slower. With heavy loads the performance deteriorates.

In this paper we introduce a Markovian random waypoint model which allows us to create diverse mobility patterns in the given movement domain. The model allows adjusting random pause times and the momentary velocity. Furthermore, the distribution used to pick the next waypoint may depend on the current location, which allows, e.g., creation of typical routes. As an application for the Markovian random waypoint we consider modelling hotspots. There are several mechanisms which may be causing a hotspot and we present how the parameters of the proposed model can be adjusted accordingly to match the scenario in question. We further illustrate how two seemingly similar mobility patterns lead to highly different estimates of achievable performance levels. Finally, we show how the state of the MWP model can be initialised in simulations such that the node starts from the stationary state without any initial transient.

In this paper we consider the problem of traffic matrix estimation. As the problem is underconstrained, some additional information has to be brought in to obtain a solution. If we have a sequence of link count measurements available, a natural candidate is to use the link count sample covariance matrix under the assumption of a functional relationship between the mean and the variance of the traffic. We propose two computationally light-weight methods for traffic matrix estimation based on the covariance matrix, the projection method and constrained minimization method. The accuracy of these methods is compared with that of other methods using second order moment estimates by simulation under synthetic traffic scenarios.

We give an example of flow level performance analysis of data traffic in wireless networks by studying a scenario where two base stations with link adaptation serve in a coordinated fashion downloading users on a road or street between the stations. Due to the dynamic nature of such systems, a detailed flow level analysis is challenging and conventional methods run into computational difficulties. We motivate the detailed analysis by studying the system under different operational goals such as maximum throughput, max-min fairness and balanced fairness, concluding that the performance under these dynamic policies differ significantly from the performance under more tractable static policies. We discuss how the corresponding numerical analyses can be facilitated by applying the notion of balanced fairness and, in particular, introduce a novel approximation method referred to as value extrapolation. Value extrapolation can be applied to approximate any performance measure expressed as the expected value of a random variable which is a function of the system state. The idea of the value extrapolation is to consider the system in the MDP (Markov Decision Processes) setting and to solve the expected value from the Howard equations written for a truncated state space. Instead of a simple truncation, the relative values of states just outside the truncated state space are estimated using a polynomial extrapolation based on the states inside. This leads to a closed system and, unless the system is heavily loaded, allows one to obtain accurate results with remarkably small truncated state spaces.

The random waypoint model (RWP) is one of the most widely used mobility models in performance analysis of ad hoc networks. We analyze the stationary spatial distribution of a node moving according to the RWP model in a given convex area. For this, we give an explicit expression, which is in the form of a one-dimensional integral giving the density up to a normalization constant. This result is also generalized to the case where the waypoints have a nonuniform distribution. As a special case, we study a modified RWP model, where the waypoints are on the perimeter. The analytical results are illustrated through numerical examples. Moreover, the analytical results are applied to study certain performance aspects of ad hoc networks, namely, connectivity and traffic load distribution.

In [3], it was shown that the optimal throughput scaling in wireless multihop networks is achieved using slotted Aloha, and quantitative performance results for this protocol were derived under the assumption of exponentially distributed transmission powers. In this paper, we extend the analysis of this MAC scheme: assuming that all nodes employ some common constant power, we evaluate the probability of successful transmission in a random time slot. When interfering nodes are assumed to be randomly located, this temporal probability is a random variable with its own distribution. We develop numerical approximations for evaluating both the mean and the tail probability of this distribution; as far as we are aware, the distribution itself has not been studied before. The accuracy of our approximations can be improved indefinitely, with the cost of added numerical computations. We validate the approximations against simulation results.

Many communication systems can be efficiently modelled using queueing networks with a stationary distribution that is insensitive to detailed traffic characteristics and depends on arrival rates and mean service requirements only. This robustness enables simple engineering rules and is thus of considerable practical interest. In this paper we extend previous results by relaxing the usual assumption of static routing and balanced service rates to account for both dynamic capacity allocation and dynamic load balancing. This relaxation is necessary to model systems like grid computing, for instance. Our results identify joint dynamic allocation and routing policies for single input reversible networks that are optimal for a wide range of performance metrics. A simple two-pass algorithm is presented for finding the optimal policy. The derived analytical results are applied in a number of simple numerical examples that illustrate their modelling potential.

We consider wireless multicast tree construction for energy efficiency. We introduce a novel algorithm, incremental shortest path tree (ISPT), to generate source-based multicast trees and analyse its performance. Additionally, the potential of further improvements in the tree construction is addressed comparing the performance of the algorithm with the results from a simulated annealing optimisation.

We consider the problem of estimating blocking probabilities in a multicast loss system via simulation, applying the static Monte Carlo method with importance sampling. An approach is introduced where the original estimation problem is first decomposed into independent simpler sub-problems, each roughly corresponding to estimating the blocking probability contribution from a single link. Then we apply importance sampling to solve each sub-problem. The importance sampling distribution is the original distribution conditioned on that the state is in the blocking state region of a single link. Samples can be generated from this distribution using the so called inverse convolution method. Finally, a dynamic control algorithm is used for optimally allocating the samples between different sub-problems. The numerical results demonstrate that the variance reduction obtained with the method is remarkable, between 400 and 36000 in the considered examples.

The problem of call admission control and routing in a multiservice circuit-switched loss network can be solved optimally under certain assumptions by the tools of Markov decision theory. However, in networks of practical size a number of simplifying approximations are needed to make the solution feasible. Assuming link independence, we propose a new method for approximating the state-dependent link costs accurately and relatively efficiently, even on links with extremely large state spaces. The proposed polynomial approximations are optimal in the sense of minimizing the residual in the continuous-time Howard equations of the Markov decision processes associated with the links. Numerical results are presented, and the proposed approximations are found superior to some earlier link-cost approximation methods.

The parameter estimation of a traffic model based on the fractional Brownian motion (FBM) is studied. The model has three parameters: the mean rate m, variance parameter a and the Hurst parameter H. Explicit expressions for the maximum likelihood (ML) estimates m/spl circ/ and a/spl circ/ in terms of H are given, as well as the expression for the log likelihood function from which the estimate H/spl circ/ is obtained as the maximizing argument. A geometric sequence of sampling points, t/sub i/=/spl alpha//sup i/, is introduced, which fits neatly into the self-similar property of the process and also reduces the number of samples needed to cover several time scales. It is shown that by a proper 'descaling' the traffic process is stationary on this grid leading to a Toeplitz-type covariance matrix. Approximations for the inverted covariance matrix and its determinant are introduced. The accuracy of the estimations is studied by simulations. Comparisons with estimates obtained with linear sampling and with the wavelet-based A-V estimator show that the geometrical sampling indeed improves the accuracy of the estimate H/spl circ/ with a given number of samples.

With standard assumptions the routing and wavelength assignment problem (RWA) can be viewed as a Markov decision process (MDP). The problem, however defies an exact solution because of the huge size of the state space. Only heuristic algorithms have been presented up till now. We propose an approach where, starting from a given heuristic algorithm, one obtains a better algorithm by the first policy iteration. In order to estimate the relative costs of states, we make a simulation on the fly studying, at each decision epoch, the consequences of all the alternatives actions. Being computationally intensive, this method can be used in real time only for systems with slow dynamics. Offline it can be used to assess how close the heuristic algorithms come to the optimal policy. Numerical examples are given about the policy improvement.

The author considers the performance evaluation of an advanced capacity reservation system using the CCITT defined reserved call establishment mode. A simple model for the traffic process is introduced: calls are assumed to be offered uniformly to the reservation book. The state of the system can then be described statistically in terms of the population of various types of islands of free time slots. The limit where the length of the reservation book tends to infinity is, in particular, considered. For single-server systems with a deterministic holding time of one or two time slots, a closed-form solution is found. For a general holding time distribution, an asymptotic analytical solution is derived and corrections to this asymptotic solution are calculated numerically. For multiserver systems with geometric holding time distribution, the author presents numerical results obtained by simulations. An interpolation formula valid for all traffic intensities is developed. A procedure is given to extrapolate the results to larger systems than were actually simulated.>

When variable-bit-rate sources are multiplexed in an asynchronous transfer mode (ATM) network, there arise queues with a particular form of correlated arrival process. Such queues are analyzed by exploiting a result expressing the distribution of work in system of the G/G/1 queue originally derived by V.E. Benes (1963). A simple alternative demonstration of this result is analyzed and extended to the case of fluid input systems. The result is applied first to a queue where the arrival process is a superposition of periodic sources (the Sigma D/sub i//D/1 queue), and then to a variable-input-rate constant-output-rate fluid system. The latter is shown to model the so-called burst component of the considered superposition queuing process. The difference between this and the real queue, the cell component, can be evaluated by means of the results obtained for the Sigma D/sub i//D/1 queue. The relative importance of these two components is explored with reference to the particular case of a superposition of on/off sources.>

The authors consider the queue arising in a multiservice network using ATM (asynchronous transfer mode) when a superposition of periodic streams of constant-length cells is multiplexed on a high-speed link. An exact closed formula is derived for the queue length distribution in the case where all streams have the same period, and tight upper and lower bounds are obtained on this distribution when the periods are different. Numerical results confirm that the use of a Poisson approximation (i.e. the M/D/1 queue) can lead to a significant overestimation of buffer requirements, particularly in the case of heavy loads. Buffer requirements for a mixture of different period streams can be accurately estimated from the upper bound on the queue length distribution. For given load, requirements increase with the number of long-period (i.e. low-bit rate) sources. The results are deduced from a novel characterization of the single-server constant service time queue, which should be useful in other applications.>

A general reciprocity relation is pointed out that is obeyed by the blocking probabilities in multiservice loss systems managed under a coordinate convex access. This in turn means that several user classes compete for a common pool of resource, the mutual differential influences on the blocking probabilities of the traffic streams are equal.>