Esa Hyytiä

Spatial node distribution of the random waypoint mobility model with applications

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.

Random waypoint mobility model in cellular networks

In this paper we study the so-called random waypoint (RWP) mobility model in the context of cellular networks. In the RWP model the nodes, i.e., mobile users, move along a zigzag path consisting of straight legs from one waypoint to the next. Each waypoint is assumed to be drawn from the uniform distribution over the given convex domain. In this paper we characterise the key performance measures, mean handover rate and mean sojourn time from the point of view of an arbitrary cell, as well as the mean handover rate in the network. To this end, we present an exact analytical formula for the mean arrival rate across an arbitrary curve. This result together with the pdf of the node location, allows us to compute all other interesting measures. The results are illustrated by several numerical examples. For instance, as a straightforward application of these results one can easily adjust the model parameters in a simulation so that the scenario matches well with, e.g., the measured sojourn times in a cell.

Floating content: Information sharing in urban areas

Content sharing using personal web pages, blogs, or online social networks is a common means for people to maintain contact with their friends, colleagues, and acquaintances. While such means are essential to overcome distances, using infrastructure services for location-based services may not be desirable. In this paper, we analyze a fully distributed variant of an ephemeral content sharing service, solely dependent on the mobile devices in the vicinity using principles of opportunistic networking. The net result is a best effort service for floating content in which: 1) information dissemination is geographically limited; 2) the lifetime and spreading of information depends on interested nodes being available; 3) content can only be created and distributed locally; and 4) content can only be added, but not explicitly deleted. First we present our system design and summarize its analytical modeling. Then we perform extensive evaluation for a map-based mobility model in downtown Helsinki to assess the operational range for floating content, which, at the same time also validate the analytical results obtained for a more abstract model of the system.

Optimal Degree Distribution for LT Codes with Small Message Length

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.

On traffic load distribution and load balancing in dense wireless multihop networks

We study the load balancing problem in a dense wireless multihop network, where a typical path consists of a large number of hops, that is, the spatial scales of a typical distance between source and destination and mean distance between the neighboring nodes are strongly separated. In this limit, we present a general framework for analyzing the traffic load resulting from a given set of paths and traffic demands. We formulate the load balancing problem as a minmax problem and give two lower bounds for the achievable minimal maximum traffic load. The framework is illustrated by considering the load balancing problem of uniformly distributed traffic demands in a unit disk. For this special case, we derive efficient expressions for computing the resulting traffic load for a given set of paths. By using these expressions, we are able to optimize a parameterized set of paths yielding a particularly flat traffic load distribution which decreases the maximum traffic load in the network by in comparison with the shortest-path routing.

Connectivity Properties of Random Waypoint Mobility Model for Ad Hoc Networks

We study the connectivity properties of an ad hoc network consisting of n nodes each moving according to the Random Waypoint mobility model. In particular, we focus on estimating two quantities, the probability that the network is connected, and the mean durations of the connectivity periods. The accuracy of the approximations is compared against numerical simulations. For the probability of connectivity, an approximation is given that is remarkably accurate. By numerical examples we also show that in sparse network the mobility has a positive effect on connectivity, whereas in dense network the situation becomes the opposite. For the mean length of the connectivity periods results are also accurate in the important region where the probability of connectivity rises rapidly.

On load balancing in a dense wireless multihop network

We study the load balancing problem in a dense wireless multihop network, where a typical path consists of large number of hops, i.e., the spatial scales of a typical distance between source and destination, and mean distance between the neighboring nodes are strongly separated. In this limit, we present a general framework for analyzing the traffic load resulting from a given set of paths and traffic demands. We formulate the load balancing problem as a minmax problem and give two lower bounds for the achievable minimal maximum traffic load. The framework is illustrated by an example of uniformly distributed traffic demands in a unit disk with a few families of paths given in advance. With these paths we are able to decrease the maximum traffic load by factor of 33-40% depending on the assumptions. The obtained traffic load level also comes quite near the tightest lower bound

Random waypoint model in n-dimensional space

The random waypoint model (RWP) is one of the most widely used mobility models in performance analysis of mobile wireless networks. In this paper we extend the previous work by deriving an analytical formula for the stationary distribution of a node moving according to a RWP model in n-dimensional space.

Size- and State-Aware Dispatching Problem with Queue-Specific Job Sizes

We consider the dispatching problem in a size- and state-aware multi-queue system with Poisson arrivals and queue-specific job sizes. By size- and state-awareness, we mean that the dispatcher knows the size of an arriving job and the remaining service times of the jobs in each queue. By queue-specific job sizes, we mean that the time to process a job may depend on the chosen server. We focus on minimizing the mean sojourn time (i.e., response time) by an MDP approach. First we derive the so-called size-aware relative values of states with respect to the sojourn time in an M/G/1 queue operating under FIFO, LIFO, SPT or SRPT disciplines. For FIFO and LIFO, the size-aware relative values turn out to be insensitive to the form of the job size distribution. The relative values are then exploited in developing efficient dispatching rules in the spirit of the first policy iteration.

Floating content for probabilistic information sharing

People are increasingly using online social networks for maintaining contact with friends and colleagues irrespective of their physical location. While such services are essential to overcome distances, using infrastructure services for location-based services may not be desirable. In contrast, we design and analyze a fully distributed variant of an ephemeral content sharing service, solely dependent on the mobile devices in the vicinity using principles of opportunistic networking. The result is a best effort service for floating content in which content is created locally, its availability is geographically limited and its lifetime and spreading depends on interested nodes being available. In this paper, we present our system design, algorithms, and protocol specification in detail. A set of real world experiments is then used to assess the achievable transmission rates and transmission ranges in such a system. We validate our previous analytical results and assess the performance of floating content in general and especially of different replication and deletion strategies by means of extensive simulations using a map-based mobility model in downtown Helsinki.