Pasi E. Lassila

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.

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.

When does content float? Characterizing availability of anchored information in opportunistic content sharing

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.

Analysis of PDCCH performance for M2M traffic in LTE

As Long-Term Evolution (LTE) is starting to be widely deployed, the volume of machine-to-machine (M2M) traffic is increasing very rapidly. From the M2M traffic point of view, one of the issues to be addressed is the overload of the random access channel. The limitation in the physical downlink control channel (PDCCH) resources may severely constrain the number of devices that an LTE Evolved Node B (eNB) can serve. We develop a Markov model that describes the evolution of the Message 4 queue in the eNB formed by several users performing the random access procedure simultaneously, and then, we study its stability and performance. Our model explicitly takes into account the four initial steps in the random access procedure. By utilizing the model, we are able to determine the stability limit of the system, which defines the maximum throughput and the probability of failure of the random access procedure due to different causes. We observe that the sharing of the PDCCH resources between Messages 2 and 4 with different priorities makes the performance of the whole random access procedure deteriorate very rapidly near the stability limit. However, we can extend the maximum throughput and improve the overall performance by increasing the PDCCH resource size. Furthermore, we estimate the upper limit of the number of devices that can be served by an LTE eNB and determine the minimum PDCCH resource size needed to satisfy a given traffic demand.

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.

Flow-level stability and performance of channel-aware priority-based schedulers

Channel-aware scheduling in modern wireless networks enables the system to exploit the random rate variations across different users to increase the performance of the system. We analyze channel-aware priority-based downlink scheduling policies at the so-called flow level with a stochastically varying number of users. The priority can be any monotonously increasing function of the instantaneous rate of the user, which generalizes the well-known linear weight-based policies. Also, ties are allowed within a user class, as well as between user classes. As the main result, we characterize when these priority-based policies are stable under an intuitive necessary condition, which holds for arbitrary tie breaking rules and is independent of the flow size distribution. Additionally, for the policies for which the necessary condition is not sufficient, a more stringent condition is derived in the case of two traffic classes. Finally, extensive simulations have been performed to compare the performance of different priority-based and utility-based policies.

On the optimal trade-off between SRPT and opportunistic scheduling

We consider service systems where new jobs not only increase the load but also improve the service ability of such a system, cf. opportunistic scheduling gain in wireless systems. We study the optimal trade-off between the SRPT (Shortest Remaining Processing Time) discipline and opportunistic scheduling in the systems characterized by compact and symmetric capacity regions. The objective is to minimize the mean delay in a transient setting where all jobs are available at time 0 and no new jobs arrive thereafter. Our main result gives conditions under which the optimal rate vector does not depend on the sizes of the jobs as long as their order (in size) remains the same. In addition, it shows that in this case the optimal policy applies the SRPT principle serving the shortest job with the highest rate of the optimal rate vector, the second shortest with the second highest rate etc. We also give a recursive algorithm to determine both the optimal rate vector and the minimum mean delay. In some special cases, the rate vector, as well as the minimum mean delay, have even explicit expressions as demonstrated in the paper. For the general case, we derive both an upper bound and a lower bound of the minimum mean delay.

Energy-performance trade-off for processor sharing queues with setup delay

Despite the extensive literature on energy efficient control mechanisms for servers, only few studies address the processor sharing discipline. We study the energy-performance trade-off in an energy-aware M X / G / 1-PS system using two popular cost metrics. Among a family of control policies that can possibly stay idle before going to sleep to save energy, the optimal policy is found to be a simple control that either leaves the server idle, or puts it to sleep immediately whenever it becomes idle.

Criticality condition for information floating with random walk of nodes

In an opportunistic content sharing system referred to as floating content, information is copied between mobile nodes upon node encounters inside an area which is called the anchor zone. We study the conditions under which information can be sustained in such a system. The anchor zone is assumed to be a circular disk, and a random walk type mobility model is adopted. First, we consider the one-speed case where all the nodes have a common velocity. Using the transport equation, adopted from nuclear reactor theory, we derive the criticality condition that defines a lower limit for the product of node density, communication distance and the radius of the anchor zone necessary for information floating. The dependence of this criticality parameter on the mean step size of the random walk is numerically established. Complemented by the asymptotic behavior, found by diffusion theory, an accurate approximation formula is derived. While the velocity of the nodes does not appear at all in the criticality condition of the one-speed system, in general, the shape of the velocity distribution has an important effect: the higher the spread of the distribution, the lower the criticality threshold is. This effect is analyzed and discussed.

Whittle Index Approach to Size-aware Scheduling with Time-varying Channels

We consider the optimal opportunistic scheduling problem for downlink data traffic in a wireless cell with time-varying channels. The scheduler itself operates in a very fast timescale of milliseconds, but the objective function is related to minimizing the holding costs in a much longer timescale, at the so-called flow level. The Whittle index approach is a powerful tool in this context, since it renders the flow level optimization problem with heterogeneous users tractable. Until now, this approach has been applied to the opportunistic scheduling problem to generate non-anticipating index policies that may depend on the amount of attained service but do not utilize the exact size information. In this paper, we produce a size-aware (i.e., anticipating) index policy by applying the Whittle index approach in a novel way. By a numerical study based on simulations, we demonstrate that the resulting size-aware index policy systematically improves performance. As a side result, we show that the opportunistic scheduling problem is indexable when the file sizes follow the Pascal distribution, and we derive the corresponding Whittle index, which generalizes earlier results.