The three main research topics we are focusing on are:

We are developing models for the demand and quality of service of web pages, accessed over wireless broadcast channels. This includes representing demand using stochastic models and computing the expected service time for various scheduling algorithms. The objective is to use the demand and service models to develop scheduling protocols for broadcasting web pages in a way that optimizes the overall quality of service. The tools needed in this research include probability theory and combinatorics.
We consider a model where we wish to broadcast two files to mobile clients. We are allowed to split each of the files into two halves, which can be sent separately. We wish to schedule the broadcast of these pieces in a way that minimizes the average time the clients must wait to receive the files. This figure shows the optimal broadcast schedules for two files. The colored regions indicate where each schedule is optimal, as a function of the demand probabilities and lengths of the items.
We are developing covering algorithms to efficiently place base stations in a wireless network in which the clients are mobile. We are also studying the connectivity properties of the obtained covering, using a probabilistic model related to percolation theory. Finally, we are interested in ways to model the information capacity of a wireless network. The tools needed in this research include probability theory, geometry, combinatorics, and information theory.
In the picture below, each disk is an abstraction of a broadcast domain. A covering algorithm places disks on the plane, according to the distribution of the clients,
in such a way that each disk covers at least one client and each client
is covered by at least a disk.
The algorithm can be a distributed, selforganizing one, in a model
where both base stations and clients are mobile; or a more centralized
one, in a model where the clients are mobile and the base stations
are static. In the latter case, the base stations could be laid on
a fixed grid and the covering algorithm could determine the
(minimal) subset of them that need to be turned on at any given time to
provide coverage.
As the density of the clients that need to be covered is increased, the covering disks begin to form connected components. At a given value of the density of the clients a phase transition behavior is observed and a connected component of covering disks that spans the whole plane can be found with probability one.
In the picture below a covering algorithm is applied to a
random distribution of points of increasing density along the
horizontal axis. For this algorithm, a large connected component of
covering disks (red disks) forms, for values of the density larger
than 0.55.
A movie (7.6 Megs animated gif) that shows the phase transition
behavior is also available here.
We are studying innovative ways to store data in the mobile network so that data can be accessed efficiently even in highly dynamic environments. Also, data reliability and confidentiality are to be guaranteed.
It's very challenging work to develop data storage algorithms that will break barriers set by unpredictable data access modes, diverse user mobility patterns, dynamic network structures, and limited computation and communication resources. New data storage theories are being proposed that combine data allocation, routing and information theory. For more details about our data storage please visit here.