Research Interests
Economics of Access Networks
I work at the intersection of economics and network architecture. Specifically, I use tools from game theory and microeconomics to model how different stakeholders in an access network interact among themselves and in the process, determine the sustainability of the network.
For example, in the wireless domain, I have analysed the economics of the cognitive radio network (CRN). Dynamic spectrum access (DSA) or popularly known as the CRN technology detects the inactive periods of the legacy/primary users and dynamically assigns these 'holes' to the non-legacy/secondary users to enhance the utilisation of the electromagnetic spectrum (see Fig. 1). The very foundation of this technology relies upon a well-designed incentive mechanism. The secondary users must provide a good amount of remuneration to the primary for allowing the secondary users to intrude into their licensed spectrum. My focus is to study these contract negotiation processes between the primary and the secondary users in various networking scenarios. The results sometimes conform to our intuitive expectations but many a times deviate from it. In a cognitive cellular network, for example, I have shown that if the willingness-to-pay of the secondary users is not sufficiently high, then no matter how many secondary users are present in the network, the cognitive network is bound to be non-sustainable in the long-run. It is one of the examples where the network is technically viable but economically infeasible. I use tools such as Nash bargaining theory, mechanism design, variational optimization and optimal control theory in my analysis.
Fig. 1: A schematic diagram of the opportunistic cognitive spectrum access mechanism. The temporal spaces occupied by the primary/licensed users are marked as yellow. The secondary users tries to identify the non-yellow spaces (holes) and utilise it. The spaces where it succeeds to do that are marked as green. Unfortunately, the 'hole' identification process is not always error-free. Sometimes, the secondary may wrongly declare a space to be occupied by the primary, although, in reality, it is not. Such instances have been marked as white. In other cases, the secondary may wrongly identify an occupied space as non-occupied and in the process of utilising it, jeopardise the primary's transmission. Such missed detected instances have been marked as red.
I have also worked on the economical aspects of the optical access network, especially on the popular architecture of Time-Wavelength Division Multiplexed Passive Optical Network (TWDM-PON). Unlike its wireless counterpart, an optical network is not driven by a continuous electromagnetic spectrum but rather by optical pulses transmitted through optical fibres from a discrete number of line cards placed in an optical line terminal (OLT). I aim to understand how a profit-maximizing service provider, in such a network, would optimally deploy different discrete network resources and how that in turn, would impact the users. The problem often turns out to be a Mixed Integer Nonlinear Program (MINLP) which, in general, is NP-hard. I have devised a novel technique to solve such problems in polynomial time by imposing certain restrictions on the user demand functions. As a byproduct, my work also suggests policies that can be adopted by a benevolent government to improve the collective welfare of the users.
Stochastic Geometry
I have contributed a few articles in this field although it is not my primary research interest. Stochastic geometry is a branch of applied probability whose origin dates back to at least as far as 1940s. However, recently it has gained popularity in the telecommunications literature as it provides a convenient probabilistic model to describe the base stations' (BSs) and users' locations in a cellular network. Such a model allows one to compute simple closed-form expressions of various network performance evaluation parameters such as the spectral efficiency and the outage probability. Majority of the existing analyses assume that the BS deployment density is much lower than user density. However, such presumption becomes questionable as the networks continue to evolve towards dense and ultra-dense regime. In order to perform stochastic geometric analysis on these ultra-dense networks (UDNs), it is essential to understand the spatial distributions of the BSs that may not get associated with a single user. Such void BSs play a critical role in determining the inter-cell interference and the energy efficiency of the network. My work characterises the point process of these void BSs.