## Network sharing and the probability of ruin

There is now increasing interest in network sharing to support wireless communications, where the main focus is on how operators should get access to the scarce spectrum (at least in the radio bands). A more general question is how different parties can provide different components of the network. Although spectrum is one component, the physical transmitting devices and the backhaul are also key components.

In a previous post, I discussed some different ways that infrastructure can be owned by different parties, especially in the setting where users are in a facility (e.g., mine, power plant or large residential area). I briefly mentioned the need for new evaluation metrics in order to optimize network sharing agreements and it is this aspect I want to explore further in this post. In particular, I will introduce the notion of the probability of ruin.

## Gaussian noise channels at medium SNR

Shannon’s noisy channel coding theorem tells us that the capacity is the maximum rate we can transmit information reliably over a noisy channel in the class of memoryless channels. In general, computing the capacity is a difficult problem. As such, there has been extensive work on asymptotics.

In the case of the additive Gaussian noise channel, the capacity is well known. However, it is still interesting to characterize the behavior of the asymptotes (as the SNR tends to zero or infinity) for use in proofs or to provide simple design guidelines for real-world communication systems.

Despite the work on asymptotes, it is more difficult to characterize the behavior at medium SNR without using the exact expression for the capacity.

In this post, I look at the medium behavior of the Gaussian noise channel. It turns out the SNR of $0$ decibels is particularly special and suggests a way of obtaining simple capacity approximations at medium SNR for general classes of additive noise channels.

## Data-Driven Market Formation in On-Demand Transport

As on-demand transport providers (e.g., Uber) are adopting increasingly sophisticated mechanisms to allocate and price both passengers and drivers, new issues are arising. In a series of posts (starting here), I have been describing different aspects of these issues including the ways to allocate and price (the mechanism design) and also simulation tools to evaluate performance in realistic environments (capturing both the road network and the behavior of passengers and drivers).

In this post, I want to turn to a different aspect: the market formation problem.

## Market-Based On-Demand Transport

If you are a company providing or a municipality supporting  on-demand transport services, there is an important decision that you must make: what should be the structure of the service? By structure, I mean how drivers and passengers can interact, or how payments are made. For instance, traditional taxi services differ in their structure from providers such as Uber.

In an earlier working paper (available here) and the post here, I discussed the differences between the main classes of on-demand transport services: hackney carriage; dispatcher; dial-a-ride; and market-based. However, the classification was limited in that it did not distinguish easily between services within a given class.

With the rise in market-based on-demand transport services (e.g., Uber), there is now a need to understand the different ways that these services can operate. And this is what I intend to describe here.

## Local to global… and back again

Recently, I have had some reason to reflect on the perspective that I adopt within my research. Here, I want to explore these thoughts further.

A one-line summary of my approach could be: “local to global and back again”. The sub-text would then read: “… and implications for system design”. Of course, these could possibly be some of the most overloaded words in (technical) English literature, so it is worth elaborating.