How are block interval, block size and effective throughput related? I have two questions:


Why does the effective throughput (as defined below) decreases when the block interval is decreased?
How does a reduction in the block size results in maintaining a high effective throughput?


The origin of these questions is as follows.
First, this paper about Scaling Decentralized Blockchains says:


  To improve the system’s latency, we can in principle simply
  reduce the block interval. To do so while retaining high effective throughput,
  however, would also require a reduction in the block size. 


which implies that the effective throughput decreases when the block interval is decreased. This results in my first question.

Second, they define effective throughput as follows:

X% effective throughput := (block size)/(X% block propagation delay)


This formula indicates a decrease in effective throughput when the block size is decreased, while their goal is the opposite, i.e. maintaining a high effective throughput (by decreasing the block size). This is what my second question is about.
First off, it is worth noting: this paper is not only talking about throughput in the 'transactions/second' sense, it is also addressing the effects of block size and interval on the network's latency (which is an important factor in scaling blockchain networks). The authors define 'effective throughput' as:

Our  results  hinge  on  the  key  metric  of effective  throughput in  the  overlay network,  which  we  define  here  as  which  blocks  propagate  within  an  average block interval period the percentage of nodes to.

I find this confusingly written, but understand it to mean &quot;within the period of time defined by the average block interval, what percentage of the network's nodes will have received and validated the most recent block&quot;.
As a simple example of why this metric is important: if only 50% of nodes can download and validate blockheight X before blockheight X+1 is mined, then the other 50% of nodes will be continuously playing catch-up, and will not be able to meaningfully contribute to the network. This hurts network decentralization, as less users will be able to directly participate in the network.

Why does the effective throughput (as defined below) decreases when the block interval is decreased?

To understand this, consider an extreme example: a blockchain with 1GB blocks every 10 minutes. In order for nodes on the network to stay in sync with the chain, they will need to download and verify the validity of 1GB worth of blockdata every 10 mins. Any nodes which cannot do this, will decrease the 'effective throughput' of the network.
So now, consider what happens if you decrease the block interval to 1 min. Suddenly, a lot of nodes that could download and process that data within 10 mins will no longer be able to keep up with the rest of the network, since they now only have 1 min to do the same. Thus, our 'effective throughput' has decreased, since a much smaller percent of nodes will be able to engage and contribute to the network.

How does a reduction in the block size results in maintaining a high effective throughput?

I think your confusion here comes from thinking about throughput in terms of 'transactions/second'. Decreasing the blocksize would result in less transactions/second, but it would also mean a node would have to download and validate less data per block interval. In relation to the author's definition of 'effective throughput', we see that lowering the resource requirements for a node will allow more nodes to join the network.

Second, they define effective throughput as follows:
X% effective throughput := (block size)/(X% block propagation delay)
This formula indicates a decrease in effective throughput when the block size is decreased, while their goal is the opposite, i.e. maintaining a high effective throughput (by decreasing the block size).

Decreasing the block size variable would also affect the X% block propagation delay variable. So if a lower block size results in a higher throughput, we would expect that the X% block propagation delay would see a larger relative decrease than the decrease in block size.