what's the maximum number of simultaneous java socket connections in the cluster?

Question

we work within a cluster of 1 giga bit per second of bandwidth, we use java sockets to perform some data transfer between the cluster's nodes like broadcast and shuffle (nodes of the cluster exchange data) in the cluster, in the instant t we may have multiple simultaneous transfers. here is an illustration

what is the maximum number of open socket connections in the cluster to maximize the data processing and how can we manage them?

Answer 1

what is the maximum number of open socket connections in the cluster to maximize the data processing?

Working out the optimal number of sockets will depend on a large number of factors, many of which you may not be able to predict ... let alone quantify.

and how can we manage them?

One way would be create one socket between the master and each worker, and multiplex the data transfers over the socket. Another might be to have fixed sized or variable sized pools of sockets.

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I think your best approach is to experiment with different approaches, and develop some benchmarks to allow you to decide what management strategies work best, and to tune them.

I also think that you are unlikely to get a clear answer to this kind of question on StackOverflow. This seems like a research problem , not a simple programming / software engineering problem. You might get an answer on either the Mathematics or Computer Science StackExchange sites. However, a solution based on Maths or CS theory will require a precise (ie mathematical!) formulation of the problem. Something far more precise / rigorous than your diagram.