In EWD 108 and EWD 116 Dijkstra describes the banker’s algoritm to prevent a so-called deadly embrace. This algoritm manages different scarce resources in such a manner that all in need for one or more of the managed resources, are guaranteed to get their hands on the resource at some point in time.

Of course, in computer science, a computer – it’s operating system – manages a number of resources that are required by the processes running on the computer. And how many resources each process needs is not known beforehand (and often dynamically determined).
The analogy used in the paper is that of a banker lending money to clients, with the complicating constraint that clients do not know beforehand exactly how much money they will need. So they can lend more funds later on.

The situation could occur that the banker has only left an x amount to lend out, and a client John comes with a request for an additional amount larger than x. The banker can only hope that one of the other clients will soon finish their business and return their money. Only then can the banker help John. If however none of the other clients however can finish their business without coming to the banker for an additional lending, the banker is in deep trouble. His clients are waiting for eachother to finish their business, but to finish the business they all need some more money which they all hold themselves. A deadly embrace – “dodelijke omarming”.

Paper EWD 108 is a first exploration of the algorithm.
The core of the algorithm is the “trick” that the sum of the amount lended + the maximum amount needed of the last lender accepted is never larger than the amount of money the banker has available. As such the banker can always guarantee that he will get the money back because the last lender can always be satisfied. So the last lender is a sort of clinet of last resort. She can always guarantee return to a safe state is possible. An because for that state the algorithm also guarantee (inductively) that: “the sum of the amount lended + the maximum amount needed of the last lender accepted is never larger than the amount of money the banker has available”. (All my words.)

EWD 108 describes a small banker’s algorithm in pseudocode. The algorithm is somewhat clumsily written, and (because it )holds a goto (!) (goto consideren harmful). 
In EWD 116 the algorithm is refined, and no longer presented in pseudocode.The algorithm EWD 108 requires the claims for money to be sorted, the algorithm in EWD116 has removes this constraint.

Also in EDW 116 Dijkstra make a remark about different type of claims (in banker’s term, different currencies, for example). Apparently someone has made remarks that there may be different types of resources that need to be managed by the operating system – or Dijkstra himself thought it necessary to add this nuance. Dijkstra writes the algorithm is only applicable for a single type of resource (currency).

From a technical perspective the paper is interesting from an algorithmic perspective, and a story-telling perspective – it illustrates Dijkstra great use of metaphors from the mundane world to explain complex problems. 

Also from a historical computing perspective the paper is remarkable. Dijkstra totally discards the possibility of pre-emptive scheduling – that is: have the banker tell one of his clients to pause his business until other clients have returned their money. In not even very modern computing this is very common: processes can be “pre-emptively” put to rest to make sure other processes can progress. Apparently at the time of writing, which we do not know for sure (both EWD’s are not dated; somewhere before 1964?) pre-emptive scheduling was to be invented (or Dijkstra would have been aware for sure).