Философтардың тамақтану мәселесі: синхронизация және шешімдері

Problem used to illustrate synchronization issues and techniques for resolving them

In computer science, the dining philosophers problem is an example problem often used in concurrent algorithm design to illustrate synchronization issues and techniques for resolving them. It was originally formulated in 1965 by Edsger Dijkstra as a student exam exercise, presented in terms of computers competing for access to tape drive peripherals. Soon after, Tony Hoare gave the problem its present form.

Five philosophers dine together at the same table. Each philosopher has his own plate at the table. There is a fork between each plate. The dish served is a kind of spaghetti which has to be eaten with two forks. Each philosopher can only alternately think and eat. Moreover, a philosopher can only eat his spaghetti when he has both a left and right fork. Thus two forks will only be available when his two nearest neighbors are thinking, not eating. After an individual philosopher finishes eating, he will put down both forks. The problem is how to design a regimen (a concurrent algorithm) such that any philosopher will not starve; i. e., each can forever continue to alternate between eating and thinking, assuming that no philosopher can know when others may want to eat or think (an issue of incomplete information).

Another approach is to guarantee that a philosopher can only pick up both forks or none by introducing an arbitrator, e. g., a waiter. In order to pick up the forks, a philosopher must ask permission of the waiter. The waiter gives permission to only one philosopher at a time until the philosopher has picked up both of his forks. Putting down a fork is always allowed. The waiter can be implemented as a mutex. In addition to introducing a new central entity (the waiter), this approach can result in reduced parallelism: if a philosopher is eating and one of his neighbors is requesting the forks, all other philosophers must wait until this request has been fulfilled even if forks for them are still available.

A solution presented by William Stallings is to allow a maximum of n 1 philosophers to sit down at any time. The last philosopher would have to wait (for example, using a semaphore) for someone to finish dining before he "sits down" and requests access to any fork. This guarantees at least one philosopher may always acquire both forks, allowing the system to make progress.

In 1984, K. Mani Chandy and J. Misra proposed a different solution to the dining philosophers problem to allow for arbitrary agents (numbered P1, , Pn) to contend for an arbitrary number of resources, unlike Dijkstra's solution. It is also completely distributed and requires no central authority after initialization. However, it violates the requirement that "the philosophers do not speak to each other" (due to the request messages). For every pair of philosophers contending for a resource, create a fork and give it to the philosopher with the lower ID (n for agent Pn). Each fork can either be dirty or clean. Initially, all forks are dirty. When a philosopher wants to use a set of resources (i. e., eat), said philosopher must obtain the forks from his contending neighbors. For all such forks the philosopher does not have, he sends a request message. When a philosopher with a fork receives a request message, he keeps the fork if it is clean, but give it up when it is dirty. If the philosopher sends the fork over, he cleans the fork before doing so. After a philosopher is done eating, all his forks become dirty. If another philosopher had previously requested one of the forks, the philosopher that has just finished eating cleans the fork and sends it. This solution also allows for a large degree of concurrency, and will solve an arbitrarily large problem. It also solves the starvation problem. The clean/dirty labels act as a way of giving preference to the most "starved" processes, and a disadvantage to processes that have just "eaten". One could compare their solution to one where philosophers are not allowed to eat twice in a row without letting others use the forks in between. Chandy and Misra's solution is more flexible than that, but has an element tending in that direction. In their analysis, they derive a system of preference levels from the distribution of the forks and their clean/dirty states. They show that this system may describe a directed acyclic graph, and if so, the operations in their protocol cannot turn that graph into a cyclic one. This guarantees that deadlock cannot occur. However, if the system is initialized to a perfectly symmetric state, like all philosophers holding their left side forks, then the graph is cyclic at the outset, and their solution cannot prevent a deadlock. Initializing the system so that philosophers with lower IDs have dirty forks ensures the graph is initially acyclic.