Dining philosophers problem

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, in terms of computers competing for access to tape drive peripherals. Soon after, Tony Hoare gave the problem its present formulation.^[1][2][3]

Problem statement

Illustration of the dining philosophers problem

Five silent philosophers sit at a table around a bowl of spaghetti. A fork is placed between each pair of adjacent philosophers.

Each philosopher must alternately think and eat. Eating is not limited by the amount of spaghetti left: assume an infinite supply. However, a philosopher can only eat while holding both the fork to the left and the fork to the right (an alternative problem formulation uses rice and chopsticks instead of spaghetti and forks).

Each philosopher can pick up an adjacent fork, when available, and put it down, when holding it. These are separate actions: forks must be picked up and put down one by one.

The problem is how to design a discipline of behavior (a concurrent algorithm) such that each philosopher won't starve, i.e. can forever continue to alternate between eating and thinking.

Issues

The problem was designed to illustrate the problem of avoiding deadlock, a system state in which no progress is possible.

One idea is to instruct each philosopher to behave as follows:

• think until the left fork is available; when it is, pick it up;
• think until the right fork is available; when it is, pick it up
• eat
• put the left fork down
• put the right fork down
• repeat from the start

This solution is incorrect: it allows the system to reach deadlock, namely, the state in which each philosopher has picked up the fork to the left, waiting for the fork to the right to be put down.^[4].

Resource starvation might also occur independently of deadlock if a particular philosopher is unable to acquire both forks because of a timing problem. For example there might be a rule that the philosophers put down a fork after waiting five minutes for the other fork to become available and wait a further five minutes before making their next attempt. This scheme eliminates the possibility of deadlock (the system can always advance to a different state) but still suffers from the problem of livelock. If all five philosophers appear in the dining room at exactly the same time and each picks up the left fork at the same time the philosophers will wait five minutes until they all put their forks down and then wait a further five minutes before they all pick them up again.

Mutual exclusion is the core idea of the problem, and the dining philosophers create a generic and abstract scenario useful for explaining issues of this type. The failures these philosophers may experience are analogous to the difficulties that arise in real computer programming when multiple programs need exclusive access to shared resources. These issues are studied in the branch of Concurrent Programming. The original problems of Dijkstra were related to external devices like tape drives. However, the difficulties studied in the Dining philosophers problem arise far more often when multiple processes access sets of data that are being updated. Systems that must deal with a large number of parallel processes, such as operating system kernels, use thousands of locks and synchronizations that require strict adherence to methods and protocols if such problems as deadlock, starvation, or data corruption are to be avoided.

Solutions

Conductor solution

A relatively simple solution is achieved by introducing a waiter at the table. Philosophers must ask his permission before taking up any forks. Because the waiter is aware of how many forks are in use, he is able to arbitrate and prevent deadlock. When four of the forks are in use, the next philosopher to request one has to wait for the waiter's permission, which is not given until a fork has been released. The logic is kept simple by specifying that philosophers always seek to pick up their left hand fork before their right hand fork (or vice versa). The waiter acts as a semaphore, a concept introduced by Dijkstra in 1965^[5].

To illustrate how this works, consider that the philosophers are labelled clockwise from A to E. If A and C are eating, four forks are in use. B sits between A and C so has neither fork available, whereas D and E have one unused fork between them. Suppose D wants to eat. Were he to take up the fifth fork, deadlock becomes likely. If instead he asks the waiter and is told to wait, we can be sure that next time two forks are released there will certainly be at least one philosopher who could successfully request a pair of forks. Therefore deadlock cannot happen.

Resource hierarchy solution

Another simple solution is achieved by assigning a partial order to the resources (the forks, in this case), and establishing the convention that all resources will be requested in order, and released in reverse order, and that no two resources unrelated by order will ever be used by a single unit of work at the same time. Here, the resources (forks) will be numbered 1 through 5, in some order, and each unit of work (philosopher) will always pick up the lower-numbered fork first, and then the higher-numbered fork, from among the two forks he plans to use. Then, he will always put down the higher numbered fork first, followed by the lower numbered fork. In this case, if four of the five philosophers simultaneously pick up their lower-numbered fork, only the highest numbered fork will remain on the table, so the fifth philosopher will not be able to pick up any fork. Moreover, only one philosopher will have access to that highest-numbered fork, so he will be able to eat using two forks. When he finishes using the forks, he will put down the highest-numbered fork first, followed by the lower-numbered fork, freeing another philosopher to grab the latter and begin eating.

This solution to the problem is the one originally proposed by Dijkstra.

While the resource hierarchy solution avoids deadlocks, it is not always practical, especially when the list of required resources is not completely known in advance. For example, if a unit of work holds resources 3 and 5 and then determines it needs resource 2, it must release 5, then 3 before acquiring 2, and then it must re-acquire 3 and 5 in that order. Computer programs that access large numbers of database records would not run efficiently if they were required to release all higher-numbered records before accessing a new record, making the method impractical for that purpose.

Monitor solution

The example below shows a solution where the forks are not represented explicitly. Philosophers can eat if neither of their neighbors are eating. This is comparable to a system where philosophers that cannot get the second fork must put down the first fork before they try again.

In the absence of locks associated with the forks, philosophers must ensure that the decision to begin eating is not based on stale information about the state of the neighbors. E.g. if philosopher B sees that A is not eating, then turns and looks at C, A could begin eating while B looks at C. This solution avoids this problem by using a single mutual exclusion lock. This lock is not associated with the forks but with the decision procedures that can change the states of the philosophers. This is ensured by the monitor. The procedures test, pickup and putdown are local to the monitor and share a mutual exclusion lock. Notice that philosophers wanting to eat do not hold a fork. When the monitor allows a philosopher who wants to eat to continue, the philosopher will reacquire the first fork before picking up the now available second fork. When done eating, the philosopher will signal to the monitor that both forks are now available.

Notice that this example does not tackle the starvation problem. For example, philosopher B can wait forever if the eating periods of philosophers A and C always overlap.

To also guarantee that no philosopher starves, one could keep track of the number of times a hungry philosopher cannot eat when his neighbors put down their forks. If this number exceeds some limit, the state of the philosopher could change to Starving, and the decision procedure to pick up forks could be augmented to require that none of the neighbors are starving.

A philosopher that cannot pick up forks because a neighbor is starving, is effectively waiting for the neighbor's neighbor to finish eating. This additional dependency reduces concurrency. Raising the threshold for transition to the Starving state reduces this effect.

Chandy / Misra solution

In 1984, K. Mani Chandy and J. Misra proposed a different solution to the dining philosophers problem to allow for arbitrary agents (numbered P₁, ..., P_n) 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).

1. For every pair of philosophers contending for a resource, create a fork and give it to the philosopher with the lower ID. Each fork can either be dirty or clean. Initially, all forks are dirty.
2. When a philosopher wants to use a set of resources (i.e. eat), he must obtain the forks from his contending neighbors. For all such forks he does not have, he sends a request message.
3. When a philosopher with a fork receives a request message, he keeps the fork if it is clean, but gives it up when it is dirty. If he sends the fork over, he cleans the fork before doing so.
4. After a philosopher is done eating, all his forks become dirty. If another philosopher had previously requested one of the forks, he 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. Their 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 an 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 ensure the graph is initially acyclic.

Example solution

Rosetta Code has solutions in a variety of languages.^[6]

See also

• Cigarette smokers problem
• Producers-consumers problem
• Readers-writers problem
• Sleeping barber problem

References

1. ^ Dijkstra, Edsger W. EWD-1000. E.W. Dijkstra Archive. Center for American History, University of Texas at Austin.  (original; transcription)
2. ^ J. Díaz; I. Ramos (1981). Formalization of Programming Concepts: International Colloquium, Peniscola, Spain, April 19–25, 1981. Proceedings. Birkhäuser. pp. 323 , 326. ISBN 9783540106999. http://books.google.com/books?id=pl4VJKQlcG4C. 
3. ^ Hoare, C. A. R. (2004). "Communicating Sequential Processes". usingcsp.com (originally published in 1985 by Prentice Hall International). http://www.usingcsp.com/cspbook.pdf. 
4. ^ Dijkstra, Edsger W. EWD-310. E.W. Dijkstra Archive. Center for American History, University of Texas at Austin.  (original; transcription)
5. ^ Dijkstra, Edsger W. EWD-123. E.W. Dijkstra Archive. Center for American History, University of Texas at Austin.  (original; transcription)
6. ^ Rosetta Code: Dining philosophers

• Silberschatz, Abraham; Peterson, James L. (1988). Operating Systems Concepts. Addison-Wesley. ISBN 0-201-18760-4. 
• Chandy, K.M.; Misra, J. (1984). The Drinking Philosophers Problem. ACM Transactions on Programming Languages and Systems.
• Dijkstra, E. W. (1971, June). Hierarchical ordering of sequential processes. Acta Informatica 1(2): 115–138.
• Lehmann, D. J., Rabin M. O, (1981). On the Advantages of Free Choice: A Symmetric and Fully Distributed Solution to the Dining Philosophers Problem. Principles Of Programming Languages 1981 (POPL'81), pp. 133–138.

External links

• Illustration of the dining philosophers problem (Java applet)
• Discussion of the problem with solution code for 2 or 4 philosophers
• Discussion of various solutions 1
• Discussion of various solutions 2
• Discussion of a solution using continuation based threads (cbthreads)
• Distributed symmetric solutions
• Programming the Dining Philosophers with Simulation
• Interactive example of the Philosophers problem (Java required)
• Satan Comes to Dinner
• Wot No Chickens? - Peter H. Welch proposed the Starving Philosophers variant that demonstrates an unfortunate consequence of the behaviour of Java thread monitors is to make thread starvation more likely than strictly necessary.
• ThreadMentor
• Solving The Dining Philosophers Problem With Asynchronous Agents