Monday, February 21, 2011

MCS 042 Question 2: Write a semaphore based solution to Dining Philosopher problem and explain all the assumptions and the algorithm.

The dining philosophers problem is summarized as five philosophers sitting at a table doing one of two things: eating or thinking. While eating, they are not thinking, and while thinking, they are not eating. The five philosophers sit at a circular table with a large bowl of spaghetti in the center. A fork is placed in between each pair of adjacent philosophers, and as such, each philosopher has one fork to his left and one fork to his right. As spaghetti is difficult to serve and eat with a single fork, it is assumed that a philosopher must eat with two forks. Each philosopher can only use the forks on his immediate left and immediate right.

philosophers problem
The dining philosophers problem is sometimes explained using rice and chopsticks rather than spaghetti and forks, as it is more intuitively obvious that two chopsticks are required to begin eating.
The philosophers never speak to each other, which creates a dangerous possibility of deadlock when every philosopher holds a left fork and waits perpetually for a right fork (or vice versa).
Originally used as a means of illustrating the problem of deadlock, this system reaches deadlock when there is a 'cycle of unwarranted requests'. In this case philosopher P1 waits for the fork grabbed by philosopher P2 who is waiting for the fork of philosopher P3 and so forth, making a circular chain.
Starvation (and the pun was intended in the original problem description) might also occur independently of deadlock if a 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.
In general the dining philosophers problem is a generic and abstract problem used for explaining various issues which arise in problems which hold mutual exclusion as a core idea. The various kinds of 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.

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 testpickup 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.

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.


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