Classic Concurrency Problems.

1. Mutual Exclusion.

Let's assume that two processess want to access critical section of code. They are acting as such:

process P;

  while true do

Critical section is this program fragment, that can be executed by at most one process at once.

We assume that each process which enters critical section, will leave it in finite time.

See also: Petersen's Algorithm.

2. Producers & Consumers.

There are P>0 processes in system, which produce certain data, and K>0 processes which receive data from producers. Between producers and consumers there can be buffer with capacity B, whose task is balancing temporary differences during processes execution time. Processes that produce data we'll call producers, and processes receiving data --- consumers. Task is about synchronizing work of producers and consumers, such as that:

* Consumer would wait for data receive in situation when buffer is empty.
* Producer, when putting data in buffer would not overwrite data already written, but not received yet by consumer. It requires stopping temporarily producer in situation when there is no empty space in buffer.
* If many consumers wait for when data arrives in buffer, and if constantly new data is produced, then each waiting consumer will get something from buffer.
* Won't happen such situation, that certain consumer will wait infinitely for getting data, if data arrives in buffer constantly.
* If many producers wait for buffer's free space, and consumers constantly get something from buffer, then each of waiting producers will be able to put something into buffer. There won't happen situation such as certain producer will wait infinitely, if constantly something is taken from buffer.

There are variants to this problem:

* Buffer might be infinite.
* Cyclic buffer with finite space.
* No buffer at all.
* Many producers or only one.
* Many consumers or only one.
* Data might be produced and consumed at quicker rate (more than one unit at once).
* Data has to be read in writing order, or not.

Producers and consumers problem is abstraction of many situations existing in computer systems, for example: keyboard data write to buffer by keyboard device driver, and it's read by operating system.

3. Readers and Writers.

There are C>0 processes working in system. They read certain data. There are P>0 processes which write data. Processes writing data we'll call writers, processes reading data --- readers. Moment when processes have access to data, we'll call 'reading room visit' or 'reading room stay'.

Let's notice that many processes can read data at once. If someone wants to modify that data, then it's reasonable to block access to this data for all other processes for the time of read. It prevents read of inconsistent data (for example, partially modified data). Overall schema for processes work is such:

process Reader;

  until false

process Writer;

  until false

Beginning and ending protocols of selected processes should be written in a way, that allows for these conditions to be met:

* Many readers should have simultaneous access to reading room.
* If in reading room there's writer, then no one else does not write or read.
* Each reader, which wishes for data read, at some point will read them.
* Each writer, which wishes for data modification, at some point will write such modifications.

There are variants to this problem:

* In reading room many readers can spend their time at once.
* Reading room may have limited capacity.
* Writers may have priority over readers (but then we'll resign from readers liveness).
* Readers may have priority over writers (but then we'll resign from writers liveness).

4. Five Philosophers.

This problem does not have practical analogies, unlike previous classic problems, but it very well illustrates problems happening when concurrent programs are made.

Five philosophers dine by round table. Before each there's plate. Between plates lie forks. In middle of the table there's serving dish with fish. Each philosopher thinks. When he gets hungry, he reaches for forks laying at his right and left side, then starts eating. When he's done eating, he puts forks away and again devotes himself to thinking.

Scheme of such philospoher is such then:

process Philospher (i: 0..4);

  until false

Task is to write beginning and ending protocols, such as following conditions would be met:

* Only one philospoher ate with the same fork at the same time.
* Each of the philosophers ate only and always with two (and always those which lay near his plate) forks.
* No philosopher would die of starvation.
* Also we want that each of the philosophers would act the same way.

Solution to this riddle is to use waiter to let only four philosophers at the dining table at the same time, and let fifth wait. When philosopher is done eating, he leaves table and joins queue and can only return to table when waiter allows him to do this.

1 comment:

  1. i'll use concurrency model similar to Petri Nets, to solve such problems using Stitie Space.