No abstract

In the parallel work-stealing load balancers, each core owns personal buffer of tasks called deque. One end of the deque is used by its owner to add and retrieve tasks, while the second end is used by other cores to steal tasks. In the paper two representation methods of deques are analyzed: partitioned serial cyclic representation of deques (one of the conventional techniques); and the new approach proposed by our team, without partition of shared memory in advance between deques moving one after another in a circle. Previously we analyzed these methods for representing FIFO queues in network applications, where the “One after another” way gave the best result for some values of the system parameters. Purpose of this research is to construct and analyze models of the process of work with two circular deques located in shared memory, where they movie one after another in a circle. The mathematical model is constructed in the form of a random walk by integer points in the pyramid. The simulation model is constructed using the Monte Carlo method. The used work-stealing strategy is stealing of one element. We propose the mathematical and simulation models of this process and carry out numerical experiments.

In the parallel work-stealing load balancers, each core owns a personal buffer of tasks called deque. One end of the deque is used by its owner to add and retrieve tasks, while the second end is used by other cores to steal tasks. Our experience in software implementations has shown that it is important to optimize work with cache memory in parallel work-stealing load balancers. For example, by modifying deques so that they can hold task objects instead of pointers, we managed to increase the performance more than 2.5 times on the CPU-bound applications and decrease last-level cache misses up to 30 % compared to Intel TBB (Threading Building Blocks) and Intel / MIT (Massachusetts Institute of Technology) Cilk work-stealing schedulers. Therefore, it is important to investigate special methods of working with deques in two-level memory, and not just try to optimize the use of universal cache implementations. The paper analyzes the problem of optimal control of a work-stealing deque in two-level memory (for example, registers – random access memory), where probabilities of parallel operations with the deque are known. The classic sequential cyclic method for representing a deque in memory is considered. If a deque overflows or empty, we transfer elements from its middle part from the fast memory to the slow memory, since data from the end parts of the deque may be needed earlier. The problem is to find the optimal number of elements from both sides of the deque to leave in the fast memory if the deque is full or empty. The average time to get into the states when it is necessary to reallocate the memory is maximized.The simulation model and the mathematical model in the form of an absorbing Markov chain were constructed. The results of numerical experiments are presented.

В work-stealing балансировщиках параллельных задач, каждое ядро имеет свой буфер задач—дек (англ. deque). Владелец дека использует один конец для добавления и извлечения задач, а из второго конца задачи перехватываются другими ядрами. В статье анализируются два метода представления деков: один из распространенных методов—раздельное последовательное циклическое представление деков; и новый предложенный нами метод, где общая память для деков заранее не делится и они двигаются друг за другом по кругу. Ранее эти методы анализировались нами для представления FIFO-очередей в сетевых приложениях, где для некоторых значений параметров системы метод «Друг за другом» давал лучший результат. Целью исследования является построение и анализ модели процесса работы с двумя последовательными деками, когда они двигаются друг за другом по кругу в общей памяти. Математическую модель мы будем строить как случайное блуждание по целым точкам в пирамиде. Имитационная модель строится с помощью метода Монте-Карло. Используемая стратегия work-stealing—перехват одного элемента. Предложены математическая и имитационная модели данного процесса и проведены численные эксперименты.