Integrating Amdahl-like Laws and Divisible Load Theory

A simple means of integrating the characteristics of networked processors under divisible loads into Amdahl’s Law is presented. Amdahl’s Law serves as an upper bound to these speedup results. Amdahl’s Law with divisible load processing characteristics included serves as an upper bound to speedup for any model taking into consideration more detailed peculiarities of real systems such as the overhead of task creation, synchronization, resource contention and memory issues.

Scheduling divisible loads with time and cost constraints

In distributed computing, divisible load theory provides an important system model for allocation of data-intensive computations to processing units working in parallel. The main task is to define how a computation job should be split into parts, to which processors those parts should be allocated and in which sequence. The model is characterized by multiple parameters describing processor availability in time, transfer times of job parts to processors, their computation times and processor usage costs. The main criteria are usually the schedule length and cost minimization. In this paper, we provide the generalized formulation of the problem, combining key features of divisible load models studied in the literature, and prove its NP-hardness even for unrestricted processor availability windows. We formulate a linear program for the version of the problem with a fixed number of processors. For the case with an arbitrary number of processors, we close the gaps in the study of special cases, developing efficient algorithms for single criterion and bicriteria versions of the problem, when transfer times are negligible.