Coordination mechanisms for selfish multi-organization scheduling

Abstract

We conduct a game theoretic analysis on the problem of scheduling jobs on computing platforms composed of several independent and selfish organizations, known as the MultiOrganization Scheduling Problem (MOSP). Each organization shares resources and jobs with others, expecting to decrease the makespan of its own jobs.We modeled MOSP as a non-cooperative game where each agent is responsible for assigning all jobs belonging to a particular organization to the available processors. The local scheduling of these jobs is defined by coordination mechanisms that first prioritize local jobs and then schedule the jobs from others according to some given priority. When different priorities are given individually to the jobs -like in classical scheduling algorithms such as LPT or SPT -then no pure -approximate equilibrium is possible for values of less than 2. We also prove that even deciding whether a given instance admits or not a pure Nash equilibrium is co-NP hard. When these priorities are given to entire organizations, we show the existence of an algorithm that always computes a pure ρ-approximate equilibrium using any ρ-approximation list scheduling algorithm. Finally, we prove that the price of anarchy of the MOSP game using this mechanism is asymptotically bounded by 2.

Coordination mechanisms for decentralized parallel systems

“…Using tools from algorithmic game theory, we extend the notions of independence and selfishness of each participating organization. We first revisit previous results that were limited to sequential jobs and extend them to the more general case where the jobs are composed of parallel rigid jobs, showing that the characteristics of the workload actually defines how costly is the decentralization of the decision‐making process.…”

“…The first attempt to study a distributed approach (using Algorithmic Game Theory ) for the problem is due to Cohen et al . , who studied the problem for the restricted case of sequential, bag‐of‐tasks jobs; their results will be discussed in depth in Section 5.…”

“…First, they have showed that the best solutions that do not allow any organization to change the devised schedule are at most ( 2 − 2 ∕ N ) times worst than the optimal solutions that respect the classical MOSP constraints. Second, in a more detailed study , they proposed the first game‐theoretic model for MOSP (still restricted to the case with sequential jobs). They first showed that games using coordination mechanisms based on classical scheduling algorithms like LPT or shortest processing time (SPT), where the local schedules are given by some priority‐rule based on some characteristic of the jobs, does not always admit a pure Nash equilibrium.…”

“…An interesting question would be to know in advance if an instance admits at all a pure Nash equilibrium. Unfortunately, it is known that for the MOSP game, this problem is co‐NP hard.…”

Energy-Aware Multi-Organization Scheduling Problem

“…They considered a problem where n jobs with release dates r i , deadlines d i and processing volumes w i , must be scheduled in a variablespeed processor with the objective of minimizing the energy consumption on that processor. The energy consumption is given by the integral over time of the power function P (s(t)) = s(t) α , where s(t) is the speed in which the processor is running on time t and α > 1 is a constant real number that depends on the technical characteristics of the processor -usually α ∈ [2,3]. There are two assumptions to simplify the model: the processor spectrum of speeds is continuous and can be any real number between 0 ≤ s ≤ +∞.…”