Well-behaved online load balancing against strategic jobs

In the online load balancing problem on related machines, we have a set of jobs (with different sizes) arriving online, and task is to assign each job machine immediately upon its arrival, so as minimize makespan, i.e., maximum completion time. classic mechanism design problems, assume that are controlled by selfish agents, with sizes being their private information. Each (agent) aims at minimizing own cost, which time plus payment charged mechanism. Truthful mechanisms guaranteeing every minimizes cost reporting true size been well studied (Aspnes et al. JACM 44(3):486–504, 1997, Feldman in: EC, 2017). this paper, study truthful well-behaved (machine higher speed has larger workload). Good behavior important it guarantees fairness between machines implies truthfulness in some cases when agents. Unfortunately, existing not behaved. We first show guarantee producing schedule, any algorithm (even non-truthful) competitive ratio least $$\varOmega (\sqrt{m})$$ , where m number machines. Then, propose produces schedule almost well-behaved. our $$O(\log m)$$ . Moreover, for case bounded, improves O(1). Interestingly, several actually against