Research on the parallel–batch scheduling with linearly lookahead model

<p style='text-indent:20px;'>In this paper, we consider the new online scheduling model with linear lookahead intervals, which has character that at any time <inline-formula><tex-math id="M1">\begin{document}$ t $\end{document}</tex-math></inline-formula>, one can foresee jobs will coming in interval id="M2">\begin{document}$ (t, \lambda t+\beta ] $\end{document}</tex-math></inline-formula> id="M3">\begin{document}$ \lambda\geq1, \beta\geq 0 $\end{document}</tex-math></inline-formula>. We of unit length on id="M4">\begin{document}$ m identical parallel-batch machines under to minimize maximum flowtime and makespan, respectively. give some lower bounds for these problems batch capacity id="M5">\begin{document}$ b = \infty id="M6">\begin{document}$ b<\infty And bounded an algorithm competitive ratio id="M7">\begin{document}$ 1+\alpha id="M8">\begin{document}$ 1\leq <4/3, 0\leq \beta\leq \frac{4-3\lambda}{6} id="M9">\begin{document}$ \frac{3}{2} id="M10">\begin{document}$ 0\leq\beta<1 where id="M11">\begin{document}$ \alpha is positive root id="M12">\begin{document}$ \lambda\alpha^2+(\lambda+\beta)\alpha+\beta-1 The best possible when id="M13">\begin{document}$ $\end{document}</tex-math></inline-formula>.</p>