An improved greedy algorithm for stochastic online scheduling on unrelated machines

Most practical scheduling applications involve some uncertainty about the arriving times and lengths of jobs. Stochastic online is a well-established model capturing this. Here arrivals occur online, while processing are random. For this model, Gupta, Moseley, Uetz, Xie recently devised an efficient policy for non-preemptive on unrelated machines with objective to minimize expected total weighted completion time. We improve upon by adroitly combining greedy job assignment $\alpha_j$-point each machine. In way we obtain $(3+\sqrt 5)(2+\Delta)$-competitive deterministic $(8+4\Delta)$-competitive randomized stochastic policy, where $\Delta$ upper bound squared coefficients variation times. also give constant performance guarantees these policies within class all fixed-assignment policies. The single machine can be enhanced when known priori or $\delta$-NBUE $\delta \ge 1$. This implies improved competitive ratios but may independent interest.