Abstract We study an online job scheduling problem arising in networks with aggregated links. The goal is to schedule n jobs, divided into k disjoint chains, on m identical machines, without preemption, so that the jobs within each chain complete in the order of release times and the maximum flow time is minimized. We present a deterministic online algorithm Block with competitive ratio O(pn/m), and show a matching lower bound, even for randomized algorithms. The performance bound for Block we derive in the paper is, in fact, more subtle than a simple competitive analysis, and it shows that in overload conditions (when many jobs are released in a short amount of time), Block's performance is close to the optimum. We also show how to compute an offline solution efficiently for k = 1, and that minimizing the maximum flow time for k, m> = 2 is N P-hard. As by-products of our construction, we obtain a 2-approximation algorithm for minimizing makespan in our model, and an offline algorithm to minimize makespan for k = 1.

Traditionally, on-line problems have been studied under the assumption that there is a unique sequence of requests that must be served. This approach is common to most general models of on-line computation, such as Metrical Task Systems. However, there exist on-line problems in which the requests are organized in more than one independent thread. In this more general framework, at every moment the first unserved request of each thread is available. Therefore, apart from deciding how to serve a request, at each stage it is necessary to decide which request to serve among several possibilities. In this paper we introduce Multi-threaded Metrical Task Systems, that is, the generalization of Metrical Task Systems to the case in which there are many threads of tasks. We study the problem from a competitive analysis point of view, proving lower and upper bounds on the competitiveness of on-line algorithms. We consider finite and infinite sequences of tasks, as well as deterministic and ran...