Laxity Helps in Broadcast Scheduling

We study the effect of laxity, or slack time, on the online scheduling of broadcasts with deadlines. The laxity of a request is defined to be the ratio between its span (difference between release time and deadline) and its processing time. All requests have a minimum guaranteed laxity. We give different algorithms and lower bounds on the competitive ratio for different ranges of values of laxity, which not only represents a tradeoff between the laxity and the competitive ratio of the system, but also bridges between interval scheduling and job scheduling techniques and results. We also give an improved algorithm for general instances in the case when requests can have different processing times.