Splitting the Scheduling Headache

Abstract

The broadcast disk provides an effective way to transmit information from a server to many clients. Information is broadcast cyclically and clients pick the information they need out of the broadcast. An example of such a system is a wireless web service where web servers broadcast to browsing clients. Work has been done to schedule the information broadcast so as to minimize the expected waiting time of the clients. This work has treated the information as indivisible blocks that are transmitted in their entirety. We propose a new way to schedule the broadcast of information, which involves splitting items into smaller sub-items, which need not be broadcast immediately after each other. This relaxes the previous restrictions, and hence allows us to have better schedules with lower expected waiting times. We look at the case of two items of the same length, each split into two halves, and show that we can achieve optimal performance by choosing the appropriate schedule from a small set of schedules. We derive a set of optimal schedules and show which one to use, as a function of the demand probabilities. In fact we prove the surprising result that there are only two possible types of optimal cyclic schedules for items 1 and 2. The first starts with 1122 and the second with 122122. For example, with demand probabilities p1 = .19 and p2 = 31, the best order to use in broadcasting the halves of items 1 and 2 is a cyclic schedule with cycle 122122.

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