Splitting Schedules for Internet Broadcast Communication

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 broadcast of information in a way that minimizes the expected waiting time of the clients. This work has treated the information as indivisible blocks. We propose a new way to schedule the broadcast of information, which involves splitting items into smaller pieces that need not be broadcast consecutively. This relaxes the previous restrictions, and 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. These start with 1122 and 122122. For example, with demand probabilities p subscript1 = .08 and p subscript2 = .92, the best order to use in broadcasting the halves of items 1 and 2 is a cyclic schedule with cycle 122122222. We also show that much of the analysis remains the same if we consider items of different lengths. We present numerical data that suggests that the set of optimal schedules for different length items also consists of two types, starting with 1122 and 122122. For example, with demand probabilities p subscriptl = .08 and p subscript2 = .92 as above but lsubscript2 = 2lsubscript1, the best schedule is 11222222