Stochastic Models of Computer Communication Systems

(Read before the Royal Statistical Society at a meeting organized by the Research Section on Wednesday, May 8th, 1985, Professor J. B. Copas in the Chair) SUMMARY This paper describes some examples of the stochastic models found useful in the design and analysis of advanced computer and communication systems. Our major theme might be termed the control of contention. As illustrations of this theme we discuss concurrency control procedures for databases, dynamic channel assignment for cellular radio, and random access schemes for the control of a broadcast channel. We emphasize asymptotic properties of product-form distributions and we present some new results on the stability of acknowledgement based random access schemes. This paper is intended to describe to the Society some examples of the stochastic models found useful in the design and analysis of advanced computer and communication systems. The examples chosen are broadly concerned with what might be termed the control of contention, and an attempt has been made to provide enough of the technical background to motivate the models considered. In Section 2 we describe a probabilistic model, due to Mitra (1985), for conflicts anlong tran- sactions in a database. Such conflicts can arise in distributed computer systems, where to ensure the consistency of a database it is often necessary to forbid the concurrent execution of transactions involving common items: a transaction must then contend with other transactions for access to the items it requires. Mitra (1985) has shown that his model can be used to answer some important design questions concerning concurrency control procedures which use exclusive and non-exclusive locks. Mitra's results are based upon a product-form solution; we indicate how his asymptotic formulae can be extended beyond the range of light traffic and the assumption of an unstructured database. In Section 3 we discuss one of the many interesting problems which arise in connection with cellular radio. Cellular radio makes efficient use of a limited number of radio channels by allowing the repeated reuse of each channel in sufficiently separated spatial regions. The topic we consider is contention between different regions for the use of dynamically assigned channels. Everitt and Macfadyen (1983) have described an analytically tractable method of dynamic channel assign- ment, which they term the maximum packing strategy. Again a product form solution is involved: from this it is easy to obtain asymptotic formulae applicable in light traffic. These formulae establish the advantage of the strategy over a fixed channel assignment for low enough loss pro- babilities, but the advantage disappears as traffic and the number of channels increase. The real potential of dynamic schemes is their ability to cope automatically with traffic intensities which fluctuate in space and time.