on time. 2. Unsuccessful period, equal to the idle period plus the conten- Benes V.E. (1956) On Queues with Poisson Arrivals, Annals of tion period. Mathematical Statistics, 28, pp. 670-677. Feller W. (1958) An Introduction to Probability Theory and Its The mean duration of an idle period is Applications, 1, 3rd edn., Wiley. The definition of Z takes into account both contention and a Feller W. (1970) An Introduction to Probability Theory and Its successful transmission. The mean for this second part of the cycle Applications, 2, Wiley. is given by expression 3.101. Gallager R.G. (1977) A Minimum Delay Distributed Routing Algo- rithm, I.E.E.E. Transactions on Communications, Com 23 (1) l+T+E[Z] (3.101) January, pp. 73-85. Gallager R.G. and Bertsekas D.M. (1987) Data Networks, Prentice- The system throughput C is then determined as in Equation 3.102. Hall. Kelly F.P. (1979) Reversibility and Stochastic Networks, Wiley. 3/18 Queuing theory Kelly F.P. (1985) Stochastic Models of Computer Communication Systems, Journal Royal Statistical Society, Series B, 47 (3), pp. 379 -395. Kelly F.P. (1989) On a Class of Queuing Approximations for Closed Queuing Networks, Queuing Systems, 4, pp. 69-76. Kleinrock L. (1975a) Queuing Theory, 1, Wiley Interscience. Kleinrock L. (1975b) Queuing Theory, 2, Wiley Interscience. Tackacs L. (1962) An Introduction to the Theory of Queues, Oxford University Press. Information theory William J Fitzgerald University of Cambridge Contents Introduction 4/3 Information capacity of a store 4/4 Information and thermodynamics 4/5 Mutual and self information 4/5 Discrete memoryless channels 4/6 Discrete channels with memory 4/9 Continuous channels 4/11 References 4/12 This page intentionally left blank Introduction 4/3 4.1 Introduction 7. von Mises; The exact science of mass phenomena and repeti- tive events. In this chapter, the ideas associated with information and entropy are considered and related to probability defined in terms of incom- For over one hundred years, controversy has raged between 