# Applied Probability – Computer Science: The Interface by Ralph L. Disney, Teunis J. Ott

By Ralph L. Disney, Teunis J. Ott

These volumes are the court cases of the 1st detailed curiosity assembly instigated and arranged by means of the joint Technical part and school in utilized chance of ORSA and THlS. This assembly, which came about January 5-7, 1981 at Florida Atlantic collage in Boca Raton, Florida, had an identical identify as those lawsuits: utilized Probability-Computer technological know-how, the Interface. The aim of that convention was once to accomplish a gathering of, and a pass fertilization among, teams of researchers who, from varied beginning issues, had come to paintings on related difficulties, frequently constructing comparable methodologies and instruments. this kind of teams are the utilized probabilists, lots of whom give some thought to their box an offspring of arithmetic, and who locate their motivation in lots of parts of software. the opposite is that crew of computing device scientists who, through the years, have chanced on an expanding desire of their paintings for using probabilistic types. the main noticeable quarter of universal method among those teams is networks of queues, Hhich on its own might have been the topic of a complete convention. FunctionQl components that are, or have gotten, assets of interesting difficulties are laptop functionality research, information base research, research of verbal exchange protocols, facts networks, and combined voice-data cellphone networks. The reader can upload to this checklist by way of facing the papers in those Proceedings.

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Howard, J. , and Towsley, D. F. (1977) Product form and local balance in queueing networks. J. Assoc. Comput. , 24, 250-263. [6] Kelly, F. P. (1975) Networks of queues with customers of different types. J. Appl. , 12, 542-554. [7] Kelly, F. P. (1976) Networks of queues. 416-432. [8] Kelly, F. P. (1979) Reversibility and Stochastic Networks, Wiley, New York. [9] Kendall, D. G. and Reuter, G. E. H. (1957) The calculation of the ergodic projection for Markov chains and processes with a countable infinity of states.

The servers may differ in efficiency: specifically, a customer's service time at server i is exponentially distributed with parameter ~i' for i = 1,2, ... ,s. Define the state of the queue to be the vector x = (n, i l ,i 2 , ... •• ,i s _n is a list of the free servers arranged in order according to the length of time they have been free. Suppose that if a customer arrives to find the queue in state x = (n, i l ,i 2 , ••. ,i s _n ) with n < s he is allocated to server ir with probability p(r,s-n), 13 r = 1,2, ••• ,s-n.

In Appl. Probab. 8, 584-591. , Chandy, K. , Muntz, R. , and Palacios, F. G. (1975) Open, closed and mixed networks of queues with different classes of customers. J. Assoc. Comput. , 22, 248-260. [3] Beutler, F. , and Zeigler, B. P. (1977) Equilibrium properties of arbitrarily interconnected queueing networks. In P. R. ), Multivariate Analysis IV, NorthHolland, Amsterdam. pp. 351-370. 25 [4] Chandy, K. , Herzog, U. and Woo, L. (1975) Parametric analysis of queueing networks. IBM J. Res. Develop.