Showing papers on "Probability-generating function published in 1985"

Simplified technique for bounding error statistics for DFB receivers

Abstract: A new metric, termed `recovery distance?, is introduced for decision feedback receivsers, and is shown to provide the basis for a simple technique for obtaining bounds on a wide range of error statistics. The error propagation process is modelled using stochastic state transition diagrams with merging of states having the same recovery distance, providing the simplification required to render tractable the derivation of probability generating functions for error random variables of interest. The new technique is illustrated by deriving bounds on error statistics for various signal formats of interest for practical applications.

The probability generating function of empty cell variable in a randomized occupancy problem

Abstract: Let Mo denote the number of empty cells when n distinguishable balls are distributed independently and at random in ra cells such that each ball stays with probability p in its cell, and falls through with probability 1-p. We find the probability generating function of Mo by solving a partial differential equation satisfied by a suitable generating function. The corresponding function for the classical case p = 1 is well-known, but obtained by different methods.

An approximate numerical solution for multiclass preemptive priority queues with general service time distributions

Abstract: In this paper an approximate numerical solution for a multiclass preemptive priority single server queue is developed The arrival process of each class follows a Poisson distribution The service time distribution must have a rational Laplace transform, but is otherwise arbitrary and may be different for different classes The work reported here was motivated by a desire to compute the equilibrium probability distribution of networks containing preemptive priority servers Such networks are frequently encountered when modeling computer systems, medical care delivery systems and communication networks We wish to use an iterative technique which constructs a series of two station networks consisting of one station from the original network and one “complementary” station whose behavior with respect to the original station mimics that of the rest of the network At each iteration, it is necessary to compute the equilibrium probability distribution of one or more preemptive priority queuesAlthough such queues have been studied for some time, the resulting solutions have most often been developed utilizing transforms or probability generating functions, eg Jaiswal [1968]; in many cases of interest, inversion has not been attempted Miller [1981] presented explicit solutions for two class priority queues but Miller's work, which is based on that of Neuts, is limited to exponential service times and two classes The approach presented here is applicable to many classes and to more general service time distributions than have previously been consideredThe algorithm utilizes a bootstrap approach, a concept borrowed from dynamic programming The solution for class 1 is trivial Once we have solved the system with k different classes, we have available all the necessary information to solve the system with k+l classes We shall assume that each class has a distinct service time distribution Gk, with mean gk and variance s2k Let class k have preemptive priority over class l if k 1, we consider a model with one machine whose service time distribution is Gk The breakdown rate of the machine is the sum of the arrival rates of all higher priority jobs The downtime or repairtime of the machine has mean gk-l and variance s2k-l; these parameters are the mean and variance of the busy period in a preemptive priority system with k-l classesThe first step in the solution of all the machine breakdown and repair models considered herein is to construct the infinitesimal generator