Stopping problems for compound processes with applications to queues
type: Item
instance of: scholarly article
title: Stopping problems for compound processes with applications to queues
zbMATH Open document ID: 0970.60050
DOI: 10.1016/S0378-3758(00)00103-8
author: David Perry
published in: Journal of Statistical Planning and Inference
publication date: 2000-12-12T00:00:00Z
review text: For a compound Poisson process (CPP) the author considers the first time at which the process crosses (i) an upper straight line or (ii) a lower straight line both of slope 1. The probability that (i) happens before (ii) is expressed in terms of the stationary distribution of the corresponding M/G/1 workload process. This yields elegant formulas for the maximum deviation of the CPP and the linear boundary before crossing in both cases (i) and (ii). The corresponding distributions for a compound renewal process with exponential upward jumps are derived by means of a duality argument. En passant it is also shown that the two formulas in the literature (due to Takacs and Cohen) for the distribution function of the maximum workload of an M/G/1 queue during a busy period both follow from the same level crossing argument.
Mathematics Subject Classification ID: 60G40
Mathematics Subject Classification ID: 60K25
Mathematics Subject Classification ID: 60G52
Mathematics Subject Classification ID: 60J65
zbMATH DE Number: 1542437
zbMATH Keywords: compound Poisson process
zbMATH Keywords: linear boundaries
zbMATH Keywords: dual process
zbMATH Keywords: time reversal
reviewed by: Wolfgang Stadje
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1542437