Rejection rules in the \(M/G/1\) queue
type: Item
instance of: scholarly article
title: Rejection rules in the \(M/G/1\) queue
zbMATH Open document ID: 0835.60080
DOI: 10.1007/BF01148942
author: David Perry
author: Søren Asmussen
published in: Queueing Systems
publication date: 1996-04-08T00:00:00Z
review text: It is considered the \(M/G/1\) queue with impatient customers. The following basic cases are investigated: 1) the waiting time is restricted by a random barricade (r.b.), 2) the sojourn time (waiting time plus service time) does not exceed a r.b., and service time may be reduced if necessary, 3) a customer is totally lost if sojourn time exceeds a r.b. It is assumed that the workload upon arrival is known either to the server or to the arriving customer in the cases 1) and 3). The paper gives new results and some review material. Both steady-state distribution (as the solution of Volterra equation) and busy period analysis (including martingale one) are considered. The authors concentrate on the exponential service times and deterministic or exponential barricade. In the last case a birth-death process is used to find an explicit solution for busy period Laplace transformation.
Mathematics Subject Classification ID: 60K25
Mathematics Subject Classification ID: 90B22
zbMATH DE Number: 765312
zbMATH Keywords: birth-death process
zbMATH Keywords: busy period
zbMATH Keywords: coupling
zbMATH Keywords: impatient customers
zbMATH Keywords: martingale stopping theorem
zbMATH Keywords: queue
zbMATH Keywords: storage process
zbMATH Keywords: waiting time
zbMATH Keywords: Volterra equation
reviewed by: Evsei Morozov
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01148942
OpenAlex ID: W2025740888
description: scientific article; zbMATH DE number 765312