Repair systems with exchangeable items and the longest queue mechanism
type: Item
instance of: scholarly article
title: Repair systems with exchangeable items and the longest queue mechanism
zbMATH Open document ID: 1276.60103
author: David Perry
author: Rachel Ravid
author: Onno Boxma
published in: Queueing Systems
publication date: 2013-04-08T00:00:00Z
review text: The authors consider a repair facility with one server and two arrival streams of failed items. Arrivals and service times are modelled classically: the arrival processes are independent Poisson processes, and the service times are independent and identically exponentially distributed. The item types are exchangeable, and a failed item from base 1 could just as well be returned to base 2, and vice versa. The queueing policy is the longest queue rule: At the completion of a service, the repaired item is delivered to the base that has the largest number of failed items. The authors explain a correspondence between their model and the classical longer queue model. The authors obtain formulae for several probabilities of interest, and show how all two-dimensional queue length probabilities may be obtained. They also provide sojourn time distributions.
Mathematics Subject Classification ID: 60K25
Mathematics Subject Classification ID: 90B22
Mathematics Subject Classification ID: 90B25
zbMATH DE Number: 6151423
zbMATH Keywords: repair system
zbMATH Keywords: longest queue
zbMATH Keywords: queue lengths
zbMATH Keywords: sojourn time
reviewed by: Tommi Sottinen
MaRDI profile type: Publication
full work available at URL: s11134-012-9319-5
OpenAlex ID: W2056610880
cites work: Q3938929
cites work: A two-queue, one-server model with priority for the longer queue
cites work: Q3662408
cites work: Calculation of Steady-State Probabilities for Repair Facilities with Multiple Sources and Dynamic Return Priorities
cites work: The Longer Queue Model
cites work: The symmetric longest queue system
cites work: Poisson Arrivals See Time Averages
cites work: A Queueing Model to Analyze the Value of Centralized Inventory Information
DOI: 10.1007/S11134-012-9319-5
description: scientific article; zbMATH DE number 6151423