Some results for the queues \(M^ X/M/c\) and \(GI^ X/G/c\)
type: Item
instance of: scholarly article
title: Some results for the queues \(M^ X/M/c\) and \(GI^ X/G/c\)
zbMATH Open document ID: 0572.60091
DOI: 10.1016/0167-6377(85)90037-9
published in: Operations Research Letters
publication date: 1985-01-01T00:00:00Z
review text: For the queue \(M^ X/M/c\) a lower bound for the delay probability and an upper bound for the mean queue length are derived. Both bounds are close to the exact results. Further, a simple closed-form approximate formula for the mean queue length of \(GI^ X/G/c\) queues is proposed which shows good accuracy.
Mathematics Subject Classification ID: 60K25
Mathematics Subject Classification ID: 90B22
zbMATH DE Number: 3913415
zbMATH Keywords: lower bound for the delay probability
zbMATH Keywords: upper bound for the mean queue length
zbMATH Keywords: closed-form approximate formula for the mean queue length
author: David D. Yao
MaRDI profile type: Publication
full work available at URL: 0167-6377(85)90037-9
OpenAlex ID: W2063664689
cites work: Algorithmic methods for multi-server queues with group arrivals and exponential services
cites work: Technical Note—Delays in Single-Server Queues with Batch Input
cites work: The queueing system MX/G/1 and its ramifications
cites work: Further Results for the Queueing System M x /M/c
cites work: Some results of the queueing system Ekx/M/c
cites work: A Diffusion Approximation for an M/G/m Queue with Group Arrivals
cites work: An approximation formula \(L_q\cong\alpha\cdot\rho^\beta /(1-\rho)\)
cites work: On bounds for bulk arrival queues
cites work: A note on some relations in the queue \(GI^ X/M/c\)
cites work: Analyzing the Steady-State Queue GI x /G/1
description: scientific article; zbMATH DE number 3913415