Distribution of number served during a busy period of GI/M/1/N queues: Lattice path approach
type: Item
instance of: scholarly article
title: Distribution of number served during a busy period of GI/M/1/N queues: Lattice path approach
zbMATH Open document ID: 1002.60084
DOI: 10.1016/S0378-3758(01)00148-3
published in: Journal of Statistical Planning and Inference
publication date: 2002-05-15T00:00:00Z
review text: The lattice path approach is employed to derive the joint probability distribution of the busy period and the number served for a single server queueing system with finite capacity. The service time is exponential and the interarrival time distribution is a two phase Cox distribution. As distributions with rational Laplace transforms and squared coefficient of variation in the range \([1/2,\infty)\) can be approximated by \(C_2\) distribution, these results are applicable to GI/M/1/N systems.
Mathematics Subject Classification ID: 60K25
Mathematics Subject Classification ID: 90B22
zbMATH DE Number: 1741586
zbMATH Keywords: finite queues
zbMATH Keywords: transient solution
zbMATH Keywords: Cox distribution
zbMATH Keywords: lattice paths
author: Manju Agarwal
reviewed by: S. Kalpakam
MaRDI profile type: Publication
cites work: Q5332626
cites work: Q4317943
cites work: Transient analysis of queues with heterogeneous arrivals
cites work: Characterizations of generalized hyperexponential distribution functions
cites work: Q3227148
cites work: Q5538132
cites work: Q4070096
cites work: Lattice path approach to transient analysis of M/G/1/N non-Markovian queues using Cox distributions
cites work: Q4353168
cites work: Lattice paths combinatorics applied to transient queue length distribution of C\(_2/\)M/1 queues and busy period analysis of bulk queues C\(_2^b/\)M/1
cites work: Q4327130
cites work: Combinatorial approach to Markovian queueing models
cites work: Lattice path approach to transient solution of \(M/M/1\) with (\(0,k\)) control policy
cites work: Q4234742
cites work: Q3859254
cites work: Discrete-Time Queuing Theory
cites work: Q3212100
cites work: Q3358023
cites work: Q3844682
cites work: Q4001942
cites work: Transient behaviour of an M/M/1/N queue
cites work: A Combinatorial Method in the Theory of Queues
Wikidata QID: Q126527169
full work available at URL: s0378-3758(01)00148-3
OpenAlex ID: W2003323545
description: scientific article; zbMATH DE number 1741586