Analysis of the ΣPhi/Ph/1 Queue

In this paper, we analyze a queue to which the arrival process is the superposition of separate arrival streams, each of whose interarrival time distributions is of phase type, and the service time distribution is also of phase type. The performance measures derived for this queue include: the distr...

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Bibliographic Details
Published in:Operations research Vol. 42; no. 1; pp. 158 - 174
Main Authors: Bitran, Gabriel R., Dasu, Sriram
Format: Journal Article
Language:English
Published: Linthicum, MD INFORMS 01.01.1994
Operations Research Society of America
Institute for Operations Research and the Management Sciences
Subjects:
Algorithms
algorithms: algorithms for analyzing the ΣPhi/Ph/1 queue
Applied sciences
Approximation
approximations: for departure processes
birth-death: quasibirth-death processes
Covariance
Customers
Eigenvalues
Eigenvectors
Exact sciences and technology
Markov chains
Mathematical moments
Matrices
Operational research and scientific management
Operational research. Management science
Operations research
Performance metrics
Queueing networks
queues
Queuing theory
Queuing theory. Traffic theory
Studies
Markov chain
Queue length
Departure process
Queue
Waiting time
ISSN:0030-364X, 1526-5463
Online Access:Get full text
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Summary:In this paper, we analyze a queue to which the arrival process is the superposition of separate arrival streams, each of whose interarrival time distributions is of phase type, and the service time distribution is also of phase type. The performance measures derived for this queue include: the distribution of the number in the system as seen by each customer class upon arrival, Laplace-Stieltjes transform (LST) of the waiting-time distribution for each customer class, stationary interdeparture time distribution and the lag correlation coefficients of the departure process, and characteristics of the tails of the waiting time and queue length distributions.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
content type line 14
ISSN:0030-364X
1526-5463
DOI:10.1287/opre.42.1.158