A New and Pragmatic Approach to the GIX/Geo/c/N Queues Using Roots

A simple and complete solution to determine the distributions of queue lengths at different observation epochs for the model GI X / Geo / c / N is presented. In the past, various discrete-time queueing models, particularly the multi-server bulk-arrival queues with finite-buffer have been solved usin...

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Bibliographic Details
Published inMethodology and computing in applied probability Vol. 23; no. 1; pp. 273 - 289
Main Authors Kim, J. J., Chaudhry, M. L., Goswami, V., Banik, A. D.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.03.2021
Springer Nature B.V
Subjects
Business and Management
Economics
Eigenvalues
Eigenvectors
Electrical Engineering
Life Sciences
Mathematics and Statistics
Original Article
Queues
Statistics
Queueing
heavy-tailed
bulk-arrivals
multi-server
discrete-time
finite-buffer
and roots
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Summary:A simple and complete solution to determine the distributions of queue lengths at different observation epochs for the model GI X / Geo / c / N is presented. In the past, various discrete-time queueing models, particularly the multi-server bulk-arrival queues with finite-buffer have been solved using complicated methods that lead to results in a non-explicit form. The purpose of this paper is to present a simple derivation for the model GI X / Geo / c / N that leads to a complete solution in an explicit form. The same method can also be used to solve the GI X / Geo / c / N queues with heavy-tailed inter-batch-arrival time distributions. The roots of the underlying characteristic equation form the basis for all distributions of queue lengths at different time epochs. All queue-length distributions are in the form of sums of geometric terms.
ISSN:1387-5841
1573-7713
DOI:10.1007/s11009-020-09836-4