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

J. J. Kim (), M. L. Chaudhry (), V. Goswami () and A. D. Banik ()
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J. J. Kim: Royal Military College of Canada
M. L. Chaudhry: Royal Military College of Canada
V. Goswami: Kalinga Institute of Industrial Technology
A. D. Banik: Indian Institute of Technology Bhubaneswar

Methodology and Computing in Applied Probability, 2021, vol. 23, issue 1, 273-289

Abstract: Abstract A simple and complete solution to determine the distributions of queue lengths at different observation epochs for the model GIX/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 GIX/Geo/c/N that leads to a complete solution in an explicit form. The same method can also be used to solve the GIX/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.

Keywords: Queueing; multi-server; discrete-time; bulk-arrivals; finite-buffer; heavy-tailed; and roots (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11009-020-09836-4

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