Some explicit formulas for mixed exponential service systems
type: Item
instance of: scholarly article
title: Some explicit formulas for mixed exponential service systems
zbMATH Open document ID: 0661.60117
DOI: 10.1016/0305-0548(88)90047-0
author: Vernon Rego
published in: Computers \& Operations Research
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://docs.lib.purdue.edu/cgi/viewcontent.cgi
review text: We present some explicit formulas for queue length and waiting time distributions of customers in the \(M/HE_ m/1\) queue. The formulas are obtained with the aid of roots of quadratic, cubic, and quartic polynomials constructed from a recurrence equation. With an example, we demonstrate that the formulas for queueing distributions are extremely accurate, while the corresponding infinite history M/GI/1 recurrence equation is not. Applications include computation of queueing distributions, accurate tail probabilities, and systems where exponentiality can be replaced by hyperexponentiality. The explicit solutions are easier to use than the problem-specific partial fraction expansions of the Pollachek-Khinchin transform.
Mathematics Subject Classification ID: 60K25
Mathematics Subject Classification ID: 90B22
zbMATH DE Number: 4080591
zbMATH Keywords: formulas for queue length and waiting time distributions
zbMATH Keywords: Pollachek- Khinchin transform
MaRDI profile type: Publication
OpenAlex ID: W1982245704
cites work: Q4188554
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cites work: Single server queues with hyperexponential service times
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description: scientific article; zbMATH DE number 4080591