Abstract
By using the Hille-Yosida theorem, Phillips theorem, and Fattorini theorem in functional analysis we prove that theMX/G/1 queueing model with vacation times has a unique nonnegative time-dependent solution.
Highlights
The queueing system when the server become idle is not new
By using the Hille-Yosida theorem, Phillips theorem, and Fattorini theorem in functional analysis we prove that the MX/G/1 queueing model with vacation times has a unique nonnegative time-dependent solution
Miller [1] was the first to study such a model, where the server is unavailable during some random length of time for the M/G/1 queueing system
Summary
Miller [1] was the first to study such a model, where the server is unavailable during some random length of time for the M/G/1 queueing system. The M/G/1 queueing models of similar nature have been reported by a number of authors, since Levy and Yechiali [2] included several types of generalizations of the classical M/G/1 queueing system. Most studies are devoted to batch arrival queues with vacation because of its interdisciplinary character. In 2002, Choudhury [15] studied the MX/G/1 queueing model with vacation times. According to Choudhury [15], the MX/G/1 queueing system with vacation times can be described by the following system of equations: dQ (t) dt.
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