Applied Discrete-Time Queues by Attahiru S. Alfa

Author:Attahiru S. Alfa [Alfa, Attahiru S.]
Language: eng
Format: epub, pdf
Publisher: Springer New York
Published: 2015-12-25T23:00:00+00:00

5.6.1.1 Transform Approach

The associated transition matrix can be written as follows: Let the z-transform of the process be

Minh (1978) and Dafermos and Neuts (1971) have derived the transforms of this system under time-inhomogeneous conditions. Here we focus on stationary distributions only. In that effect we assume the system is stable and consider the case where

hence we have

For this stationary system it was shown by Chaudhry (2000) that

(5.58)

By setting z 2 = 1 in we can get the z−transform of the marginal distribution, i.e. where Knowing that , setting z 2 = 1 and replacing z = z 1 in , we have which is given as

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