Introduction to Queueing Systems with Telecommunication Applications by László Lakatos & László Szeidl & Miklós Telek

Author:László Lakatos & László Szeidl & Miklós Telek
Language: eng
Format: epub
ISBN: 9783030151423
Publisher: Springer International Publishing

From (5.42) and (5.43) we have

Using this and substituting into (5.43) we obtain

(5.44)

From the definition of G ij and G ij(k), we have and similarly, . From (5.40) and (5.44), at z → 1 we obtain (5.38) and (5.39).

5.4 G/M/1 Type Process

The G/M/1 type process [10, Chapter 3] is an extension of the level independent QBD process, where downward state transitions can occur to any lower levels. More precisely, an G/M/1 type process is a CTMC with two parameters, {N(t), J(t)}, where N(t) is the “level” process (e.g., number of customers in a queue),

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