Delayed and Network Queues by Haghighi Aliakbar Montazer; Mishev Dimitar P.; & Dimitar P. Mishev

Author:Haghighi, Aliakbar Montazer; Mishev, Dimitar P.; & Dimitar P. Mishev
Language: eng
Format: epub
Publisher: John Wiley & Sons, Incorporated
Published: 2015-08-29T00:00:00+00:00

Note that the model under these assumptions seems to be equivalent to the geometric/geometric/1 queuing system given in Hunter (1983, Chapter 9), as the authors acknowledge.

Now, let and represent the ith idle and ith busy period, respectively. Define as follows:

Let denote the number of tasks waiting at time n. For simplicity, the authors have chosen their goals as to find

5.136

and

5.137

All other cases, such as the server being idle at time n and at time 0, can be treated with the same method as in special cases.

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