The waiting time analysis of a discrete-time queue with arrivals as a discrete autoregressive process of order 1
2002 ◽
Vol 39
(3)
◽
pp. 619-629
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Keyword(s):
We consider a discrete-time queueing system with the discrete autoregressive process of order 1 (DAR(1)) as an input process and obtain the actual waiting time distribution and the virtual waiting time distribution. As shown in the analysis, our approach provides a natural numerical algorithm to compute the waiting time distributions, based on the theory of the GI/G/1 queue, and consequently we can easily investigate the effect of the parameters of the DAR(1) on the waiting time distributions. We also derive a simple approximation of the asymptotic decay rate of the tail probabilities for the virtual waiting time in the heavy traffic case.
2002 ◽
Vol 39
(03)
◽
pp. 619-629
◽
2015 ◽
Vol 47
(04)
◽
pp. 989-1014
◽
2015 ◽
Vol 47
(4)
◽
pp. 989-1014
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Keyword(s):
1997 ◽
Vol 34
(03)
◽
pp. 795-799
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2002 ◽
Vol 30
(3)
◽
pp. 174-180
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Keyword(s):
1985 ◽
Vol 14
(3)
◽
pp. 709-717
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Keyword(s):