Limiting diffusions for the conditioned M/G/1 queue
1974 ◽
Vol 11
(02)
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pp. 355-362
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Keyword(s):
The virtual waiting time process, W(t), in the M/G/1 queue is investigated under the condition that the initial busy period terminates but has not done so by time n ≥ t. It is demonstrated that, as n → ∞, W(t), suitably scaled and normed, converges to the unsigned Brownian excursion process or a modification of that process depending whether ρ ≠ 1 or ρ = 1, where ρ is the traffic intensity.
Keyword(s):
1977 ◽
Vol 9
(01)
◽
pp. 169-186
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1972 ◽
Vol 9
(01)
◽
pp. 117-128
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Keyword(s):
Keyword(s):
1989 ◽
Vol 21
(02)
◽
pp. 485-487
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1969 ◽
Vol 6
(01)
◽
pp. 122-136
◽
Keyword(s):
1983 ◽
Vol 20
(03)
◽
pp. 675-688
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Keyword(s):
Keyword(s):