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Suppose s = 1:
For example, s = 1, t = 1:
Suppose s = 2:
For example, s = 2, t = 21:
As indicated by the examples, the interarrival times depend on s. Thus, the source is not memoryless.
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Suppose s and t are >= 0:
For example, s = 1, t = 1:
For example, s = 2, t = 21:
As indicated by the examples, the interarrival times do not depend on s. Thus, the source is memoryless.
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