$\infty$ queue of depositors with compound interest

4 events

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May 29, 2011 at 1:00	comment	added	James Martin		OK - but you asked for the "steady-state distribution of M". If the reserve has a negative drift in this way, it will converge to $-\infty$; there will not be a steady-state distribution.
May 28, 2011 at 17:35	comment	added	Ronaldo Carpio		Yes, it will go negative. I would like to have an asset process that is basically the mirror image of this one (borrowers arrive in a queue; they take money out when they arrive, then put back more money when they depart) to balance it out, but I'd like to understand one queue before trying to solve two together.
May 28, 2011 at 14:13	comment	added	James Martin		I must be missing something. Where is the bank's money coming from? Each depositor, upon leaving, is taking away more than they gave. So the bank's reserve should decrease approximately linearly in time, eventually becoming negative. The only increase is due to customers who have arrived but not yet left; but since the queue is stable, the number of such customers at any time is bounded in distribution.
May 28, 2011 at 8:14	history	asked	Ronaldo Carpio	CC BY-SA 3.0