Abstract
We consider the maximum queue length and the maximum number of idle servers in the classical Erlang delay model and the generalization allowing customer abandonment-the M/M/n+M queue. We use strong approximations to show, under regularity conditions, that properly scaled versions of the maximum queue length and maximum number of idle servers over subintervals [0,t] in the delay models converge jointly to independent random variables with the Gumbel extreme value distribution in the quality-and-efficiency-driven (QED) and ED many-server heavy-traffic limiting regimes as n and t increase to infinity together appropriately; we require that tn→∞ and tn=o(n1/2-ε) as n→∞ for some ε>0.
Original language | English (US) |
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Pages (from-to) | 13-32 |
Number of pages | 20 |
Journal | Queueing Systems |
Volume | 63 |
Issue number | 1 |
DOIs | |
State | Published - Jan 2009 |
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Computer Science Applications
- Management Science and Operations Research
- Computational Theory and Mathematics