Steady-state analysis of a multi-server queue in the Halfin-Whitt regime

Details Steady-state analysis of a multi-server queue in the Halfin-Whitt regime Steady-state analysis of a multi-server queue in the Halfin-Whitt regime

2007-10-02

arxiv.org/abs/0710.0654v2

Mathematics

Probability

34 pages

Scientific paper

We consider a multi-server queue in the Halfin-Whitt regime: as the number of servers $n$ grows without a bound, the utilization approaches 1 from below at the rate $\Theta(1/\sqrt{n})$. Assuming that the service time distribution is lattice-valued with a finite support, we characterize the limiting stationary queue length distribution in terms of the stationary distribution of an explicitly constructed Markov chain. Furthermore, we obtain an explicit expression for the critical exponent for the moment generating function of a limiting (scaled) steady-state queue length. This exponent has a compact representation in terms of three parameters: the amount of spare capacity and the coefficients of variation of interarrival and service times. Interestingly, it matches an analogous exponent corresponding to a single-server queue in the conventional heavy-traffic regime.

Affiliated with

Also associated with

No associations

Rating

Steady-state analysis of a multi-server queue in the Halfin-Whitt regime does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Steady-state analysis of a multi-server queue in the Halfin-Whitt regime, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Steady-state analysis of a multi-server queue in the Halfin-Whitt regime will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-285134