Steady-state analysis of a multiserver queue in the Halfin-Whitt regime Academic Article uri icon


  • We consider a multiserver queue in the Halfin-Whitt regime: as the number of serversngrows without a bound, the utilization approaches 1 from below at the rateAssuming that the service time distribution is lattice valued with a finite support, we characterize the limiting scaled 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 stationary 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.

published proceedings


author list (cited authors)

  • Gamarnik, D., & Momcilovic, P.

complete list of authors

  • Gamarnik, David||Momcilovic, Petar

publication date

  • January 1, 2008 11:11 AM