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 servers n grows without a bound, the utilization approaches 1 from below at the rate Θ(1/√n). Assuming 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. © Applied Probability Trust 2008.

author list (cited authors)

  • Gamarnik, D., & Momčilović, P.

citation count

  • 21

publication date

  • June 2008