Heavy Traffic Limits for Queues with Many Deterministic Servers
Queueing Systems: Theory and Applications
Dynamic Routing in Large-Scale Service Systems with Heterogeneous Servers
Queueing Systems: Theory and Applications
Analysis of join-the-shortest-queue routing for web server farms
Performance Evaluation
Insensitivity for PS server farms with JSQ routing
ACM SIGMETRICS Performance Evaluation Review
Corrected asymptotics for a multi-server queue in the Halfin-Whitt regime
Queueing Systems: Theory and Applications
Dynamics of New Product Introduction in Closed Rental Systems
Operations Research
Control of systems with flexible multi-server pools: a shadow routing approach
Queueing Systems: Theory and Applications
State Space Collapse in Many-Server Diffusion Limits of Parallel Server Systems
Mathematics of Operations Research
Refining Square-Root Safety Staffing by Expanding Erlang C
Operations Research
Basic theory and some applications of martingales
Proceedings of the 12th ACM SIGMETRICS/PERFORMANCE joint international conference on Measurement and Modeling of Computer Systems
Overflow Networks: Approximations and Implications to Call Center Outsourcing
Operations Research
Queues in tandem with customer deadlines and retrials
Queueing Systems: Theory and Applications
Scaled control in the QED regime
Performance Evaluation
Abandonment versus blocking in many-server queues: asymptotic optimality in the QED regime
Queueing Systems: Theory and Applications
| Hi-index | 0.00 |
We establish heavy-traffic stochastic-process limits for queue-length, waiting-time and overflow stochastic processes in a class ofG/GI/n/m queueing models withn servers andm extra waiting spaces. We let the arrival process be general, only requiring that it satisfy a functional central limit theorem. To capture the impact of the service-time distribution beyond its mean within a Markovian framework, we consider a special class of service-time distributions, denoted byH2*, which are mixtures of an exponential distribution with probabilityp and a unit point mass at 0 with probability 1- p. These service-time distributions exhibit relatively high variability, having squared coefficients of variation greater than or equal to one. As in Halfin and Whitt (1981, Heavy-traffic limits for queues with many exponential servers,Oper. Res.29 567-588), Puhalskii and Reiman (2000, The multiclassGI/PH/N queue in the Halfin-Whitt regime.Adv. Appl. Probab.32 564-595), and Garnett, Mandelbaum, and Reiman (2002. Designing a call center with impatient customers.Manufacturing Service Oper. Management,4 208-227), we consider a sequence of queueing models indexed by the number of servers,n, and letn tend to infinity along with the traffic intensities ? nso that v n (1 - ? n ) ?for -8