State Space Collapse for Parallel Server Systems in Many-Server Limits
نویسندگان
چکیده
We consider a class of queueing systems that consist of server pools in parallel and multiple customer classes. Customer service times are assumed to be exponentially distributed. We study the asymptotic behavior of these queueing systems in a heavy traffic regime that is known as the Halfin and Whitt many-server asymptotic regime. Our main contribution is a general framework for establishing state space collapse results in this regime for parallel server systems. In our work, state space collapse refers to a decrease in the dimension of the processes tracking the number of customers in each class waiting for service and the number of customers in each class being served by various server pools. We define and introduce a “state space collapse” function, which governs the exact details of the state space collapse. We show that a state space collapse result holds in many-server heavy traffic if a corresponding deterministic hydrodynamic model satisfies a similar state space collapse condition. Our methodology is similar in spirit to that in Bramson [10], which focuses on the conventional heavy traffic regime. We illustrate the applications of our results by establishing state space collapse results in many-server diffusion limits for V-model systems under static-buffer-priority policy and the threshold policy proposed in [3].
منابع مشابه
State Space Collapse in Many-Server Diffusion Limits of Parallel Server Systems
We consider a class of queueing systems that consist of server pools in parallel and multiple customer classes. Customer service times are assumed to be exponentially distributed. We study the asymptotic behavior of these queueing systems in a heavy traffic regime that is known as the Halfin and Whitt many-server asymptotic regime. Our main contribution is a general framework for establishing s...
متن کاملState Space Collapse in Many-Server Diffusion Limits of Parallel Server Systems and Applications
متن کامل
On Two-Echelon Multi-Server Queue with Balking and Limited Intermediate Buffer
In this paper we study two echelon multi-server tandom queueing systems where customers arrive according to a poisson process with two different rates. The service rates at both echelons are independent of each other. The service times of customers is assumed to be completed in two stages. The service times at each stage are exponentially distributed. At the first stage, the customers may balk ...
متن کاملDynamic Control of N-Systems with Many Servers: Asymptotic Optimality of a Static Priority Policy in Heavy Traffic
We consider a class of parallel server systems that are known as N-systems. In an N-system, there are two customer classes that are catered by servers in two pools. Servers in one of the pools are cross-trained and can serve customers from both classes whereas all the servers in the other pool can only serve one of the customer classes. A customer reneges from his queue if his waiting time in t...
متن کاملScheduling Parallel Servers in the Nondegenerate Slowdown Diffusion Regime: Asymptotic Optimality Results1 by Rami Atar
We consider the problem of minimizing queue-length costs in a system with heterogenous parallel servers, operating in a many-server heavy-traffic regime with nondegenerate slowdown. This regime is distinct from the wellstudied heavy traffic diffusion regimes, namely the (single server) conventional regime and the (many-server) Halfin–Whitt regime. It has the distinguishing property that waiting...
متن کامل