Many-server asymptotics for join-the-shortest-queue: Large deviations and rare events

Large deviations methods and the join-the-shortest-queue model

We develop a methodology for studying “large deviations type” questions. Our approach does not require that the large deviations principle holds, and is thus applicable to a larg class of systems. We study a system of queues with exponential servers, which share an arrival stream. Arrivals are routed to the (weighted) shortest queue. It is not known whether the large deviations principle holds ...

Large deviations without principle: join the shortest queue

We develop a methodology for studying “large deviations type” questions. Our approach does not require that the large deviations principle holds, and is thus applicable to a large class of systems. We study a system of queues with exponential servers, which share an arrival stream. Arrivals are routed to the (weighted) shortest queue. It is not known whether the large deviations principle holds...

Large Deviations for Join the Shorter Queue

Join the Shortest Queue: Stability and Exact Asymptotics

We consider the stability of a network serving a patchwork of overlapping regions where customers from a local region are assigned to a collection of local servers. These customers join the queue of the local server with the shortest queue of waiting customers. We then describe how the backlog in the network overloads. We do this in the simple case of two servers each of which receives a dedica...

5 A large deviation principle for join the shortest queue

We consider a join-the-shortest-queue model which is as follows. There are K single FIFO servers and M arrival processes. The customers from a given arrival process can be served only by servers from a certain subset of all servers. The actual destination is the server with the smallest weighted queue length. The arrival processes are assumed to obey a large deviation principle while the servic...