Section: New Results

Analyzing the choice of the least loaded queue between two neighboring queues

A model of N queues, with a local choice policy, is studied. Each one-server queue has a Poissonian arrival of customers. When a customer arrives at a queue, he joins the least loaded queue between this queue and the next one, ties solved at random. Service times have exponential distribution. The system is stable if the arrival-to-service rate ratio, also called load, is less than one. When the load tends to zero, we derive the first terms of the expansion in this parameter for the stationary probabilities that a queue has few customers. Then we provide explicit asymptotics, as the load tends to zero, for the stationary probabilities of the queue length. We used the analyticity of the stationary probabilities as a function of the load. It shows the behavior difference between this local choice policy and the 2-choice policy (supermarket model).