An Approximate Analysis of Load Balancing Using Stale State Information for Servers in Parallel

That a load balancing strategy using stale information carelessly will incur system performance degradation is easy to verify. However it is not so obvious that routing a customer to the expected shortest queue has the same problem when information for decision is stale. We consider a queueing system with a load balancer and a pool of identical FCFS queues in parallel. The arrival process is assumed to be Poisson and the service times have identical independent exponential distributions. The pool of servers informs the load balancer the number of customers in each server at some regularly spaced time instances. The load balancer routes each customer to the expected shortest queue based on available stale information and elapsed time since the last time instance of system sate information updating. The system performance analysis of this type of model is usually difficult because the involved state space is very large. However when taking the number of servers to the infinite limit, we have a set of differential equations which is easier to handle than the finite case. Using the approximation of infinite number of severs, we show that the average waiting time for the system is not always minimized by routing each customer to the expected shortest queue when information for decision is stale.