Load balancing in a multi-server queuing system

A queuing system consists of N identical, exponential service channels, each with its own Poisson stream of customers. If allowed to run unattended, the system may become unbalanced; that is, some queues may become long while others are empty. In this case, it may be beneficial to transfer jobs from the long queues to shorter ones to ‘balance the load’. We assume that the system incurs a cost for each customer waiting in the queue and a cost each time a job is transferred. We show that, in the case of light traffic intensity, it is optimal to transfer a job to the shortest queue whenever the number of jobs in its own queue exceeds the number of jobs in the shortest queue by a fixed threshold. We also include simulations to test how well this policy performs under moderate and heavy traffic intensities and to compare this policy to other reasonable, implementable policies.