Kevin Glazebrook, David Hodge and Chris Kirkbride. General notions of indexability and the dynamic allocation of individuals to teams providing service

Abstract. We present a model of dynamic service allocation across a number of
queues. We take a standard queueing model with Poisson arrivals and
exponential service, and have dynamic control over service allocation to
the various queues. The model is an example of a restless bandit with a
finitely divisible service resource, but with diminishing returns. In
our work we establish the existence of an `index' policy solving the
standard Lagrangian relaxation of the problem. We then present both an
approximative and an exact algorithm for solving this problem. Both
derived heuristics give rise to indices and extremely good performance
to our original problem.dispatch frequencies may result in decreased inventory levels.