Ps. Ansell et al., A semidefinite programming approach to the optimal control of a single server queueing system with imposed second moment constraints, J OPER RES, 50(7), 1999, pp. 765-773
Classical analyses of the dynamic control of multi-class queueing systems f
requently yield simple priority policies as optimal. However, such policies
can often result in excessive queue lengths for the low priority jobs/cust
omers. We propose a stochastic optimisation problem in the context of a two
class M/M/1 system which seeks to mitigate this through the imposition of
constraints on the second moments of queue lengths. We analyse the performa
nce of two families of parametrised heuristic policies for this problem. To
evaluate these policies we develop lower bounds on the optimum cost throug
h the achievable region approach. A numerical study points to the strength
of performance of threshold policies and to directions for future research.