Linear programming as a technique for optimization of queueing systems

For a significant number of queueing models that appear in diverse, seemingly unrelated application areas, such as routing, resource allocation and flow control, the optimal policy exhibits a certain switching-curve structure. The authors formulate the optimal control problem for such models in a unified way, using abstract linear programming. Using well-known facts from sensitivity analysis of linear programs, they show how certain properties of the optimal policy can be easily derived, even in cases where dynamic programming (DP) and stochastic dominance (SD) arguments fail. A structural property of the optimal value function of the linear program, namely piecewise linearity, is exploited to derive properties of the optimal cost function. The authors also consider additional problems in the realm of queueing system control in which DP or SD approaches are not applicable but linear programming can provide useful results