Optimization of multiclass queueing networks with changeover times via the achievable region method: Part II, the multi-station case

We address the problem of scheduling a multi-station multiclass queueing network (MQNET) with server changeover times to minimize steady-state mean job holding costs. We present new lower bounds on the best achievable cost that emerge as the values of mathematical programming problems (linear, semide nite, and convex) over relaxed formulations of the system's achievable performance region. The constraints on achievable performance de ning these formulations are obtained by formulating system's equilibrium relations. Our contributions include: (1) a ow conservation interpretation and closed formulae for the constraints previously derived by the potential function method; (2) new work decomposition laws for MQNETs; (3) new constraints (linear, convex, and semide nite) on the performance region of rst and second moments of queue lengths for MQNETs; (4) a fast bound for a MQNET with N customer classes computed in N steps; (5) two heuristic scheduling policies: a priority-index policy, and a policy extracted from the solution of a linear programming relaxation.