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

We address the problem of scheduling a multi-station multiclass queueing ne twork (MQNET) with server changeover times to minimize steady-state mean jo b holding costs. We present new lower bounds on the best achievable cost th at emerge as the values of mathematical programming problems (linear, semid efinite, and convex) over relaxed formulations of the system's achievable p erformance region. The constraints on achievable performance defining these formulations are obtained by formulating system's equilibrium relations. O ur contributions include: (1) a flow 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 (li near, convex, and semidefinite) on the performance region of first and seco nd 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 policie s: a priority-index policy, and a policy extracted from the solution of a l inear programming relaxation.