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Optimization of multiclass queueing networks with changeover times via the achievable region approach: Part I, the single-station case
Bertsimas, Dimitris; Niño-Mora, José
Universitat Pompeu Fabra. Departament d'Economia i Empresa
We address the performance optimization problem in a single-stationmulticlass queueing network with changeover times by means of theachievable region approach. This approach seeks to obtainperformance bounds and scheduling policies from the solution of amathematical program over a relaxation of the system's performanceregion. Relaxed formulations (including linear, convex, nonconvexand positive semidefinite constraints) of this region are developedby formulating equilibrium relations satisfied by the system, withthe help of Palm calculus. Our contributions include: (1) newconstraints formulating equilibrium relations on server dynamics;(2) a flow conservation interpretation of the constraintspreviously derived by the potential function method; (3) newpositive semidefinite constraints; (4) new work decomposition lawsfor single-station multiclass queueing networks, which yield newconvex constraints; (5) a unified buffer occupancy method ofperformance analysis obtained from the constraints; (6) heuristicscheduling policies from the solution of the relaxations.
15-09-2005
Operations Management
multiclass queueing networks
optimal scheduling
achievable region
changeover times
polling systems
stochastic scheduling
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