Performance analysis of multiclass queueing networks
ACM SIGMETRICS Performance Evaluation Review
A Marginal Productivity Index Rule for Scheduling Multiclass Queues with Setups
Network Control and Optimization
Analysis of transient queues with semidefinite optimization
Queueing Systems: Theory and Applications
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We address the performance optimization problem in a single-station multiclass queueing network with changeover times by means of the achievable region approach. This approach seeks to obtain performance bounds and scheduling policies from the solution of a mathematical program over a relaxation of the system's performance region. Relaxed formulations (including linear, convex, nonconvex and positive semidefinite constraints) of this region are developed by formulating equilibrium relations satisfied by the system, with the help of Palm calculus. Our contributions include: (1) new constraints formulating equilibrium relations on server dynamics; (2) a flow conservation interpretation of the constraints previously derived by the potential function method; (3) new positive semidefinite constraints; (4) new work decomposition laws for single-station multiclass queueing networks, which yield new convex constraints; (5) a unified buffer occupancy method of performance analysis obtained from the constraints; (6) heuristic scheduling policies from the solution of the relaxations.