Paper #314

Title:

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

Authors:

Dimitris Bertsimas and José Niño-Mora

Date:

September 1996 (Revised: August 1998)

Abstract:

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, semidefinite, and convex) over relaxed formulations of the system's achievable performance region. The constraints on achievable performance defining these formulations are obtained by formulating system's equilibrium relations. Our 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 (linear, convex, and semidefinite) on the performance region of first 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.

Keywords:

Multiclass queueing network, changeover times, optimal scheduling, performance region, linear programming relaxation, semidefinite programming, convex programming

JEL codes:

C61, C63

Area of Research:

Operations Management

Published in:

Mathematics of Operations Research, 24, (1999), pp. 331-361

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