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

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  • Dimitris Bertsimas
  • José Niño-Mora
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    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.

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    File URL: http://www.econ.upf.edu/docs/papers/downloads/314.pdf
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    Bibliographic Info

    Paper provided by Department of Economics and Business, Universitat Pompeu Fabra in its series Economics Working Papers with number 314.

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    Date of creation: Sep 1996
    Date of revision: Aug 1998
    Handle: RePEc:upf:upfgen:314

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    Web page: http://www.econ.upf.edu/

    Related research

    Keywords: Multiclass queueing network; changeover times; optimal scheduling; performance region; linear programming relaxation; semidefinite programming; convex programming;

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