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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

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.

Suggested Citation

  • Dimitris Bertsimas & José Niño-Mora, 1996. "Optimization of multiclass queueing networks with changeover times via the achievable region method: Part II, the multi-station case," Economics Working Papers 314, Department of Economics and Business, Universitat Pompeu Fabra, revised Aug 1998.
    • Handle: RePEc:upf:upfgen:314
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    References listed on IDEAS

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    1. Bertsimas, Dimitris., 1995. "The achievable region method in the optimal control of queueing systems : formulations, bounds and policies," Working papers 3837-95., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    2. S. W. Fuhrmann & Robert B. Cooper, 1985. "Stochastic Decompositions in the M / G /1 Queue with Generalized Vacations," Operations Research, INFORMS, vol. 33(5), pages 1117-1129, October.
    3. J. George Shanthikumar & David D. Yao, 1992. "Multiclass Queueing Systems: Polymatroidal Structure and Optimal Scheduling Control," Operations Research, INFORMS, vol. 40(3-supplem), pages 293-299, June.
    4. Bertsimas, Dimitris. & Niño-Mora, Jose., 1994. "Restless bandit, linear programming relaxations and a primal-dual heuristic," Working papers 3727-94., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    5. E. G. Coffman & I. Mitrani, 1980. "A Characterization of Waiting Time Performance Realizable by Single-Server Queues," Operations Research, INFORMS, vol. 28(3-part-ii), pages 810-821, June.
    6. Lawrence M. Wein, 1990. "Scheduling Networks of Queues: Heavy Traffic Analysis of a Two-Station Network with Controllable Inputs," Operations Research, INFORMS, vol. 38(6), pages 1065-1078, December.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Multiclass queueing network; changeover times; optimal scheduling; performance region; linear programming relaxation; semidefinite programming; convex programming;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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