Combining routing and buffer allocation problems in series-parallel queueing networks.

*(English)*Zbl 1040.90005Summary: Given a series-parallel queueing network topology with exponential servers of finite capacity, a systematic design methodology is presented that approximately solves the optimal routing and buffer space allocation problems within the network. The multi-objective stochastic nonlinear programming problem in integer variables is described and a two-stage iterative optimization procedure is presented which interconnects the routing and buffer space allocation problems. The algorithmic procedure couples the expansion method, a decomposition method for computing performance measures in queueing networks with finite capacity, along with Powell’s unconstrained optimization procedure which allocates the buffers and a multi-variable search procedure for determining the routing probabilities. The effectiveness and efficiency of the resulting two-stage design methodology is tested and evaluated in a series of experimental designs along with simulations of the network topologies.

##### MSC:

90B22 | Queues and service in operations research |

68M20 | Performance evaluation, queueing, and scheduling in the context of computer systems |

90C15 | Stochastic programming |

90C29 | Multi-objective and goal programming |