Browsing by Author "Galvao, R. D."

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    Location of single-server immobile facilities subject to a loss constraint
    (PALGRAVE MACMILLAN LTD, 2010) Boffey, B.; Galvao, R. D.; Marianov, V.
    Waiting may be unacceptable, even a short time, at a facility providing a service involving medical or other emergencies. Hence, it is appropriate to locate such facilities so that the rate at which users are lost is limited. Each facility will here be modelled as an M/E(r)/m/N queueing system subject to a loss restriction constraint and the single-server case (m = 1) will be treated in detail. Introduction of the Erlang distribution for service times allows a better fit of the model to actual values of both mean and variance than do currently available models that use an exponential distribution. Location of facilities will be such that the average travel time to a facility is minimized. It is shown how a deterministic constraint, equivalent to the loss constraint, can be generated resulting in an integer linear program, and values of a parameter (rho c) which facilitates this linearization are tabulated for various values of r, N and service level demanded. Numerical experiments are performed including an application loosely related to the location of neonatal clinics in the Municipality of Rio de Janeiro. Finally, there is a discussion of how further improved modelling of the service time distribution might be effected.
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    Optimal location of multi-server congestible facilities operating as M/E-r/m/N queues
    (TAYLOR & FRANCIS LTD, 2009) Marianov, V.; Boffey, T. B.; Galvao, R. D.
    Most models for location of immobile congested facilities assume exponentially distributed service time at the facilities. Although the resulting formulations are tractable, they do not adequately represent service time distributions with small variances, as often occur in practice. In a recent paper, the authors utilized an order r Erlang distribution for the service time, applied to the simple case of single-server facilities. We generalize this approach to multiple-server facilities, which need a different mathematical treatment. The constraint on service availability is cast as a linear constraint on the proportion of time the servers are busy, and its right-hand side parameter is provided for different situations. Extensive analysis is offered on the influence of the parameters of the service time and the capacity of the facilities on the performance of the system. Numerical results are given for a data set relating to the municipality of Rio de Janeiro.