Server positioning and response strategies for spatially arriving jobs with degradation: Light and medium traffic cases

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Abstract

This paper studies server positioning and response strategies for spatially arriving jobs with degradation, for situations of light and medium traffic. For the light traffic case it is shown that the p-median solution provides the optimum server positioning, and the optimum response strategy involves no server cooperation. To analyze the medium traffic case, an extended Hypercube queuing model tailored to handle spatially distributed jobs with degradation rate is formulated. The steady state probabilities from this model are used to obtain system performance measures.An appropriate set of preferred server assignments are developed for each region. Results are presented for different problem-size instances. To demonstrate applicability of the model, a case study is presented based on an emergency response application. The main findings for the medium traffic case are that the degree of server cooperation is strongly related to the rate of job degradation and to the cost of assigning jobs that find all servers busy to a backup server—higher job degradation rates and higher cost of assigning a job to a backup server result in lower server cooperation.