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Unformatted text preview: Spatially Distributed Queues II M/G/1 2 Servers N servers: Hypercube Queueing Model Approximations Setup: Hypercube Queueing Model a Region comprised of geographical atoms or nodes a Each node j is an independent Poisson generator, with rate λ j a Travel times: τ il = travel time from node i to node j a N servers a Server locations are random: l nj Setup: Hypercube Queueing Model  con't. a Server assignment: one assigned a State dependent dispatching a Service times: mean = 1/ µ n ; negative exponential density a Service time dependence on travel time a We allow a queue (FCFS, infinite capacity) Fixed Preference Dispatch Policies for the Model a Idea: for each atom, say Atom 12, there exists a vector of length N that is the preferenceordered list of servers to assign to a customer from that atom a Example: {3,1,7,5,6,4,2}, for N =7. a Dispatcher always will assign the most preferred available server to the customer a Usually order this list in terms of some travel time criterion. New York City EMS Hypercube New York City EMS Hypercube Illustration of Desktop Hypercube with ARCVIEW Illustration of Desktop Hypercube with ARCVIEW Illustration of Desktop Hypercube with ARCVIEW Illustration of Desktop Hypercube with ARCVIEW Example Dispatch Policies a SCM: Strict Center of Mass ` Place server at its center of mass ` Place customer at its center of mass ` Estimate travel times: center of mass to center of mass a MCM: Modified Center of Mass ` Place server at its center of mass ` Keep customer at centroid of atom ` Estimate travel times: center of mass to centroid of atom Example Dispatch Policies a EMCM: Expected Modified Center of Mass ` Do the conditional expected travel time calculation correctly, conditioned on the centroid of the atom containing the customer Are fixed preference policies optimal?...
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 Fall '06
 hansman
 Center Of Mass, Simultaneous Equations, Elementary algebra, Hypercube

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