lec13 (1)

lec13 (1) - Spatially Distributed Queues II M/G/1 2 Servers...

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Spatially Distributed Queues II M/G/1 2 Servers N servers: Hypercube Queueing Model Approximations
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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
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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)
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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 preference-ordered 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.
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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
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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
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Are fixed preference policies optimal?
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lec13 (1) - Spatially Distributed Queues II M/G/1 2 Servers...

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