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The compensation approach applied to twodimensional Markov processes
The symmetric shortest queue problem
3 other sections not shown
a,+i absolute convergence accuracy of 0.1 analysis binary tree boundary conditions boundary value problem Boxma 21 chapter coefficients Cohen and Boxma compensation approach compensation tree computed continuous-time Markov process converges absolutely decreasing define definition depicted in figure derived equilibrium distribution equilibrium equations equilibrium probabilities error exponentially distributed exponentially fast expressions feasible pairs Flatto and McKean follows function Hence horizontal boundary infinite sum Inserting integer interior points jobs join join the shortest Kingman 52 lemma linear combination nonnegative normalizing constant number of jobs numerical obtain Oi+l Pi+i product form solutions Proof properties prove quadrant quadratic equation queue length queueing system recursion relations roots sequence series of product shortest expected delay shortest queue model shortest queue problem simplifies solved space subjobs subtree symmetric shortest queue theorem threshold jockeying tion transition rates Transition-rate diagram upper bound vo,i X_(a X+(a yields