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In: MIT Press Series in transportation studies 5
In: Lecture Notes in Economics and Mathematical Systems, Operations Research 171
In: Lecture Notes in Economics and Mathematical Systems 171
I. General Theory -- 1. Introduction -- 2. Graphical Representations and Deterministic Approximation -- 3. Motion of Holes -- 4. Diffusion Equation -- 5. Queue Length Distribution -- 6. Soft Boundaries -- 7. Moments -- References -- II. A Single Server -- 1. Diffusion Equation -- 2. Queue Distribution -- 3. Service Rates -- 4. Longtime Behavior of the Joint Distributions -- 5. Service Variances -- 6. Image Solution c1 = ? -- 7. Longtime Behavior c1 = ? -- 8. Discussion -- III. Equilibrium Queue Distributions Two Servers, ?0 = ?1 = ?2, Theory -- 1. Introduction -- 2. Formulation -- 3. Conformal Mappings -- 4. Marginal Distributions -- 5. Symmetry -- 6. Saddle Points and Singularities -- 7. One Large Storage -- 8. Expansions of the Marginal Distributions -- References -- IV. Equilibrium Queue Distributions, Two Servers ?0 = ?1 = ?2, Numerical Results -- 1. Introduction -- 2. Marginal Distributions for c2 = ? -- 3. Relation between c*1, c*2 and w1, w3 -- 4. Marginal Distributions c*1 c*2 0 -- 4. Service Rate for Large But Finite c1, c2 -- VIII. Epilogue -- 1. What Was the Question? -- 2. Graphical Representations -- 3. Diffusion Approximations -- 4. A Single Server -- 5. Joint Probability Density for Q1 Q2 -- Notation.
In: Lecture Notes in Economics and Mathematical Systems, Operations Research, Computer Science, Social Science 87
In: Lecture Notes in Economics and Mathematical Systems 87
I. General Formulation -- 1. Introduction -- 2. Graphical Representations -- 3. Stochastic Properties -- II. Approximation Methods -- 1. Introduction -- 2. Approximations — No Customer Queue -- 3. Approximations with Queueing and Large Sk = s -- 4. Queueing with Random S, CS ?1 -- 5. Queueing with Random S, CS ~ 1 -- III. Approximations for Short Service Times -- 1. Introduction -- 2. Deterministic Approximations -- 3. Small Queues -- 4. Transition Behavior -- 5. The Final Transition -- IV. Equilibrium Distributions -- 1. Introduction -- 2. Approximation Equilibrium Distributions -- 3. Equilibrium Distributions for M/M/n -- 4. Equilibrium Distributions for G/M/n -- 5. Equilibrium Distributions for M/D/n or G/D/n -- 6. Concluding Comments -- References.
In: Proceedings of the International Symposium on the Theory of Traffic Flow and Transportation 5