Approximate Behavior of Tandem Queues

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 < ? -- 5. The Service Rate -- 6. Joint Distributions -- V. Time-dependent Solutions ?0 = ?1 = ?2 -- 1. Introduction -- 2. Image Solution -- 3. Time-dependent Queue Distribution -- VI. Laplace Transform Methods, Equilibrium Queue Distributions for n = 2, ?0 < ?1 ? ?2 -- 1. Analysis of Transforms -- 2. Equilibrium Distributions c1 = c2 = ?, ?0 = ?2 = 0 -- 3. Numerical Evaluations -- 4. Equilibrium Distributions c1 = c2 = ? -- 5. Other Special Cases -- 6. Interpretation -- VII. Equilibrium Queue Distributions; n=2; ?1 < ?0, ?2; c1 c2 ?? -- 1. Introduction -- 2. Joint Distribution for ?0 = ?2 = 0 -- 3. Joint Distribution for ?0, ?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.