- BrockettP. L., and HinichM. (1985). “Probability Bounds on Downtimes,” Naval Research Logistics Quarterly, 32, 329–335.
- EckbergA. E.Jr. (1977). “Sharp Bounds on Laplace-Stieltjes Transforms, with Applications to Various Queueing Problems,” Mathematics of Operations Research, 2, 135–142.
- HoltzmanJ. M. (1973). “The Accuracy of the Equivalent Random Method with Renewal Inputs.” Bell System Technical Journal, 52, 1673–1679.
- JohnsonM. A., and TaaffeM. R. (1989). “Matching Moments to Phase Distributions: Mixtures of Erlang Distributions of Common Order,” Commun. Statist.—Stochastic Models, 5:4, 711–743.
- JohnsonM. A., and TaaffeM. R. (1991a). “An Investigation of Phase-Distribution Moment-Matching Algorithms for Use in Queueing Models,” Queueing Systems, 8:2, 129–147.
- JohnsonM. A., and TaaffeM. R. (1991b). “A Graphical Investigation of Error Bounds for Moment-Based Queueing Approximations,” Queueing Systems, 8:3, 295–312.
- KarlinS. (1968). Total Positivity, Volume 1, Stanford University Press, StanfordCalifornia.
- KarlinS., and StuddenW. J. (1966). Tchebycheff Systems: With Applications in Analysis and Statistics, John Wiley & Sons, New York.
- KarrA. F. (1983). “Extreme Points of Certain Sets of Probability Measures, with Applications,” Mathematics of Operations Research, 8, 74–85.
- KolmanBernard (1977). Elementary Linear Algebra, Second Edition, MacMillan Publishing Co., New York.
- KreinM. G, and NudelmanA. A. (1977). The Markov Moment Problem and Extremal Problems, (English Translation from Russian), American Mathematical Society.
- RainvilleE. D., and BedientP. E. (1981). Elementary Differential Equations, Sixth Edition, Macmillan Publishing Co., New YorkNew York.
- RolskiT. (1972a). “Some Inequalities for GI/M/n Queues,” Zastosow. Mat., 13, 42–47.
- RolskiT. (1972b). “Some Inequalities in Queueing Theory,” Colloquia Mathematica Societatis Janos Bolyai, 9, 653–659.
- StoyanD. (1983). Comparison Methods for Queues and Other Stochastic Models, Wiley.
- WhittW. (1982). “Approximating a Point Process by a Renewal Process, I: Two Basic Methods,” Operations Research, 30:1, 125–147.
- WhittW. (1984a). “On Approximations for Queues, I: Extremal Distributions,” AT&T Bell Labs Tech Journal, 63:1, 115–138.
- WhittW. (1984b). “On Approximations for Queues, III: Mixtures of Exponential Distributions,” AT&T Bell Labs Tech Journal, 63:1, 163–175.
- ZarropM. (1979). “A Chebyshev System Approach to Optimal Input Design,” IEEE Trans. on Automatic Control, AC-24, 687–698.
Tchebycheff Systems for Probabilistic Analysis
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