An Operational Calculus for Matrix-Exponential Distributions, with Applications to a Brownian (q, Q) Inventory Model

Published Online:https://doi.org/10.1287/moor.23.1.166

References

  • Asmussen S. , Bladt M. , Alfa A. J. , Chakravarty S. Renewal theory and queueing algorithms for matrix-exponential distributions. Matrix-Analytic Methods in Stochastic Models (1996) (Marcel Dekker, New York) 313 341 CrossrefGoogle Scholar
  • Asmussen S. , Kella O. Multidimensional martingales for reflected Markov additive processes and their applications (1997) (Lund University and the Hebrew University, Jerusalem) . Manuscript Google Scholar
  • Asmussen S. , O'Cinneide C. A. , Kotz S. , Read C. B. Matrix-exponential distributions [Distributions with a rational Laplace transform. Encyclopedia of Statistical Sciences (1997) (Wiley, New York) . to appear Google Scholar
  • Asmussen S. , Rolski T. Computational methods in risk theory: A matrix-algorithmic approach. Insurance Math. Econom. (1991) 10 259 274 CrossrefGoogle Scholar
  • Baker R. C. , Urban T. L. A deterministic inventory system with an inventory dependent demand rate. J. Oper. Res. Soc. (1988) 39 823 831 CrossrefGoogle Scholar
  • Bar-Lev S. K. , Parlar M. , Perry D. On the EOQ model with inventory level dependent demand rate and random yield. Oper. Res. Lett. (1994) 16 167 196 CrossrefGoogle Scholar
  • Bather J. A continuous review model. J. Appl. Probab. (1966) 3 538 549 CrossrefGoogle Scholar
  • Beckman M. An inventory model for arbitrary interval and quantity distribution of demand. Management Sci. (1961) 8 55 57 LinkGoogle Scholar
  • Browne S. , Zipkin P. Inventory models with continuous, stochastic demands. Ann. Appl. Probab. (1994) 1 419 435 CrossrefGoogle Scholar
  • Char B. W. , Geddes K. O. , Gonnet G. H. , Leong B. L. , Monagan M. B. , Watt S. M. Maple (1992) (Springer-Verlag, New York) . V Google Scholar
  • Dunford N. , Schwarz J. T. Linear Operators (1967) (Interscience, New York) . I Google Scholar
  • Fendick K. W. , Saksena V. R. , Whitt W. Dependence in packet queues. IEEE Trans. Commun. (1989) 37 1173 1183 CrossrefGoogle Scholar
  • Gantmacher F. Matrizentheorie (1986) (Springer-Verlag, New York) CrossrefGoogle Scholar
  • Hadley G. , Whitin T. M. Analysis of Inventory Systems (1963) (Prentice Hall, Englewood Cliffs, New Jersey) Google Scholar
  • Iglehart D. L. , Whitt W. Multiple channel queues in heavy traffic. Adv. Appl. Probab. (1970) 2 150 177 355 369 . I–II CrossrefGoogle Scholar
  • Karlin S. , Taylor H. M. A First Course in Stochastic Processes (1975) 2nd ed. (Academic Press, New York) Google Scholar
  • Karlin S. , Taylor H. M. A Second Course in Stochastic Processes (1981) (Academic Press, New York) Google Scholar
  • Kella O. , Whitt W. Queues with server vacations and Lévy processes with secondary jump input. Ann. Appl. Probab. (1991) 1 104 117 CrossrefGoogle Scholar
  • Kemperman O. The Passage Problem for a Stationary Markov Chain (1961) (University of Chicago Press, Chicago, Illinois) CrossrefGoogle Scholar
  • Lipsky L. Queueing Theory—A Linear Algebraic Approach (1992) (Macmillan, New York) Google Scholar
  • Nahmias S. Production and Operations Analysis (1989) (Irwin) Google Scholar
  • Neuts M. F. Matrix-Geometric Solutions in Stochastic Models (1981) (Johns Hopkins University Press, Baltimore, London) Google Scholar
  • Neuts M. F. , Dshalalow J. Matrix-analytic methods in queueing models. Advances in Queueing (1996) (CRC Press, Boca Raton, Florida) 265 292 Google Scholar
  • Puterman M. , Geisler M. A diffusion process model for a storage system. Studies in the Management Sciences (1975) I (North-Holland, Amsterdam) 143 159 . Logistics Google Scholar
  • Sahin I. On the objective function behavior in (s, S) inventory models. Oper. Res. (1982) 30 709 724 LinkGoogle Scholar
  • Sahin I. Regenerative Inventory Systems. Operating Characteristics and Optimization (1989) (Springer-Verlag, New York) Google Scholar
  • Smith W. L. Distribution of queueing times. Proc. Cambridge Philos. Soc. (1953) 49 449 461 CrossrefGoogle Scholar
  • Stidham S. Clearing systems and (s, S) inventory systems with nonlinear costs and positive lead times. Oper. Res. (1986) 34 276 280 LinkGoogle Scholar
  • Yor M. Lectures on Brownian Motion (1993) (Birkhäuser, Basel) Google Scholar
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