Mathematical Methods in Queueing Theory

1. Front Matter

   Pages i-vii

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2. The Markov Renewal Branching Process

   • Marcel F. Neuts

   Pages 1-21

3. Some Topics in Queueing Network Theory

   • Ralph L. Disney, W. Peter Cherry

   Pages 23-44

4. Convexity and Complete Monotonicity in Queueing Distributions and Associated Limit Behavior

   • Julian Keilson

   Pages 45-62

5. Graphical Representation of Queue Evolution for Multiple-Server Systems

   • G. F. Newell

   Pages 63-79

6. Wiener-Hopf Techniques in Queueing Theory

   • N. U. Prabhu

   Pages 81-90

7. Occupation Time Problems in the Theory of Queues

   • Lajos Takács

   Pages 91-131

8. Some Finite Waiting Space Bulk Queueing Systems

   • Tapan P. Bagchi, J. G. C. Templeton

   Pages 133-137

9. Some Problems in Finite Queues

   • U. Narayan Bhat

   Pages 139-156

10. Some New Results in the Statistical Analysis of Queues

    • Carl M. Harris

    Pages 157-183

11. On the Extension of Congestion Theorems to Multi-Channel Systems

    • Richard Loulou

    Pages 185-197

12. A Theory of Traffic-Measurement Errors for Loss Systems with Renewal Input

    • S. R. Neal, A. Kuczura

    Pages 199-229

13. Optimal Operation of Queues

    • Matthew J. Sobel

    Pages 231-261

14. Optimal Control of Queueing Systems

    • S. Stidham Jr., N. U. Prabhu

    Pages 263-294

15. Algebraic Techniques for Numerical Solution of Queueing Networks

    • Victor L. Wallace

    Pages 295-305

16. Heavy Traffic Limit Theorems for Queues: A Survey

    • Ward Whitt

    Pages 307-350

17. Notes on Queueing Output Processes

    • Daryl J. Daley

    Pages 351-358

18. The Single Server Queue in a Markovian Environment

    • Peter Purdue

    Pages 359-364

19. On More Combinatorial Methods in the Theory of Queues

    • S. G. Mohanty

    Pages 365-371

20. Back Matter

    Pages 373-375

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On May 10-12, 1973 a Conference on Mathematical Methods in Graph Theory was held at Western Michigan University in Kalamazoo. The theme of this Conference was recent advances in the application of analytic and algebraic methods to the analysis of queues and queueing networks. In addition some discussion was given to statistical analy­ ses in queues, control problems and graphical methods. A total of 83 individuals from both industry and academic estab­ lishments participated in the Conference. A list of these partici­ pants can be found on page 373. A total of 18 papers were presented, with sUbstantial time being devoted to their informal discussion. This volume constitutes the proceedings of the Conference, and includes all papers presented. TABLE OF CONTENTS MARCEL F. NEUTS The Markov Renewal Branching Process • 1 RALPH L. DISNEY and W. PETER CHERRY Some Topics in Queueing Network Theory 23 JULIAN KEILSON Convexity and Complete Monotonicity in Queueing Distributions and Associated Limit Behavior . • • • • • . . • • • •• • • 45 G. F. NEWELL Graphical Representation of Queue Evolution for Multiple-Server Systems • . • • • • • • • • • • 63 N. U. PRABHU Wiener-Hopf Techniques in Queueing Theory 81 / IAJOS TAKACS Occupation Time Problems in the Theory of Queues 91 TAPAN P. BAGCHI and J. G. C. TEMPLETON Some Finite waiting Space Bulk Queueing Systems 133 U.

• Finite
• algebra
• calculus
• linear optimization
• theorem

• Department of Mathematics, Western Michigan University, Kalamazoo, USA

  A. Bruce Clarke

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