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.

Inhalt

The Markov Renewal Branching Process.- Some Topics in Queueing Network Theory.- Convexity and Complete Monotonicity in Queueing Distributions and Associated Limit Behavior.- Graphical Representation of Queue Evolution for Multiple-Server Systems.- Wiener-Hopf Techniques in Queueing Theory.- Occupation Time Problems in the Theory of Queues.- Some Finite Waiting Space Bulk Queueing Systems.- Some Problems in Finite Queues.- Some New Results in the Statistical Analysis of Queues.- On the Extension of Congestion Theorems to Multi-Channel Systems.- A Theory of Traffic-Measurement Errors for Loss Systems with Renewal Input.- Optimal Operation of Queues.- Optimal Control of Queueing Systems.- Algebraic Techniques for Numerical Solution of Queueing Networks.- Heavy Traffic Limit Theorems for Queues: A Survey.- Notes on Queueing Output Processes.- The Single Server Queue in a Markovian Environment.- On More Combinatorial Methods in the Theory of Queues.- List of Participants.