I: Introduction -- 1.1 A Perspective -- 1.2 Earlier Work -- II: Mathematical Formulation of the Bulk Queuing Problem -- 2.1 A Class of Markov Recurrence Relations -- 2.2 The Abstract Formalism -- III: A Numerical Approach to Waiting Line Problems -- 3.1 Numerical Methods in Queuing Theory -- 3.2 The Basic Theory -- 3.3 The Simple Queue with Limited Waiting Room -- 3.4 A Bulk Queue with Limited Waiting Room -- 3.5 Queues with Variable Arrival Rate -- 3.6 A Heuristic Experiment -- 3.7 Operational Solutions vs. Exact Results -- IV: Conclusions and Directions for Further Research -- References -- Appendix A: Program Listings -- Appendix B: On the Analysis of Computational Errors -- Appendix C: On Analytic Approximations.