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.