Analysis, Design, and Control of Queueing Systems
Published Online:1 Feb 2002https://doi.org/10.1287/opre.50.1.197.17783
References
- Asymptotics for M/G/1 low-priority waiting-time tail probabilities. Queueing Systems: Theory and Appl. (1997) 25:173–233Crossref, Google Scholar
- , Grassmann W. K. An introduction to numerical tranform inversion and its application to probability models. Computational Probability (2000) (Kluwer Academic Publishers, Boston, MA) 257–324Crossref, Google Scholar
- Performance Analysis of Manufacturing Systems (1997) (Springer-Verlag, New York) Crossref, Google Scholar
- Stochastic theory of a data-handling system with multiple sources. Bell Sys. Tech. J. (1982) 61:1871–1894Crossref, Google Scholar
- The genesis of “optimal inventory policy.”. Oper. Res. (2002) 50(1):1–2Link, Google Scholar
- Studies in the Mathematical Theory of Inventory and Production (1958) (Stanford Mathematical Studies in the Social Sciences, Stanford University Press) Google Scholar
- Queuing with alternating priorities. Oper. Res. (1965) 13:306–318Link, Google Scholar
- Elements of Queueing Theory. Palm-Martingale Calculus and Stochastic Recurrences (1994) 26(Springer-Verlag, Berlin, Germany) . Applications of MathematicsGoogle Scholar
- Open, closed, and mixed networks of queues with different classes of customers. J. Assoc. Comput. Mach. (1975) 22:248–260Crossref, Google Scholar
- Conservation laws for single-server fluid networks. Queueing Systems: Theory and Appl. (2001) 38:185–194Crossref, Google Scholar
- Characterization and computation of optimal policies for operating an M/G/1 queuing system with removable server. Oper. Res. (1971) 19:208–218Link, Google Scholar
- General Stochastic Processes in the Theory of Queues (1963) (Addison-Wesley, Reading MA) Google Scholar
- Data Networks (1987) (Prentice-Hall, Englewood Cliffs, NJ) Google Scholar
- Decomposition results for general polling systems and their applications. Queueing Systems Theory Appl. (1999) 31:295–316Crossref, Google Scholar
- Conservation laws, extended polymatroids and multiarmed bandit problems; a polyhedral approach to indexable systems. Oper. Res. (1996) 21:257–306Abstract, Google Scholar
- Optimization of multiclass queueing networks: Polyhedral and nonlinear characterizations of achievable performance. Ann. Appl. Probab. (1994) 4:43–75Crossref, Google Scholar
- On the convergence to diffusion processes. Theory of Probab. Appl. (1967) 12:405–431Crossref, Google Scholar
- Stochastic Processes in the Theory of Mass Service (1972) (Nauka, Moscow Russia) Google Scholar
- Pseudoconservation laws in cyclic-service systems. J. Appl. Probab. (1987) 24:949–964Crossref, Google Scholar
- Instability of FIFO queueing networks. Ann. Appl. Probab. (1994) 4:414–431Crossref, Google Scholar
- Stability of two families of queueing networks and a discussion of fluid limits. Queueing Systems Theory Appl. (1998) 28:7–31.Crossref, Google Scholar
- The dependence of delays in tandem queues. Ann. Math. Statist. (1964) 35:874–875Crossref, Google Scholar
- Stochastic Models of Manufacturing Systems (1993) (Prentice-Hall, Englewood Cliffs, NJ) Google Scholar
- Computational algorithms for closed queueing networks with exponential servers. Comm. ACM (1973) 16:527–531Crossref, Google Scholar
- Stability queue length, and delay of deterministic and stochastic queueing networks. IEEE Trans. Auto. Control (1994) 39:913–931Crossref, Google Scholar
- Queueing Networks: Customers, Signals, and Product Forms (1999) (Wiley, New York) Google Scholar
- Discrete flow networks: Bottleneck analysis and fluid approximations. Math. Oper. Res (1991) 16:408–446Link, Google Scholar
- Fundamentals of Queueing Networks: Performance, Asymptotics, and Optimization (2001) (Springer, New York) Crossref, Google Scholar
- Computing distributions and moments in polling models by numerical transform inversion. Performance Evaluation (1996) 25:267–292Crossref, Google Scholar
- A characterization of waiting time performance realizable by single server queues. Oper. Res. (1980) 28:810–821.Link, Google Scholar
- Polling systems with zero switchover times: A heavy-traffic averaging principle. Ann. Appl. Probab. (1995) 5:681–719Crossref, Google Scholar
- The generalized Engset formulae. Philips Telecomm. Rev. (1957) 18:158–170Google Scholar
- The Single Server Queue (1969) (North-Holland, Amsterdam, The Netherlands) Google Scholar
- Introduction to Queueing Theory (1972) (Macmillan, New York) Google Scholar
- Queues served in cyclic order. Bell Syst. Tech. J. (1969) 48:675–689Crossref, Google Scholar
- The analysis of non-Markovian stochastic processes by the inclusion of supplementary variables. Proc. Camb. Phil. Soc. (1955) 51:433–441Crossref, Google Scholar
- Queues (1961) (Methuen, London, U.K.) Google Scholar
- Estimating the heavy tail index from scaling properties. Methodol. Comput. Appl. Probab. (1999) 1:55–79Crossref, Google Scholar
- The achievable region approach to the optimal control of stochastic systems. J. Royal Statist. Soc. (1999) B 61:747–791Crossref, Google Scholar
- On positive Harris recurrence of multiclass queueing networks: a unified approach via fluid limit models. Ann. Appl. Probab. (1995) 5:49–77Crossref, Google Scholar
- Steady-state analysis of RBM in a rectangle: Numerical methods and a queueing application. Ann. Appl. Probab. (1991) 1:16–35Crossref, Google Scholar
- Nonexistence of Brownian models for certain multiclass queueing networks. Queueing Systems Theory Appl. (1993) 13:41–46Crossref, Google Scholar
- , Gani J. The making of a queueing theorist. The Craft of Probability Modelling (1986) (Springer-Verlag, New York) 196–212Crossref, Google Scholar
- A note on stochastic decomposition in a GI/G/1 queue with vacations or set-up times. J. Appl. Probab. (1985) 22:419–428Crossref, Google Scholar
- Richard Bellman on the birth of dynamic programming. Oper. Res. (2002) 50(1):48–51Link, Google Scholar
- Queues with periodic service and changeover times. Oper. Res. (1972) 20:440–451Link, Google Scholar
- Sample-Path Analysis of Queueing Systems (1999) (Kluwer Academic Publishers, Boston, MA) Crossref, Google Scholar
- Modelling Extremal Events for Insurance and Finance (1997) (Springer-Verlag, New York) Crossref, Google Scholar
- Characterization and optimization of achievable performance in general queueing systems. Oper. Res. (1988) 36:733–741Link, Google Scholar
- An Introduction to Probability Theory and Its Applications (1957) I3rd ed. 1968(Wiley, New York) Google Scholar
- An Introduction to Probability Theory and Its Applications (1966) II(Wiley, New York) Google Scholar
- , Chandy K. M., Reiser M. On heavy traffic diffusion analysis and dynamic routing in packet-switched network. Computer Performance (1977) (North-Holland, Amsterdam, The Netherlands) 499–513Google Scholar
- Queues and Point Processes (1981) (Akademie-Verlag, Berlin, Germany) Google Scholar
- Symmetric queues served in cyclic order. Oper. Res. Letters (1985) 4:139–144Crossref, Google Scholar
- Gani J.The Craft of Probabilistic Modelling (1986) (Springer-Verlag, New York) Crossref, Google Scholar
- Gani J. Adventures in applied probability: A celebration of applied probability. J. Appl. Probab. (1988) 25A:3–23Crossref, Google Scholar
- Bandit processes and dynamic allocation indices. J. Roy. Statist. Soc. B (1979) 41:148–177Crossref, Google Scholar
- , Gani J. A dynamic allocation index for the sequential design of experiments. Progress in Statistics (1974) (North-Holland, Amsterdam, The Netherlands) 241–266Google Scholar
- Almost optimal policies for stochastic systems which almost satisfy conservation laws. Ann. Oper. Res. (1999) 92:19–43Crossref, Google Scholar
- Introduction to Queueing Theory (1989) 2nd ed.(Birkhäuser, Boston, MA) Crossref, Google Scholar
- Cyclic queueing systems with restricted queue lengths. Oper. Res (1967) 15:266–278Link, Google Scholar
- Grassmann W. K.Computational Probability (2000) (Kluwer Academic Publishers, Boston, MA) Crossref, Google Scholar
- Regenerative analysis and steady state distributions for Markov chains. Oper. Res. (1985) 33:1107–1116Link, Google Scholar
- Sample-path conservation laws, with applications to scheduling queues and fluid systems. Queueing Systems: Theory Appl. (2000) 36:175–199Crossref, Google Scholar
- Fundamentals of Queueing Theory (1974) (Wiley, New York) Google Scholar
- A relation between stationary queue and waiting time distributions. J. Appl. Probab. (1971) 8:617–620Crossref, Google Scholar
- Heavy traffc limits for queues with many exponential servers. Oper. Res. (1981) 29:567–587Link, Google Scholar
- The diffusion approximation for tandem queues in heavy traffic. Adv. Appl. Probab. (1978) 10:886–905Crossref, Google Scholar
- Brownian Motion and Stochastic Flow Systems (1985) (John Wiley and Sons Inc., New York) Wiley Series in Probability and Mathematical StatisticsGoogle Scholar
- , Fleming W. Brownian models of queueing networks with heterogeneous customer populations. Stochastic Differential Systems, Stochastic Control Theory and Applications (1988) 10(Springer, New York) 147–186IMA Math. ApplCrossref, Google Scholar
- , Kelly F. P., Zachary S., Ziedins I. The BIGSTEP approach to flow management in stochastic processing networks. Stochastic Networks: Theory and Applications (1996) (Oxford University Press, Oxford, U.K.) Google Scholar
- Heavy traffic resource pooling in parallel-server systems. Queueing Systems Theory Appl. (1999) 33:339–368Crossref, Google Scholar
- Reflected Brownian motion on an orthant. Ann. Probab. (1981) 9:302–308Crossref, Google Scholar
- Scheduling networks of queues: Heavy traffic analysis of a simple open network. Queueing Systems Theory Appl. (1989) 5:265–279.Crossref, Google Scholar
- Brownian models of feedforward queueing networks: quasireversibility and product form solutions. Ann. Appl. Prob. (1992) 2:263–293Crossref, Google Scholar
- Comments on the origin and application of Markov decision processes. Oper. Res. (2002) 50(1):100–102Link, Google Scholar
- Diffusion approximations in applied probability. Mathematics of the Decision Sciences (1968) (American Mathematical Society, Providence, RI) 235–254Part 2Google Scholar
- Multiple channel queues in heavy traffic. I. Adv. Appl. Probab. (1970) 2:150–177Crossref, Google Scholar
- Networks of waiting lines. Oper. Res. (1957) 5:518–521Link, Google Scholar
- Jobshop-like queueing systems. Management Sci. (1963) 10:131–142Link, Google Scholar
- How networks of queues came about. Oper. Res. (2002) 50(1):112–113Link, Google Scholar
- Priority Queues (1968) (Academic Press, New York) Google Scholar
- Control of arrivals to a stochastic input-output system. Adv. Appl. Probab (1980) 12:972–999Crossref, Google Scholar
- Networks of queues with customers of different types. J. Appl. Prob. (1975) 12:542–554Crossref, Google Scholar
- Reversibility and Stochastic Networks (1979) (Wiley, New York) Google Scholar
- Effective bandwidths at multi-class queues. Queueing Systems: Theory and Appl. (1991) 9:5–16Crossref, Google Scholar
- , Kelly F. P., Zachary S., Ziedins I. B. Notes on effective bandwidths. Stochastic Networks: Theory and Applications. Royal Statistical Society Lecture Notes Series (1996) 4(Oxford University Press, Oxford, U.K.) 141–168Google Scholar
- Mathematical modelling of the Internet. Proc. 4th Internat. Congress Indust. Appl. Math. (2000) (Edinburgh, Scotland) 105–116Google Scholar
- Dynamic routing in open queueing networks: Brownian models, cut constraints, and resource pooling. Queueing Systems Theory Appl. (1993) 13:47–86Crossref, Google Scholar
- Some problems in the theory of queues. J. Royal Statist. Soc. (1951) B 13:151–173Google Scholar
- On the theory of queues with many servers. Tran. Amer. Math. Soc. (1955) 78:1–18Crossref, Google Scholar
- The single server queue in heavy traffic. Proc. Cambridge Philos. Soc. (1961) 57:902–904Crossref, Google Scholar
- Controlled Queueing Systems (1995) (CRC Press, Boca Raton, FL) Google Scholar
- Queueing Systems, Vols. I, II (1975) (Wiley Intersciences, New York) Google Scholar
- Creating a mathematical theory of computer networks. Oper. Res. (2002) 50(1):125–131Link, Google Scholar
- Individual and social optimization in a multiserver queue with a general cost-benefit structure. Econometrica (1972) 40:515–528Crossref, Google Scholar
- Cyclic queues. Oper. Res. Quart. (1958) 9:22–35Crossref, Google Scholar
- Verallgemeinerungen der Erlangschen und Engsetschen Formeln (1967) (Akademie-Verlag, Berlin, Germany) Google Scholar
- Stochastic theory of a multi-entry buffer (1). Delft Progress Report (1974) 1:10–18Google Scholar
- , Dshalalow J. Fluid models for single buffer systems. Frontiers in Queueing (1997) (CRC, Boca Raton, FL) 321–338Google Scholar
- Dynamic instabilities and stabilization methods in distributed real-time scheduling of manufacturing systems. IEEE Trans. Automat. Control (1990) 35:289–298Crossref, Google Scholar
- Heavy Traffic Analysis of Controlled Queueing and Communication Networks (2001) (Springer-Verlag, New York) Crossref, Google Scholar
- Numerical Methods for Stochastic Control Problems in Continuous Time (1992) (Springer-Verlag, New York) Crossref, Google Scholar
- The theory of queues with a single server. Proc. Camb. Phil. Soc. (1952) 48:277–289Crossref, Google Scholar
- Applying a new device in the optimization of exponential queuing systems. Oper. Res. (1975) 23:687–710Link, Google Scholar
- Individual versus social optimization in exponential congestion systems. Oper. Res. (1977) 25:233–247Link, Google Scholar
- A proof of the queuing formula: L=λW.. Oper. Res. (1961) 9:383–387Link, Google Scholar
- The stability of a queue with nonindependent inter-arrival and service times. Proc. Camb. Phil. Soc. (1962) 58:497–520Google Scholar
- Markov Chains and Stochastic Stability (1993) (Springer-Verlag, London, U.K.) Communications and Control Engineering SeriesCrossref, Google Scholar
- Queues Inventories, and Maintenance (1958) (Wiley, New York) Crossref, Google Scholar
- Perspectives on the evolution of simulation. Oper. Res. (2002) 50(1):161–172Link, Google Scholar
- On the regulation of queue size by levying tolls. Econometrica (1969) 37:15–24Crossref, Google Scholar
- Computational uses of the method of phases in the theory of queues. Comput. Math. Appl. (1975) 1:151–166Crossref, Google Scholar
- Matrix-Geometric Solutions in Stochastic Models. An Algorithmic Approach (1981) 2(Johns Hopkins University Press, Baltimore, MD) . Johns Hopkins Series in the Mathematical SciencesGoogle Scholar
- Structured Stochastic Matrices of M/G/1 Type and Their Applications. Probability: Pure and Applied (1989) 5(Marcel Dekker, New York) Google Scholar
- The transient behavior of the queue with alternating priorities, with special reference to the waiting times. Bull. Soc. Math. Belg. (1968) 20:343–376Google Scholar
- Applications of Queueing Theory (1982) 2nd ed.(Chapman and Hall, London, U.K.) Crossref, Google Scholar
- Queueing Networks with Blocking (1994) (Oxford Press, New York) Google Scholar
- A heavy traffic limit theorem for networks of queues with multiple customer types. Math. Oper. Res. (1991) 16:90–118Link, Google Scholar
- Queues and Inventories: A Study of Their Basic Stochastic Processes (1965) (Wiley, New York) Google Scholar
- Stochastic Storage Processes: Queues Insurance Risk, and Dams (1980) (Springer-Verlag, New York) Crossref, Google Scholar
- Transient phenomena in queueing processes. Liet. Mat. Rink. (1963) 3:199–206Google Scholar
- Note on queues in tandem. Ann. Math. Statist. (1963) 34:338–341Crossref, Google Scholar
- Open queueing networks in heavy traffic. Math. Oper. Res. (1984) 9:441–458Link, Google Scholar
- Mean value analysis of closed multichain queueing networks. J. Assoc. Comput. Mach. (1980) 27:313–322Crossref, Google Scholar
- On the ergodicity of random processes that describe the functioning of open queueing networks. (Russian). Problemy Peredachi Informatsii (1992) 28:3–26translation in Problems Inform. Transmission 28 199–220Google Scholar
- Elements of Queueing Theory (1961) (McGraw-Hill, New York) Google Scholar
- Stable Non-Gaussian Random Processes: Stochastic Models with Infinite Variance (1994) (Chapman & Hall, New York) Google Scholar
- Inventory theory. Oper. Res. (2002) 50(1):186–191Link, Google Scholar
- Insensitivity of steady-state distributions of generalized semi-Markov processes: Part I. Ann. Probab. (1977) 5:87–89Crossref, Google Scholar
- Stochastic Dynamic Programming and the Control of Queueing Systems (1999) (Wiley, New York) Google Scholar
- An equivalence between continuous and discrete time Markov decision processes. Oper. Res. (1979) 27:616–620Link, Google Scholar
- Introduction to Stochastic Networks (1999) (Springer-Verlag, New York) Crossref, Google Scholar
- Stochastic Orders and Their Applications. Probability and Mathematical Statistics (1994) (Academic Press Inc., Boston, MA) Google Scholar
- Multiclass queueing systems: polymatroidal structure and optimal scheduling control. Oper. Res. (1992) 40:S293–S299Link, Google Scholar
- Large Deviations for Performance Analysis: Queues, Communications, and Computing (1995) (Chapman & Hall, New York) Google Scholar
- Stationary Marked Point Processes: An Intuitive Approach (1995) (Chapman & Hall, New York) Google Scholar
- On the distribution of queueing times. Proc. Camb. Phil. Soc. (1953) 49:449–461Crossref, Google Scholar
- Regenerative stochastic processes. Proc. Royal Soc. (1955) A 232:6–31Crossref, Google Scholar
- The Wiener-Hopf equation whose kernel is a probability density. Duke Math. J. (1957) 24:327–344Crossref, Google Scholar
- Introduction to the Numerical Solution of Markov Chains (1994) (Princeton University Press, Princeton, NJ) Google Scholar
- On the optimality of single-server queueing systems. Oper. Res. (1970) 18:708–732Link, Google Scholar
- L=λW: A discounted analogue and a new proof. Oper. Res. (1972a) 20:1115–1126Link, Google Scholar
- Regenerative processes in the theory of queues ith applications to the alternating-priority queue. Adv. Appl. Probab. (1972b) 4:542–577Crossref, Google Scholar
- A last word on L=λW. Oper. Res. (1974) 22:417–421Link, Google Scholar
- Optimal control of admission to a queueing system. IEEE Trans. Auto. Control (1985) 30:705–713Crossref, Google Scholar
- , Clarke B. Optimal control of queueing systems. Mathematical Methods in Queueing Theory Lecture Notes in Econom. Math. Systems 98 (1974) (Springer-Verlag, Berlin, Germany) 263–294Crossref, Google Scholar
- A survey of Markov decision models for control of networks of queues. Queueing Systems: Theory and Appl. (1993) 13:291–314Crossref, Google Scholar
- Comparison Methods for Queues and Other Stochastic Processes (1983) (Wiley, New York) Google Scholar
- Introduction to Congestion Theory in Telephone Systems (1960) (Oliver and Boyd, Edinburgh and London, U.K.) Google Scholar
- Introduction to the Theory of Queues (1962) (Oxford University Press, New York) . University Texts in the Mathematical SciencesGoogle Scholar
- Analysis of Polling Systems (1986) (MIT Press, Cambridge, MA) Google Scholar
- , Dshalalow J. Queueing analysis of polling models: Progress in 1990–1994. Frontiers in Queueing (1997) (CRC, Boca Raton, FL) 119–146Probab. Stochastics Ser.Google Scholar
- Existence and uniqueness of semimartingale reflecting Brownian motions in an orthant. Probab. Theory Related Fields (1993) 96:283–317Crossref, Google Scholar
- And then there were none. Oper. Res. (2002) 50:217–226Link, Google Scholar
- An Introduction to Queueing Networks (1988) (Prentice-Hall, Englewood Cliffs, NJ) Google Scholar
- Optimal control of a two-station Brownian network. Math. Oper. Res. (1990) 15:215–242Link, Google Scholar
- , Clarke B. Heavy traffic limit theorems for queues: a survey. Mathematical Methods in Queueing Theory Lecture Notes in Econom. Math. Systems (1974) 98(Springer-Verlag, Berlin, Germany) 307–350Crossref, Google Scholar
- An overview of Brownian and non-Brownian FCLT's for the single-server queue. Queueing Systems: Theory Appl. (2000a) 36:39–70Crossref, Google Scholar
- The impact of a heavy-tailed service-time distribution upon the M/GI/s waiting-time distribution. Queueing Systems: Theory Appl. (2000b) 36:71–87Crossref, Google Scholar
- Stochastic Process Limits (2002) (Springer, New York) Crossref, Google Scholar
- Equilibrium distribution for an open migration process. J. Appl. Probab. (1968) 5:567–571Crossref, Google Scholar
- Applied probability in Great Britain. Oper. Res. (2002) 50:227–239Link, Google Scholar
- Diffusion approximations for open multiclass queueing networks: Sufficient conditions involving state space collapse. Queueing Systems Theory Appl. (1998) 30:27–88Crossref, Google Scholar
- On dynamic scheduling of a parallel server system with complete resource pooling. Analysis of Communication Networks: Call Centres Traffic and Performance (2000) 28(Providence, RI) 49–71Amer. Math. SocCrossref, Google Scholar
- , Kelly F. P., Williams R. J. Traffic modeling for high-speed networks: theory versus practice. Stochastic Networks (1995) 71(Springer-Verlag, New York) 169–186IMA Volumes in Mathematics and Its ApplicationsCrossref, Google Scholar
- Work-conserving priorities. J. Appl. Probab. (1970) 7:327–337Crossref, Google Scholar
- Poisson arrivals see time averages. Oper. Res. (1982) 30:223–231Link, Google Scholar

