Fundamentals of Queueing Theory
01 May 1975-Vol. 138, Iss: 3, pp 436-437
TL;DR: The Fundamentals of Queueing Theory, Fourth Edition as discussed by the authors provides a comprehensive overview of simple and more advanced queuing models, with a self-contained presentation of key concepts and formulae.
Abstract: Praise for the Third Edition: "This is one of the best books available. Its excellent organizational structure allows quick reference to specific models and its clear presentation . . . solidifies the understanding of the concepts being presented."IIE Transactions on Operations EngineeringThoroughly revised and expanded to reflect the latest developments in the field, Fundamentals of Queueing Theory, Fourth Edition continues to present the basic statistical principles that are necessary to analyze the probabilistic nature of queues. Rather than presenting a narrow focus on the subject, this update illustrates the wide-reaching, fundamental concepts in queueing theory and its applications to diverse areas such as computer science, engineering, business, and operations research.This update takes a numerical approach to understanding and making probable estimations relating to queues, with a comprehensive outline of simple and more advanced queueing models. Newly featured topics of the Fourth Edition include:Retrial queuesApproximations for queueing networksNumerical inversion of transformsDetermining the appropriate number of servers to balance quality and cost of serviceEach chapter provides a self-contained presentation of key concepts and formulae, allowing readers to work with each section independently, while a summary table at the end of the book outlines the types of queues that have been discussed and their results. In addition, two new appendices have been added, discussing transforms and generating functions as well as the fundamentals of differential and difference equations. New examples are now included along with problems that incorporate QtsPlus software, which is freely available via the book's related Web site.With its accessible style and wealth of real-world examples, Fundamentals of Queueing Theory, Fourth Edition is an ideal book for courses on queueing theory at the upper-undergraduate and graduate levels. It is also a valuable resource for researchers and practitioners who analyze congestion in the fields of telecommunications, transportation, aviation, and management science.
Citations
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Book•
01 Jan 1985
TL;DR: The Connection Machine describes a fundamentally different kind of computer that Daniel Hillis and others are now developing to perform tasks that no conventional, sequential machine can solve in a reasonable time.
Abstract: The Connection Machine describes a fundamentally different kind of computer. It offers a preview of a parallel processing computer that Daniel Hillis and others are now developing to perform tasks that no conventional, sequential machine can solve in a reasonable time.
2,124 citations
TL;DR: Two simple models of queueing on an N \times N space-division packet switch are examined, and it is possible to slightly increase utilization of the output trunks and drop interfering packets at the end of each time slot, rather than storing them in the input queues.
Abstract: Two simple models of queueing on an N \times N space-division packet switch are examined. The switch operates synchronously with fixed-length packets; during each time slot, packets may arrive on any inputs addressed to any outputs. Because packet arrivals to the switch are unscheduled, more than one packet may arrive for the same output during the same time slot, making queueing unavoidable. Mean queue lengths are always greater for queueing on inputs than for queueing on outputs, and the output queues saturate only as the utilization approaches unity. Input queues, on the other hand, saturate at a utilization that depends on N , but is approximately (2 -\sqrt{2}) = 0.586 when N is large. If output trunk utilization is the primary consideration, it is possible to slightly increase utilization of the output trunks-upto (1 - e^{-1}) = 0.632 as N \rightarrow \infty -by dropping interfering packets at the end of each time slot, rather than storing them in the input queues. This improvement is possible, however, only when the utilization of the input trunks exceeds a second critical threshold-approximately ln (1 +\sqrt{2}) = 0.881 for large N .
1,592 citations
TL;DR: An implementation for a general class of Markov processes that can be described in terms of state space S, event set E, rate vectors R, and target vectors T-abbreviated as SERT is presented.
Abstract: We present a randomization procedure for computing transient solutions to discrete state space, continuous time Markov processes. This procedure computes transient state probabilities. It is based on a construction relating a continuous time Markov process to a discrete time Markov chain. Modifications and extensions of the randomization method allow for computation of distributions of first passage times and sojourn times in Markov processes, and also the computation of expected cumulative occupancy times and expected number of events occurring during a time interval. Several implementations of the randomization procedure are discussed. In particular we present an implementation for a general class of Markov processes that can be described in terms of state space S, event set E, rate vectors R, and target vectors T-abbreviated as SERT. This general approach can handle systems whose state spaces are quite large, if they have sparse generators.
448 citations
TL;DR: It is shown that a first come, first served (FCFS) policy that schedules the video with the longest outstanding request can perform better than the maximum queue length (MQL) policy, and multicasting is better exploited by scheduling playback of the most popular videos at predetermined, regular intervals (hence, termed FCFS-n).
Abstract: In a video-on-demand environment, continuous delivery of video streams to the clients is guaranteed by sufficient reserved network and server resources. This leads to a hard limit on the number of streams that a video server can deliver. Multiple client requests for the same video can be served with a single disk I/O stream by sending (multicasting) the same data blocks to multiple clients (with the multicast facility, if present in the system). This is achieved by batching (grouping) requests for the same video that arrive within a short time. We explore the role of customerwaiting time and reneging behavior in selecting the video to be multicast. We show that a first come, first served (FCFS) policy that schedules the video with the longest outstanding request can perform better than the maximum queue length (MQL) policy that chooses the video with the maximum number of outstanding requests. Additionally, multicasting is better exploited by scheduling playback of the n most popular videos at predetermined, regular intervals (hence, termed FCFS-n). If user reneging can be reduced by guaranteeing that a maximum waiting time will not be exceeded, then performance of FCFS-n is further improved by selecting the regular playback intervals as this maximum waiting time. For an empirical workload, we demonstrate a substantial reduction (of the order of 60%) in the required server capacity by batching.
409 citations
TL;DR: Stability results for a fluid flow model of end-to-end Internet congestion control and criteria for local stability and rate of convergence are completely characterized for a single resource, single user system.
Abstract: Under the assumption that queueing delays will eventually become small relative to propagation delays, we derive stability results for a fluid flow model of end-to-end Internet congestion control. The theoretical results of the paper are intended to be decentralized and locally implemented: each end system needs knowledge only of its own round-trip delay. Criteria for local stability and rate of convergence are completely characterized for a single resource, single user system. Stability criteria are also described for networks where all users share the same round-trip delay. Numerical experiments investigate extensions to more general networks. Through simulations, we are able to evaluate the relative importance of queueing delays and propagation delays on network stability. Finally, we suggest how these results may be used to design network resources.
406 citations
References
More filters
Book•
01 Jan 1985
TL;DR: The Connection Machine describes a fundamentally different kind of computer that Daniel Hillis and others are now developing to perform tasks that no conventional, sequential machine can solve in a reasonable time.
Abstract: The Connection Machine describes a fundamentally different kind of computer. It offers a preview of a parallel processing computer that Daniel Hillis and others are now developing to perform tasks that no conventional, sequential machine can solve in a reasonable time.
2,124 citations
TL;DR: Two simple models of queueing on an N \times N space-division packet switch are examined, and it is possible to slightly increase utilization of the output trunks and drop interfering packets at the end of each time slot, rather than storing them in the input queues.
Abstract: Two simple models of queueing on an N \times N space-division packet switch are examined. The switch operates synchronously with fixed-length packets; during each time slot, packets may arrive on any inputs addressed to any outputs. Because packet arrivals to the switch are unscheduled, more than one packet may arrive for the same output during the same time slot, making queueing unavoidable. Mean queue lengths are always greater for queueing on inputs than for queueing on outputs, and the output queues saturate only as the utilization approaches unity. Input queues, on the other hand, saturate at a utilization that depends on N , but is approximately (2 -\sqrt{2}) = 0.586 when N is large. If output trunk utilization is the primary consideration, it is possible to slightly increase utilization of the output trunks-upto (1 - e^{-1}) = 0.632 as N \rightarrow \infty -by dropping interfering packets at the end of each time slot, rather than storing them in the input queues. This improvement is possible, however, only when the utilization of the input trunks exceeds a second critical threshold-approximately ln (1 +\sqrt{2}) = 0.881 for large N .
1,592 citations
TL;DR: An implementation for a general class of Markov processes that can be described in terms of state space S, event set E, rate vectors R, and target vectors T-abbreviated as SERT is presented.
Abstract: We present a randomization procedure for computing transient solutions to discrete state space, continuous time Markov processes. This procedure computes transient state probabilities. It is based on a construction relating a continuous time Markov process to a discrete time Markov chain. Modifications and extensions of the randomization method allow for computation of distributions of first passage times and sojourn times in Markov processes, and also the computation of expected cumulative occupancy times and expected number of events occurring during a time interval. Several implementations of the randomization procedure are discussed. In particular we present an implementation for a general class of Markov processes that can be described in terms of state space S, event set E, rate vectors R, and target vectors T-abbreviated as SERT. This general approach can handle systems whose state spaces are quite large, if they have sparse generators.
448 citations
TL;DR: It is shown that a first come, first served (FCFS) policy that schedules the video with the longest outstanding request can perform better than the maximum queue length (MQL) policy, and multicasting is better exploited by scheduling playback of the most popular videos at predetermined, regular intervals (hence, termed FCFS-n).
Abstract: In a video-on-demand environment, continuous delivery of video streams to the clients is guaranteed by sufficient reserved network and server resources. This leads to a hard limit on the number of streams that a video server can deliver. Multiple client requests for the same video can be served with a single disk I/O stream by sending (multicasting) the same data blocks to multiple clients (with the multicast facility, if present in the system). This is achieved by batching (grouping) requests for the same video that arrive within a short time. We explore the role of customerwaiting time and reneging behavior in selecting the video to be multicast. We show that a first come, first served (FCFS) policy that schedules the video with the longest outstanding request can perform better than the maximum queue length (MQL) policy that chooses the video with the maximum number of outstanding requests. Additionally, multicasting is better exploited by scheduling playback of the n most popular videos at predetermined, regular intervals (hence, termed FCFS-n). If user reneging can be reduced by guaranteeing that a maximum waiting time will not be exceeded, then performance of FCFS-n is further improved by selecting the regular playback intervals as this maximum waiting time. For an empirical workload, we demonstrate a substantial reduction (of the order of 60%) in the required server capacity by batching.
409 citations
TL;DR: Stability results for a fluid flow model of end-to-end Internet congestion control and criteria for local stability and rate of convergence are completely characterized for a single resource, single user system.
Abstract: Under the assumption that queueing delays will eventually become small relative to propagation delays, we derive stability results for a fluid flow model of end-to-end Internet congestion control. The theoretical results of the paper are intended to be decentralized and locally implemented: each end system needs knowledge only of its own round-trip delay. Criteria for local stability and rate of convergence are completely characterized for a single resource, single user system. Stability criteria are also described for networks where all users share the same round-trip delay. Numerical experiments investigate extensions to more general networks. Through simulations, we are able to evaluate the relative importance of queueing delays and propagation delays on network stability. Finally, we suggest how these results may be used to design network resources.
406 citations