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Mathematical study of waiting lines, or queues
Queueing theory is the mathematical study of queues, or waiting lines. A queueing model is constructed so that queue lengths and waiting times can be predicted
Queueing_theory
Type of queue model in queueing theory
In queueing theory, a discipline within the mathematical theory of probability, an M/M/1 queue represents the queue length in a system having a single
M/M/1_queue
Multi-server queueing model
In queueing theory, a discipline within the mathematical theory of probability, the M/M/c queue (or Erlang–C model) is a multi-server queueing model.
M/M/c_queue
Theorem in queueing theory
In mathematical queueing theory, Little's law (also result, theorem, lemma, or formula) is a theorem by John Little which states that the long-term average
Little's_law
Places where people queue or "line up" for goods or services
stand. Queueing is a phenomenon in a number of fields, and has been extensively analysed in the study of queueing theory. In economics, queueing is seen
Queue_area
American computer scientist (born 1934)
awards. In the early 1960s, Kleinrock pioneered the application of queueing theory to model delays in message switching networks in his Ph.D. thesis,
Leonard_Kleinrock
Collection of random variables
inference. They have found applications in areas in probability theory such as queueing theory and Palm calculus and other fields such as economics and finance
Stochastic_process
a German mathematician and statistician who made contributions to queueing theory, stochastic geometry, and spatial statistics. Stoyan studied mathematics
Dietrich_Stoyan
System for describing queueing models
standard system used to describe and classify a queueing node. D. G. Kendall proposed describing queueing models using three factors written A/S/c in 1953
Kendall's_notation
DC circuit analysis technique
equivalent of "Norton's theorem" in queuing theory is called the Chandy Herzog Woo theorem. In a reversible queueing system, it is often possible to replace
Norton's_theorem
Equation in mathematical queueing theory
In queueing theory, a discipline within the mathematical theory of probability, Kingman's formula, also known as the VUT equation, is an approximation
Kingman's_formula
Type of financial fraud
Trading. A matrix scheme is also an example of an "exploding queue'"in queueing theory. The first known matrix scheme is widely believed to be EZExpo
Matrix_scheme
Indian-American mathematician (1924–2022)
the journal Queueing Systems (1986–1994) and has edited several other journals, as well as published books on Foundations of Queueing Theory (Springer Verlag
N._U._Prabhu
Mathematical identity in queueing theory
queueing theory, a discipline within the mathematical theory of probability, the Pollaczek–Khinchine formula states a relationship between the queue length
Pollaczek–Khinchine_formula
Scheduling algorithm, the first piece of data inserted into a queue is processed first
dual-ported RAM (random access memory). FINO Leaky bucket approach Queueing theory SCHED_FIFO Andrew S. Tanenbaum; Herbert Bos (2015). Modern Operating
FIFO (computing and electronics)
FIFO_(computing_and_electronics)
Optimization for dynamical systems
central to the study of optimal control in queueing networks. A typical goal is to stabilize all network queues while optimizing some performance objective
Lyapunov_optimization
Indian mathematician (1934–2021)
Indian-born mathematician, known for his contributions to queueing theory and reliability theory. Bhat received a B.A. in mathematics (1953) and B.T. in
U._Narayan_Bhat
Theorem in queueing theory
In queueing theory, a discipline within the mathematical theory of probability, Burke's theorem (sometimes the Burke's output theorem) is a theorem (stated
Burke's_theorem
Queue model
In queueing theory, a discipline within the mathematical theory of probability, an M/G/k queue is a queue model where arrivals are Markovian (modulated
M/G/k_queue
Approximation of physical behavior
artificial intelligence, epidemic models, queueing theory, computer-network performance and game theory, as in the quantal response equilibrium[citation
Mean-field_theory
Aspect of mathematical queueing theory
In queueing theory, a discipline within the mathematical theory of probability, an M/D/1 queue represents the queue length in a system having a single
M/D/1_queue
Aspect of queueing theory
In queueing theory, a discipline within the mathematical theory of probability, an M/G/1 queue is a queue model where arrivals are Markovian (modulated
M/G/1_queue
Russian mathematician (1931–2026)
probability theory, mathematical statistics, stochastic processes, queueing theory, large deviations, random walks, and asymptotic methods. He authored
Aleksandr_Borovkov
Prabhu, N. U. (1974). "Wiener-Hopf Techniques in Queueing Theory". Mathematical Methods in Queueing Theory. Lecture Notes in Economics and Mathematical Systems
Lindley_equation
Probability theory concept
In queueing theory, a discipline within the mathematical theory of probability, the G/G/1 queue represents the queue length in a system with a single
G/G/1_queue
American computer scientist (born 1966)
Science at Carnegie Mellon University. She is known for her work on queueing theory, scheduling and resource allocation, load balancing, data center power
Mor_Harchol-Balter
Scheduling technique in computer science
deadline (i.e. shortest period) in which all processing must occur. In queueing theory, Ti is called the interarrival time, and Ci is called the service time
Rate-monotonic_scheduling
Operations researcher and applied probabilist
applied probabilist known for work on stochastic processing networks, queueing theory, and fluid and diffusion approximations. He is the Leon C. Welch Professor
Jim_Dai
Concept in queueing theory
In queueing theory, a discipline within the mathematical theory of probability, an M/D/c queue represents the queue length in a system having c servers
M/D/c_queue
Academic journal
Queueing Systems is a peer-reviewed scientific journal covering queueing theory. It is published by Springer Science+Business Media. The current editor-in-chief
Queueing_Systems
Gordon–Newell theorem is an extension of Jackson's theorem from open queueing networks to closed queueing networks of exponential servers where customers cannot leave
Gordon–Newell_theorem
Danish mathematician, statistician and engineer
and engineer, who invented the fields of teletraffic engineering and queueing theory. Erlang's 1909 paper, and subsequent papers over the decades, are regarded
Agner_Krarup_Erlang
Type of random mathematical object
can be viewed as a stochastic process. It is used, for example, in queueing theory to model random events distributed in time, such as the arrival of
Poisson_point_process
Supposition or system of ideas intended to explain something
global warming (AGW) theories (due to human activity) Computer Science: Automata theory — Queueing theory Cosmology: Big Bang Theory — Cosmic inflation
Theory
In queueing theory, a discipline within the mathematical theory of probability, a layered queueing network (or rendezvous network) is a queueing network
Layered_queueing_network
Random process independent of past history
ratios. Markov chains are the basis for the analytical treatment of queues (queueing theory). Agner Krarup Erlang initiated the subject in 1917. This makes
Markov_chain
Discipline concerning the application of advanced analytical methods
decision-making and efficiency, such as simulation, mathematical optimization, queueing theory and other stochastic-process models, Markov decision processes, econometric
Operations_research
Mathematical discipline
In queueing theory, a discipline within the mathematical theory of probability, a Jackson network (sometimes called a Jacksonian network) is a class of
Jackson_network
Special type of continuous-time Markov process
deaths. Birth–death processes have many applications in demography, queueing theory, performance engineering, epidemiology, biology and other areas. They
Birth–death_process
Model in queuing theory
In queueing theory, a discipline within the mathematical theory of probability, a polling system or polling model is a system where a single server visits
Polling_system
the mathematical theory of probability, offered load is a concept in queuing theory. The offered load is a measure of traffic in a queue. The offered load
Offered_load
In queueing theory, a discipline within the mathematical theory of probability, a BCMP network is a class of queueing network for which a product-form
BCMP_network
Topics referred to by the same term
system load of a computer's operating system Message queue Queueing theory, the study of wait lines Queue (hairstyle), a Qing dynasty Manchu hairstyle Cue
Queue
Automata theory Supervisory control theory Petri net theory Discrete event system specification Boolean differential calculus Markov chain Queueing theory Discrete-event
Discrete-event_dynamic_system
Network technique addressing head-of-line blocking
queueing (VOQ) is a technique used in certain network switch architectures where, rather than keeping all traffic in a single queue, separate queues are
Virtual_output_queueing
Arbiter on a node in a packet switching communication network
A network scheduler, also called packet scheduler, queueing discipline (qdisc) or queueing algorithm, is an arbiter on a node in a packet switching communication
Network_scheduler
Pavel Petrovich; D'Apice, C.; Pechinkin, A.V.; Salerno, S. (2004). Queueing theory. Walter de Gruyter. p. 37. ISBN 90-6764-398-X. Norris, James R. (1998)
Balance_equation
Growth function exhibiting a singularity at a finite time
other functions. Another example of hyperbolic growth can be found in queueing theory: the average waiting time of randomly arriving customers grows hyperbolically
Hyperbolic_growth
the analysis of queueing networks where the network is broken into subsystems which are independently analyzed. The individual queueing nodes are considered
Decomposition method (queueing theory)
Decomposition_method_(queueing_theory)
Load measure in telecommunications
which became foundational results in teletraffic engineering and queueing theory. His results, which are still used today, relate quality of service
Erlang_(unit)
Mathematical model
In queueing theory, a discipline within the mathematical theory of probability, a bulk queue (sometimes batch queue) is a general queueing model where
Bulk_queue
Turkish-French computer scientist (born 1945)
communications. He also developed G-networks, a class of queueing networks that extends classical queueing theory by incorporating positive and negative customers
Erol_Gelenbe
science, an input queue is a collection of processes in storage that are waiting to be brought into memory to run a program. Input queues are mainly used
Input_queue
American operations researcher and educator (born 1943)
contributions to urban service systems, disaster planning, pandemics, queueing theory, logistics, technology-enabled education, smart-energy houses, and
Richard_Larson_(academic)
Mathematical formula for queueing
compute the necessary number of servers without involving probability or queueing theory. The rule of thumb is therefore more practical to use in many situations
Queuing_Rule_of_Thumb
Computer providing a central resource or service
server components. The use of the word server in computing comes from queueing theory, where it dates to the mid 20th century, being notably used in Kendall
Server_(computing)
Bertrand's ballot theorem (probability theory, combinatorics) Burke's theorem (probability theory, queueing theory) Central limit theorem (probability)
List_of_theorems
Theorem of queueing theory about instantaneous behavior at arrival times
In queueing theory, a discipline within the mathematical theory of probability, the arrival theorem (also referred to as the random observer property,
Arrival_theorem
Algorithm employed by process and network schedulers in computing
attributed time quantum, the scheduler selects the first process in the ready queue to execute. In the absence of time-sharing, or if the quanta were large
Round-robin_scheduling
American professor of operations research and management sciences
Research department of Columbia University. His research focuses on queueing theory, performance analysis, stochastic models of telecommunication systems
Ward_Whitt
In queueing theory, a discipline within the mathematical theory of probability, Buzen's algorithm (or convolution algorithm) is an algorithm for calculating
Buzen's_algorithm
Topics referred to by the same term
vehicle spends at a scheduled stop without moving Service time, in queueing theory This disambiguation page lists articles associated with the title Dwell
Dwell_time
Twelfth letter of the Greek alphabet
function in number theory The population mean or expected value in probability and statistics The service or departure rate in queueing theory The Ramanujan–Soldner
Mu_(letter)
In queueing theory, a discipline within the mathematical theory of probability, a retrial queue is a model of a system with finite capacity, where jobs
Retrial_queue
Algorithm in queueing theory
In queueing theory, a discipline within the mathematical theory of probability, the backpressure routing algorithm is a method for directing traffic around
Backpressure_routing
In queueing theory, a discipline within the mathematical theory of probability, mean value analysis (MVA) is a recursive technique for computing expected
Mean_value_analysis
1287/opre.32.2.343. Grassmann, W. K. (1977). "Transient solutions in markovian queueing systems". Computers & Operations Research. 4: 47–00. doi:10.1016/0305-0548(77)90007-7
Uniformization (probability theory)
Uniformization_(probability_theory)
Form of resource sharing for tasks in computing
available. In such a system all jobs start service immediately (there is no queueing). The processor sharing algorithm "emerged as an idealisation of round-robin
Processor_sharing
In queueing theory, a discipline within the mathematical theory of probability, Beneš approach or Beneš method is a result for an exact or good approximation
Beneš_method
Part of mathematical queueing theory
In queueing theory, a discipline within the mathematical theory of probability, the M/M/∞ queue is a multi-server queueing model where every arrival experiences
M/M/∞_queue
Mathematical model
In queueing theory, a discipline within the mathematical theory of probability, a fluid queue (fluid model, fluid flow model or stochastic fluid model)
Fluid_queue
In queueing theory, an adversarial queueing network is a model where the traffic to the network is supplied by an opponent rather than as the result of
Adversarial_queueing_network
Mathematical process
Norton's theorem for queueing networks or the Chandy–Herzog–Woo method) is a divide-and-conquer method to solve product form queueing networks inspired by
Flow-equivalent_server_method
Dutch mathematician (born 1970)
known for several contributions to queueing theory and applied probability theory. His research interests include queueing models for telecommunications,
Michel_Mandjes
contributions to applied mathematics, in particular traffic flow analysis and queueing theory. Newell authored over one hundred articles and wrote several books
Gordon_F._Newell
Abstract data type in computer science
repeatedly pulling the top of the queue and executing the event thereon. See also: Scheduling (computing), queueing theory When the graph is stored in the
Priority_queue
American sociologist
Mentorship Award. Barbara Reskin is known for her expansion and use of queuing theory to explain the persistence sex segregation in the workplace despite
Barbara_Reskin
Concept in queueing theory
In queueing theory, a discipline within the mathematical theory of probability, a heavy traffic approximation (sometimes called heavy traffic limit theorem
Heavy_traffic_approximation
Probability distribution for branching processes
distribution, arising in contexts including branching processes and queueing theory. It is named after the French mathematician Émile Borel. If the number
Borel_distribution
Professor of operations research at MIT
algorithms and optimization, quantum computing, stochastic processes and queueing theory. Gamarnik was born in Tbilisi, Georgia and completed part of his undergraduate
David_Gamarnik
Mathematical model in queueing theory
In queueing theory, a discipline within the mathematical theory of probability, a Markovian arrival process (MAP or MArP) is a mathematical model for the
Markovian_arrival_process
In queueing theory, a discipline within the mathematical theory of probability, quasireversibility (sometimes QR) is a property of some queues. The concept
Quasireversibility
tends to be more limited, with researchers trying to identify suitable queueing theory and operations research models to represent the problems that are raised
Skills-based_routing
In queueing theory, the method of supplementary variables is a technique to solve for the stationary distribution of an M/G/1 queue. It was introduced
Method of supplementary variables
Method_of_supplementary_variables
In queueing theory, a discipline within the mathematical theory of probability, a Kelly network is a general multiclass queueing network. In the network
Kelly_network
Doing something at or before a previously designated time
econometrics and to considering the effects of non-punctuality on others in queueing theory.[citation needed] Etiquette – Customary code of polite behaviour Time
Punctuality
American computer scientist
scheduling (computing), heavy tails, green computing, queueing theory, and algorithmic game theory. Wierman studied at Carnegie Mellon University, where
Adam_Wierman
Inverse of a finite difference
of divergent series in quantum field theory (e.g., the Casimir effect), performance analysis in queueing theory, scalar evolution in compilers such as
Indefinite_sum
simulation is often a less expensive approach. An analytical approach using queueing theory may be possible for a simplified traffic model but is often too complicated
Traffic_generation_model
In queueing theory, the Engset formula is used to determine the blocking probability of an M/M/c/c/N queue (in Kendall's notation). The formula is named
Engset_formula
Discipline within mathematical theory
In queueing theory, a discipline within the mathematical theory of probability, the G/M/1 queue represents the queue length in a system where interarrival
G/M/1_queue
CPU optimization unit
(1878-1929) who first conceived of a queue as a solution to congestion in telephone traffic. Different queueing models are proposed in order to approximately
Prefetch_input_queue
Representation of a type of random process
Bühlmann Cramér–Lundberg Risk process Sparre–Anderson Queueing models Bulk Fluid Generalized queueing network M/G/1 M/M/1 M/M/c Properties Càdlàg paths Continuous
Autoregressive_model
Mathematical model for understanding queueing systems
In queueing theory, a discipline within the mathematical theory of probability, a G-network (generalized queueing network, often called a Gelenbe network)
G-network
In queueing theory, a loss network is a stochastic model of a telephony network in which calls are routed around a network between nodes. The links between
Loss_network
Early packet switching network (1969–1990)
network and find areas for improvement. Building on his earlier work on queueing theory and optimization of message delay in communication networks, Kleinrock
ARPANET
In queueing theory, a discipline within the mathematical theory of probability, a D/M/1 queue represents the queue length in a system having a single
D/M/1_queue
Operations research and management sciences award
optimization of stochastic systems 2001 Ward Whitt for his contributions to queueing theory, applied probability and stochastic modelling 2000 Ellis L. Johnson
John_von_Neumann_Theory_Prize
In queueing theory, a discipline within the mathematical theory of probability, Ross's conjecture gives a lower bound for the average waiting-time experienced
Ross's_conjecture
Method of analysis in probability theory
Ramaswami, V. (1990). "A duality theorem for the matrix paradigms in queueing theory". Communications in Statistics. Stochastic Models. 6: 151–161. doi:10
Matrix_geometric_method
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