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Mathematical study of waiting lines, or queues
Queueing theory is the mathematical study of waiting lines, or queues. A queueing model is constructed so that queue lengths and waiting time 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
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
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
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
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
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
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
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
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
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)
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
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
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
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
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
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
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
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
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
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)
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)
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
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
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
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
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
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
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
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
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
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
In queueing theory, a discipline within the mathematical theory of probability, a heavy traffic approximation (sometimes called heavy traffic limit theorem
Heavy_traffic_approximation
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
Danish mathematician, statistician and engineer
statistician and engineer, who invented the fields of traffic engineering and queueing theory. Erlang's 1909 paper, and subsequent papers over the decades, are regarded
Agner_Krarup_Erlang
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
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)
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
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
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
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
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)
Bertrand's ballot theorem (probability theory, combinatorics) Burke's theorem (probability theory, queueing theory) Central limit theorem (probability)
List_of_theorems
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
Russian mathematician (1931–2026)
probability theory, mathematical statistics, stochastic processes, queueing theory, large deviations, random walks, and asymptotic methods. He authored
Aleksandr_Borovkov
Type of queue
In queueing theory, a discipline within the mathematical theory of probability, a fork–join queue is a queue where incoming jobs are split on arrival
Fork–join_queue
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
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
Form of solution in probability theory
independence. Initially the term was used in queueing networks where the sub-components would be individual queues. For example, Jackson's theorem gives the
Product-form_solution
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
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)
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 retrial queue is a model of a system with finite capacity, where jobs
Retrial_queue
Prabhu, N. U. (1974). "Wiener-Hopf Techniques in Queueing Theory". Mathematical Methods in Queueing Theory. Lecture Notes in Economics and Mathematical Systems
Lindley_equation
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
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
Reduced quality of service due to high network traffic
Network congestion in computer networking and queueing theory is the reduced quality of service that occurs when a network node or link is carrying or
Network_congestion
Indian-American mathematician (1924–2022)
of the Queueing Systems (journal) (1986–1994) and has edited several other journals, as well as published books on Foundations of Queueing Theory (Springer
N._U._Prabhu
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
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
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
Office dealing with a large volume of enquiries by telephone
model call arrival, queueing and service levels. Call centre operations have been supported by mathematical models beyond queueing, with operations research
Call_centre
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
Method for transmitting data over a computer network
Roberts' from MIT, Leonard Kleinrock had researched the application of queueing theory in the field of message switching for his doctoral dissertation in
Packet_switching
In computer networking, micro-bursting is a behavior seen on fast packet-switched networks, where rapid bursts of data packets are sent in quick succession
Micro-bursting
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
"A paradigm of Markov additive processes for queues and their networks". Matrix-Analytic Methods - Theory and Applications - Proceedings of the Fourth
Ladder_height_process
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
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
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
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
Random set of points on a space with random number and random position
for random events in time, such as the arrival of customers in a queue (queueing theory), of impulses in a neuron (computational neuroscience), particles
Point_process
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
Time a job or message waits in a queue until it can be executed or sent
latency Little's law – queueing formula Network delay Packet loss Processing delay Queueing theory Transmission delay "Queuing Delay". Archived from the
Queuing_delay
Seminar Theories
In queueing theory, Bartlett's theorem gives the distribution of the number of customers in a given part of a system at a fixed time. Suppose that customers
Bartlett's_theorem
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
American computer scientist
scheduling (computing), heavy tails, green computing, queueing theory, and algorithmic game theory. Wierman studied at Carnegie Mellon University, where
Adam_Wierman
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
Austrian-French engineer and mathematician
theory, mathematical analysis, mathematical physics and probability theory. He is best known for the Pollaczek–Khinchine formula in queueing theory (1930)
Félix_Pollaczek
Symbols for constants, special functions
occurrences in a Poisson distribution in probability the arrival rate in queueing theory the failure rate in reliability engineering the Lagrange multiplier
Greek letters used in mathematics, science, and engineering
Greek_letters_used_in_mathematics,_science,_and_engineering
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
Engineering discipline focused on physical infrastructure
planning, traffic engineering, some aspects of urban engineering, queueing theory, pavement engineering, Intelligent Transportation System (ITS), and
Civil_engineering
a German mathematician and statistician who made contributions to queueing theory, stochastic geometry, and spatial statistics. Stoyan studied mathematics
Dietrich_Stoyan
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
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, a discipline within the mathematical theory of probability, a BCMP network is a class of queueing network for which a product-form
BCMP_network
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
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
Swedish electrical engineer and statistician
statistician, known for several contributions to teletraffic engineering and queueing theory. Palm enrolled at the School of Electrical Engineering at the Royal
Conny_Palm
Textbook by Patrick Billingsley
within burgeoning fields of applied probability such as queueing theory and empirical process theory in statistics. Schweizer, M., "Review of Convergence
Convergence of Probability Measures
Convergence_of_Probability_Measures
In queueing theory, a discipline within the mathematical theory of probability, a fluid limit, fluid approximation or fluid analysis of a stochastic model
Fluid_limit
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
Hungarian mathematician
mathematician, known for his contributions to probability theory and, in particular, queueing theory. He wrote over two hundred scientific papers and six books
Lajos_Takács
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)
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
QUEUEING THEORY
QUEUEING THEORY
Surname or Lastname
English, Scottish, and Irish (of Norman origin)
English, Scottish, and Irish (of Norman origin) : of disputed origin. It may be from a Celtic personal name derived from the element cam ‘bent’, ‘crooked’ (compare Cameron and Campbell). This was relatively frequent in Norfolk, Lincolnshire, and Yorkshire in the 12th and 13th centuries, perhaps as a result of Breton immigration. According to another theory it is a habitational name from Comines near Lille, but there is no evidence for this (no early forms with de have been found). In southern Ireland this Anglo-Norman name has been confused with 2.Irish : Anglicized form of Gaelic Mac CuimÃn (or Ó CuimÃn) ‘son (or ‘descendant’) of CuimÃn’, a personal name formed from a diminutive of cam ‘crooked’.Americanized form of French Canadian Vien, Viens, based on the misconception that these derive from French venire ‘to come’.
Male
Arthurian
, the questing beast.
Surname or Lastname
English and Scottish
English and Scottish : topographic name for someone who lived by a patch of wet ground overgrown with brushwood, northern Middle English kerr (Old Norse kjarr). A legend grew up that the Kerrs were left-handed, on theory that the name is derived from Gaelic cearr ‘wrong-handed’, ‘left-handed’.Irish : see Carr.This surname has also absorbed examples of German Kehr.
Surname or Lastname
English
English : according to Reaney this is a nickname from an unattested Old English word cybbe meaning ‘clumsy’ or ‘thickset’. Reaney’s speculation is apparently based on taking the Middle English word kibble ‘cudgel’ as a diminutive of an unattested Old English word. Corresponding personal names have been postulated for the place names Kibworth (‘enclosure of a man called Cybba’) and Kibblesworth (‘enclosure of a man called Cybbel’); so, in theory, the surname could be a reflex of these Old English personal names.North German : nickname for a cantankerous person, from Middle Low German, Middle High German kiven ‘to quarrel’.
Surname or Lastname
English
English : unexplained. It may be a variant of a medieval name, Preville, a habitational name from a Norman place named with the elements pré ‘meadow’ + ville ‘settlement’. However, this theory is not supported by evidence of early forms.
Surname or Lastname
English
English : from a short form of the personal names Giles, Julian, or William. In theory the name would have a soft initial when derived from the first two of these, and a hard one when from William or from the other possibilities discussed in 2–4 below. However, there has been much confusion over the centuries.Northern English : topographic name for someone who lived by a ravine or deep glen, Middle English gil(l), Old Norse gil ‘ravine’.Scottish and Irish : reduced Anglicized form of Gaelic Mac Gille (Scottish), Mac Giolla (Irish), patronymics from an occupational name for a servant or a short form of the various personal names formed by attaching this element to the name of a saint. See McGill. The Old Norse personal name Gilli is probably of this origin, and may lie behind some examples of the name in northern England.Scottish and Irish : reduced Anglicized form of Gaelic Mac An Ghoill (see Gall 1).Norwegian : habitational name from any of three farmsteads in western Norway named Gil, from Old Norse gil ‘ravine’.Dutch : cognate of Giles.Jewish (Israeli) : ornamental name from Hebrew gil ‘joy’.German : from a vernacular short form of the medieval personal name Aegidius (see Gilger).Indian (Panjab) : Sikh name, probably from Panjabi gil ‘moisture’, also meaning ‘prosperity’. There is a Jat tribe that bears this name; the Ramgarhia Sikhs also have a clan called Gill.
Surname or Lastname
English (mainly Gloucestershire), Dutch, and German (also Türk)
English (mainly Gloucestershire), Dutch, and German (also Türk) : from Middle English, Old French turc, Middle High and Low German Turc ‘Turk’, from Turkish türk. In theory this could be an ethnic name but, both in England and northwest Europe, it is generally a nickname for a person with black hair and a swarthy complexion or a cruel, rowdy, or unruly person. The Dutch and German surname also represents a house name, derived from the use of a picture of a Turk as a house sign. It is also found as a nickname for someone who had taken part in the wars against the Turks.English : from a medieval personal name, a back-formation from Turkel, misanalyzed as containing the Old French diminutive suffix -el.Scottish : reduced Anglicized form of Gaelic Mac Tuirc, a patronymic from the byname Torc ‘boar’.Jewish (Ashkenazic) : ethnic name denoting someone from Turkey or anywhere in the Ottoman Empire, or a nickname for someone thought to resemble a Turk.Americanized form of the Greek ethnic name Tourkos ‘Turk’. See also Turco.
QUEUEING THEORY
QUEUEING THEORY
Male
Russian
(Яша) Pet form of Russian Yakov, YASHA means "supplanter."
Surname or Lastname
English
English : from Old English dēmung ‘judgement’, ‘act of judging’, hence a metonymic occupational name for a judge or for an arbiter of minor disputes. Compare Deemer and Deem.
Male
Croatian
, man, warrior.
Female
English
Variant spelling of English Sharmaine, SHARMAIN means "sing."
Boy/Male
Indian, Punjabi, Sikh
Embodiment of Courage
Boy/Male
Arabic
Endurance; Durability; Strength; Worshippers
Boy/Male
Arabic, Muslim
Abu Salih as Saman Az-ziyat had this Name; Narrator of Hadith
Girl/Female
Muslim
Example, Copy, Torch, Light, Lightened, Sparkling, Shining
Girl/Female
American, British, Chinese, Christian, English, French, German, Indian, Latin
Second; To Open Up; Opening of Flowers in Spring
Surname or Lastname
English
English : unexplained.
QUEUEING THEORY
QUEUEING THEORY
QUEUEING THEORY
QUEUEING THEORY
QUEUEING THEORY
n.
A believer in the theory of vitalism; -- opposed to physicist.
a.
Pertaining to, or involving, vitalism, or the theory of a special vital principle.
n.
An exposition of the general or abstract principles of any science; as, the theory of music.
v. t.
To be at the basis of; to form the foundation of; to support; as, a doctrine underlying a theory.
n.
The change of one species into another, which is assumed to take place in any development theory of life; transformism.
n.
A supposed collection of particles of very subtile matter, endowed with a rapid rotary motion around an axis which was also the axis of a sun or a planet. Descartes attempted to account for the formation of the universe, and the movements of the bodies composing it, by a theory of vortices.
a.
Of or pertaining to volcanoes; specifically, relating to the geological theory of the Vulcanists, or Plutonists.
p. pr. & vb. n.
of Queen
n.
Any one of several kinds of apples, as summer queening, scarlet queening, and early queening. An apple called the queening was cultivated in England two hundred years ago.
n.
A doctrine, or scheme of things, which terminates in speculation or contemplation, without a view to practice; hypothesis; speculation.
n.
The science, as distinguished from the art; as, the theory and practice of medicine.
p. pr. & vb. n.
of Query
pl.
of Theory
n.
One who advocates the undulatory theory of light.
n.
A plan or theory something to be done; a design; a project; as, to form a scheme.
n.
The theory or practice of living upon vegetables and fruits.
v. i.
To form a theory or theories; to form opinions solely by theory; to speculate.
n.
The philosophical explanation of phenomena, either physical or moral; as, Lavoisier's theory of combustion; Adam Smith's theory of moral sentiments.
p. pr. & vb. n.
of Quell
n.
The act or product of theorizing; the formation of a theory or theories; speculation.