# Category: Queueing theory

Queuing delay
In telecommunication and computer engineering, the queuing delay or queueing delay is the time a job waits in a queue until it can be executed. It is a key component of network delay. In a switched ne
Jyotiprasad Medhi was a professor of statistics at Gauhati University and Institute of Advanced Study in Science and Technology.
Residence time
The residence time of a fluid parcel is the total time that the parcel has spent inside a control volume (e.g.: a chemical reactor, a lake, a human body). The residence time of a set of parcels is qua
Layered queueing network
In queueing theory, a discipline within the mathematical theory of probability, a layered queueing network (or rendezvous network) is a queueing network model where the service time for each job at ea
Queueing theory
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 is generally considered
Palm calculus
In the study of stochastic processes, Palm calculus, named after Swedish teletrafficist Conny Palm, is the study of the relationship between probabilities conditioned on a specified event and time-ave
Erlang (unit)
The erlang (symbol E) is a dimensionless unit that is used in telephony as a measure of offered load or carried load on service-providing elements such as telephone circuits or telephone switching equ
Kelly network
In queueing theory, a discipline within the mathematical theory of probability, a Kelly network is a general multiclass queueing network. In the network each node is quasireversible and the network ha
In probability theory, the ladder height process is a record of the largest or smallest value a given stochastic process has achieved up to the specified point in time. The Wiener-Hopf factorization g
G-network
In queueing theory, a discipline within the mathematical theory of probability, a G-network (generalized queueing network or Gelenbe network) is an open network of G-queues first introduced by Erol Ge
Teletraffic engineering
Teletraffic engineering, telecommunications traffic engineering, or just traffic engineering when in context, is the application of transportation traffic engineering theory to telecommunications. Tel
Matrix geometric method
In probability theory, the matrix geometric method is a method for the analysis of quasi-birth–death processes, continuous-time Markov chain whose transition rate matrices with a repetitive block stru
Product-form solution
In probability theory, a product-form solution is a particularly efficient form of solution for determining some metric of a system with distinct sub-components, where the metric for the collection of
Rational arrival process
In queueing theory, a discipline within the mathematical theory of probability, a rational arrival process (RAP) is a mathematical model for the time between job arrivals to a system. It extends the c
Decomposition method (queueing theory)
In queueing theory, a discipline within the mathematical theory of probability, the decomposition method is an approximate method for the analysis of queueing networks where the network is broken into
Fluid queue
In queueing theory, a discipline within the mathematical theory of probability, a fluid queue (fluid model, fluid flow model or stochastic fluid model) is a mathematical model used to describe the flu
Input queue
In computer 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 in Operating System Scheduling whi
Backpressure routing
In queueing theory, a discipline within the mathematical theory of probability, the backpressure routing algorithm is a method for directing traffic around a queueing network that achieves maximum net
Burke's theorem
In queueing theory, a discipline within the mathematical theory of probability, Burke's theorem (sometimes the Burke's output theorem) is a theorem (stated and demonstrated by while working at Bell Te
Markovian arrival process
In queueing theory, a discipline within the mathematical theory of probability, a Markovian arrival process (MAP or MArP) is a mathematical model for the time between job arrivals to a system. The sim
Gordon–Newell theorem
In queueing theory, a discipline within the mathematical theory of probability, the Gordon–Newell theorem is an extension of Jackson's theorem from open queueing networks to closed queueing networks o
Engset formula
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 after its developer, T. O. Engset.
Quasi-birth–death process
In queueing models, a discipline within the mathematical theory of probability, the quasi-birth–death process describes a generalisation of the birth–death process. As with the birth-death process it
Fluid limit
In queueing theory, a discipline within the mathematical theory of probability, a fluid limit, fluid approximation or fluid analysis of a stochastic model is a deterministic real-valued process which
In 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 is given by Little's law: the arrival rate
Drift plus penalty
In the mathematical theory of probability, the drift-plus-penalty method is used for optimization of queueing networks and other stochastic systems. The technique is for stabilizing a queueing network
Kelly's lemma
In probability theory, Kelly's lemma states that for a stationary continuous time Markov chain, a process defined as the time-reversed process has the same stationary distribution as the forward-time
Ross's conjecture
In queueing theory, a discipline within the mathematical theory of probability, Ross's conjecture gives a lower bound for the average waiting-time experienced by a customer when arrivals to the queue
Balance equation
In probability theory, a balance equation is an equation that describes the probability flux associated with a Markov chain in and out of states or set of states.
Jackson network
In queueing theory, a discipline within the mathematical theory of probability, a Jackson network (sometimes Jacksonian network) is a class of queueing network where the equilibrium distribution is pa
Palm–Khintchine theorem
In probability theory, the Palm–Khintchine theorem, the work of Conny Palm and Aleksandr Khinchin, expresses that a large number of renewal processes, not necessarily Poissonian, when combined ("super
Quasireversibility
In queueing theory, a discipline within the mathematical theory of probability, quasireversibility (sometimes QR) is a property of some queues. The concept was first identified by and further develope
Birth–death process
The birth–death process (or birth-and-death process) is a special case of continuous-time Markov process where the state transitions are of only two types: "births", which increase the state variable
Traffic generation model
A traffic generation model is a stochastic model of the traffic flows or data sources in a communication network, for example a cellular network or a computer network. A packet generation model is a t
Uniformization (probability theory)
In probability theory, uniformization method, (also known as Jensen's method or the randomization method) is a method to compute transient solutions of finite state continuous-time Markov chains, by a
Lindley equation
In probability theory, the Lindley equation, Lindley recursion or Lindley processes is a discrete-time stochastic process An where n takes integer values and: An + 1 = max(0, An + Bn). Processes of th
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 a stochastic process. The model has seen use in
Arrival theorem
In queueing theory, a discipline within the mathematical theory of probability, the arrival theorem (also referred to as the random observer property, ROP or job observer property) states that "upon a
Mean value analysis
In queueing theory, a discipline within the mathematical theory of probability, mean value analysis (MVA) is a recursive technique for computing expected queue lengths, waiting time at queueing nodes
Little's law
In mathematical queueing theory, Little's result, theorem, lemma, law, or formula is a theorem by John Little which states that the long-term average number L of customers in a stationary system is eq
Beneš method
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 to the probability distribution of queue l
Buzen's algorithm
In queueing theory, a discipline within the mathematical theory of probability, Buzen's algorithm (or convolution algorithm) is an algorithm for calculating the normalization constant G(N) in the Gord
Ehrenfest model
The Ehrenfest model (or dog–flea model) of diffusion was proposed by Tatiana and Paul Ehrenfest to explain the second law of thermodynamics. The model considers N particles in two containers. Particle
Lyapunov optimization
This article describes Lyapunov optimization for dynamical systems. It gives an example application to optimal control in queueing networks.
Retrial queue
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 which arrive and find the system busy wait for s
Loss 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 nodes have finite capacity and thus some cal
Queuing Rule of Thumb
The Queuing Rule of Thumb (QROT) is a mathematical formula, known as the queuing constraint equation when it is used to find an approximation of servers required to service a queue. The formula is wri
Processor sharing
Processor sharing or egalitarian processor sharing is a service policy where the customers, clients or jobs are all served simultaneously, each receiving an equal fraction of the service capacity avai
Traffic equations
In queueing theory, a discipline within the mathematical theory of probability, traffic equations are equations that describe the mean arrival rate of traffic, allowing the arrival rates at individual
Heavy traffic approximation
In queueing theory, a discipline within the mathematical theory of probability, a heavy traffic approximation (sometimes heavy traffic limit theorem or diffusion approximation) is the matching of a qu
Method of supplementary variables
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 by David Cox and David George Kendall.
Polling system
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 a set of queues in some order. The model has
Bartlett's theorem
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.
Flow-equivalent server method
In queueing theory, a discipline within the mathematical theory of probability, the flow-equivalent server method (also known as flow-equivalent aggregation technique, Norton's theorem for queueing ne
Queue management system
A queue management system is used to control queues. Queues of people form in various situations and locations in a queue area. The process of queue formation and propagation is defined as queuing the
Spectral expansion solution
In probability theory, the spectral expansion solution method is a technique for computing the stationary probability distribution of a continuous-time Markov chain whose state space is a semi-infinit
BCMP network
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 equilibrium distribution exists. It is named afte
Punctuality
Punctuality is the characteristic of being able to complete a required task or fulfill an obligation before or at a previously designated time. "Punctual" is often used synonymously with "on time". An
Micro-bursting (networking)
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, leading to periods of full line-rate transm
Cumulative flow diagram
A cumulative flow diagram is a tool used in queuing theory. It is an area graph that depicts the quantity of work in a given state, showing arrivals, time in queue, quantity in queue, and departure. C