Related Research Articles
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 a branch of operations research because the results are often used when making business decisions about the resources needed to provide a service.
In queueing theory, a discipline within the mathematical theory of probability, the Pollaczek–Khinchine formula states a relationship between the queue length and service time distribution Laplace transforms for an M/G/1 queue. The term is also used to refer to the relationships between the mean queue length and mean waiting/service time in such a model.
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 server, where arrivals are determined by a Poisson process and job service times have an exponential distribution. The model name is written in Kendall's notation. The model is the most elementary of queueing models and an attractive object of study as closed-form expressions can be obtained for many metrics of interest in this model. An extension of this model with more than one server is the M/M/c queue.
In queueing theory, a discipline within the mathematical theory of probability, Kingman's formula also known as the VUT equation, is an approximation for the mean waiting time in a G/G/1 queue. The formula is the product of three terms which depend on utilization (U), variability (V) and service time (T). It was first published by John Kingman in his 1961 paper The single server queue in heavy traffic. It is known to be generally very accurate, especially for a system operating close to saturation.
In probability theory, lumpability is a method for reducing the size of the state space of some continuous-time Markov chains, first published by Kemeny and Snell.
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 components can be written as a product of the metric across the different components. Using capital Pi notation a product-form solution has algebraic form
In queueing theory, a discipline within the mathematical theory of probability, the arrival theorem states that "upon arrival at a station, a job observes the system as if in steady state at an arbitrary instant for the system without that job."
In queueing theory, a discipline within the mathematical theory of probability, quasireversibility is a property of some queues. The concept was first identified by Richard R. Muntz and further developed by Frank Kelly. Quasireversibility differs from reversibility in that a stronger condition is imposed on arrival rates and a weaker condition is applied on probability fluxes. For example, an M/M/1 queue with state-dependent arrival rates and state-dependent service times is reversible, but not quasireversible.
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.
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 for service by numerous servers and joined before departure. The model is often used for parallel computations or systems where products need to be obtained simultaneously from different suppliers. The key quantity of interest in this model is usually the time taken to service a complete job. The model has been described as a "key model for the performance analysis of parallel and distributed systems." Few analytical results exist for fork–join queues, but various approximations are known.
In queueing theory, a discipline within the mathematical theory of probability, the M/M/c queue is a multi-server queueing model. In Kendall's notation it describes a system where arrivals form a single queue and are governed by a Poisson process, there are c servers, and job service times are exponentially distributed. It is a generalisation of the M/M/1 queue which considers only a single server. The model with infinitely many servers is the M/M/∞ queue.
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 nodes to be determined. Mitrani notes "if the network is stable, the traffic equations are valid and can be solved."
In queueing theory, a discipline within the mathematical theory of probability, an M/G/1 queue is a queue model where arrivals are Markovian, service times have a General distribution and there is a single server. The model name is written in Kendall's notation, and is an extension of the M/M/1 queue, where service times must be exponentially distributed. The classic application of the M/G/1 queue is to model performance of a fixed head hard disk.
In queueing theory, a discipline within the mathematical theory of probability, a fluid queue is a mathematical model used to describe the fluid level in a reservoir subject to randomly determined periods of filling and emptying. The term dam theory was used in earlier literature for these models. The model has been used to approximate discrete models, model the spread of wildfires, in ruin theory and to model high speed data networks. The model applies the leaky bucket algorithm to a stochastic source.
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 immediate service and does not wait. In Kendall's notation it describes a system where arrivals are governed by a Poisson process, there are infinitely many servers, so jobs do not need to wait for a server. Each job has an exponentially distributed service time. It is a limit of the M/M/c queue model where the number of servers c becomes very large.
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 calls arriving may find no route available to their destination. These calls are lost from the network, hence the name loss networks.
In probability theory, the matrix analytic method is a technique to compute the stationary probability distribution of a Markov chain which has a repeating structure and a state space which grows unboundedly in no more than one dimension. Such models are often described as M/G/1 type Markov chains because they can describe transitions in an M/G/1 queue. The method is a more complicated version of the matrix geometric method and is the classical solution method for M/G/1 chains.
In queueing theory, a discipline within the mathematical theory of probability, the flow-equivalent server method is a divide-and-conquer method to solve product form queueing networks inspired by Norton's theorem for electrical circuits. The network is successively split into two, one portion is reconfigured to a closed network and evaluated.
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 structure. The method was developed "largely by Marcel F. Neuts and his students starting around 1975."
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 length. It was introduced by Václav E. Beneš in 1963.
References
- ↑ Harrison, Peter G. (1986). "An Enhanced Approximation by Pair-Wise Analysis of Servers for Time Delay Distributions in Queueing Networks". IEEE Transactions on Computers. Institute of Electrical and Electronics Engineers. 35 (1 (January)): 54–61. doi:10.1109/TC.1986.1676657. S2CID 41389350.
- ↑ Peter G. Harrison at the Mathematics Genealogy Project
- ↑ "Harrison's Personal Home Page". Imperial College London.
- ↑ ""Turning Back Time - What Impact on Performance?" lecturer biography". bcs.org. British Computer Society . Retrieved 17 March 2009.
- ↑ Gelenbe, Erol (2000). System performance evaluation: methodologies and applications. CRC Press. p. 330. ISBN 0-8493-2357-6.
- ↑ "Peter Harrison biography". doc.ic.ac.uk. Analysis, Engineering, Simulation & Optimization of Performance group at Imperial College.
- ↑ Field, Anthony J.; Harrison, Peter G. (1988). Functional programming . Addison-Wesley. ISBN 9780201192490.
- ↑ Harrison, Peter G.; Patel, Naresh M. (1992). Performance Modelling of Communication Networks and Computer Architectures . Addison-Wesley. ISBN 9780201544190.
- ↑ "Professor Peter Harrison's Publications". Imperial College London. Retrieved 1 May 2009.
- ↑ "Editorial board of The Computer Journal". Oxford Journals. Archived from the original on 24 May 2011. Retrieved 17 March 2009.
- ↑ "List of Department of Computing, Imperial College staff by Erdős number".
| International | |
|---|---|
| National | |
| Academics | |
| Other | |
