Adversarial queueing network

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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 describing the impact of packet injections on the performance of communication networks. [1] The model was first introduced in 1996. [2]

Queueing theory 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 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 computer science, an online algorithm measures its competitiveness against different adversary models. For deterministic algorithms, the adversary is the same as the adaptive offline adversary. For randomized online algorithms competitiveness can depend upon the adversary model used.

Stochastic process mathematical object usually defined as a collection of random variables

In probability theory and related fields, a stochastic or random process is a mathematical object usually defined as a collection of random variables. Historically, the random variables were associated with or indexed by a set of numbers, usually viewed as points in time, giving the interpretation of a stochastic process representing numerical values of some system randomly changing over time, such as the growth of a bacterial population, an electrical current fluctuating due to thermal noise, or the movement of a gas molecule. Stochastic processes are widely used as mathematical models of systems and phenomena that appear to vary in a random manner. They have applications in many disciplines including sciences such as biology, chemistry, ecology, neuroscience, and physics as well as technology and engineering fields such as image processing, signal processing, information theory, computer science, cryptography and telecommunications. Furthermore, seemingly random changes in financial markets have motivated the extensive use of stochastic processes in finance.

The stability of an adversarial queueing network can be determined by considering a fluid limit. [3]

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 approximates the evolution of a given stochastic process, usually subject to some scaling or limiting criteria.

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In computational complexity theory, a nonelementary problem is a problem that is not a member of the class ELEMENTARY.

In queueing theory, a discipline within the mathematical theory of probability, a G-network is an open network of G-queues first introduced by Erol Gelenbe as a model for queueing systems with specific control functions, such as traffic re-routing or traffic destruction, as well as a model for neural networks. A G-queue is a network of queues with several types of novel and useful customers:

WADS, the Algorithms and Data Structures Symposium, is an international academic conference in the field of computer science, focusing on algorithms and data structures. WADS is held every second year, usually in Canada and always in North America. It is held in alternation with its sister conference, the Scandinavian Symposium and Workshops on Algorithm Theory (SWAT), which is usually held in Scandinavia and always in Northern Europe. Historically, the proceedings of both conferences were published by Springer Verlag through their Lecture Notes in Computer Science series. Springer continues to publish WADS proceedings, but starting in 2016, SWAT proceedings are now published by Dagstuhl through their Leibniz International Proceedings in Informatics.

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.

Fork–join 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 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, mean value analysis (MVA) is a recursive technique for computing expected queue lengths, waiting time at queueing nodes and throughput in equilibrium for a closed separable system of queues. The first approximate techniques were published independently by Schweitzer and Bard, followed later by an exact version by Lavenberg and Reiser published in 1980.

In computational complexity theory, and more specifically in the analysis of algorithms with integer data, the transdichotomous model is a variation of the random access machine in which the machine word size is assumed to match the problem size. The model was proposed by Michael Fredman and Dan Willard, who chose its name "because the dichotomy between the machine model and the problem size is crossed in a reasonable manner."

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In computer science, the Brodal queue is a heap/priority queue structure with very low worst case time bounds: for insertion, find-minimum, meld and decrease-key and for delete-minimum and general deletion. They are the first heap variant to achieve these bounds without resorting to amortization of operational costs. Brodal queues are named after their inventor Gerth Stølting Brodal.

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.

Amos Fiat is an Israeli computer scientist, a professor of computer science at Tel Aviv University. He is known for his work in cryptography, online algorithms, and algorithmic game theory.

In queueing theory, a discipline within the mathematical theory of probability, a layered queueing network is a queueing network model where the service time for each job at each service node is given by the response time of a queueing network. Resources can be nested and queues form along the nodes of the nesting structure. The nesting structure thus defines "layers" within the queueing model.

Peter Ružička Slovak scientist

Peter Ruzicka was a Slovak computer scientist and mathematician who worked in the fields of distributed computing and computer networks. He was a Professor at the Comenius University, Faculty of Mathematics, Physics and Informatics working in several research areas of theoretical computer science throughout his long career.

In probability theory, a transition rate matrix is an array of numbers describing the rate a continuous time Markov chain moves between states.

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 G/G/1 queue represents the queue length in a system with a single server where interarrival times have a general distribution and service times have a (different) general distribution. The evolution of the queue can be described by the Lindley equation.

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 applications in computer networks and telecommunications, manufacturing and road traffic management. The term polling system was coined at least as early as 1968 and the earliest study of such a system in 1957 where a single repairman servicing machines in the British cotton industry was modelled.

Peter Sanders is a German computer scientist who works as a professor of computer science at the Karlsruhe Institute of Technology. His research concerns the design, analysis, and implementation of algorithms and data structures, and he is particularly known for his research on finding shortest paths in road networks.

References

  1. ↑ Sethuraman, J.; Teo, C. P. (2003). "Effective Routing and Scheduling in Adversarial Queueing Networks". Approximation, Randomization, and Combinatorial Optimization.. Algorithms and Techniques (PDF). Lecture Notes in Computer Science. 2764. p. 153. doi:10.1007/978-3-540-45198-3_14. ISBN   978-3-540-40770-6.
  2. ↑ Borodin, A.; Kleinberg, J.; Raghavan, P.; Sudan, M.; Williamson, D. P. (1996). "Adversarial queueing theory". Proceedings of the twenty-eighth annual ACM symposium on Theory of computing – STOC '96. p. 376. doi:10.1145/237814.237984. ISBN   0897917855.
  3. ↑ Gamarnik, D. (1998). "Stability of adversarial queues via fluid models". Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280). p. 60. doi:10.1109/SFCS.1998.743429. ISBN   0-8186-9172-7.
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