Search results
Results from the WOW.Com Content Network
In queueing theory, a discipline within the mathematical theory of probability, a Markovian arrival process (MAP or MArP [1]) is a mathematical model for the time between job arrivals to a system. The simplest such process is a Poisson process where the time between each arrival is exponentially distributed. [2] [3]
The system is described in Kendall's notation where the G denotes a general distribution for both interarrival times and service times and the 1 that the model has a single server. [3] [4] Different interarrival and service times are considered to be independent, and sometimes the model is denoted GI/GI/1 to emphasise this.
A M/M/1 queue means that the time between arrivals is Markovian (M), i.e. the inter-arrival time follows an exponential distribution of parameter λ. The second M means that the service time is Markovian: it follows an exponential distribution of parameter μ. The last parameter is the number of service channel which one (1).
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 concept of a Markov arrival process , allowing for dependent matrix-exponential distributed inter-arrival times.
The matrix geometric method and matrix analytic methods have allowed queues with phase-type distributed inter-arrival and service time distributions to be considered. [18] Systems with coupled orbits are an important part in queueing theory in the application to wireless networks and signal processing. [19]
For example, if the renewal process is modelling the numbers of breakdown of different machines, then the holding time represents the time between one machine breaking down before another one does. The Poisson process is the unique renewal process with the Markov property , [ 2 ] as the exponential distribution is the unique continuous random ...
More colloquially, a first passage time in a stochastic system, is the time taken for a state variable to reach a certain value. Understanding this metric allows one to further understand the physical system under observation, and as such has been the topic of research in very diverse fields, from economics to ecology.
Sociography has taken on increasing importance in recent years, as many authors have begun to speak out on issues of race and culture. Although their writing is done without benefit of academic study, it is still considered a valid explication of a given cultural regime.