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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 (meaning arbitrary) distribution and service times have a (different) general distribution. [1] The evolution of the queue can be described by the ...
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).
M/G/1 queue. In queueing theory, a discipline within the mathematical theory of probability, an M/G/1 queue is a queue model where arrivals are M arkovian (modulated by a Poisson process), service times have a G eneral distribution and there is a single server. [1] The model name is written in Kendall's notation, and is an extension of the M/M ...
The stationary distribution is the limiting distribution for large values of t. Various performance measures can be computed explicitly for the M/M/1 queue. We write ρ = λ/μ for the utilization of the buffer and require ρ < 1 for the queue to be stable. ρ represents the average proportion of time which the server is occupied.
G/M/1 queue. 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 times have a general (meaning arbitrary) distribution and service times for each job have an exponential distribution. [1] The system is described in Kendall's notation where the ...
Markovian arrival process. 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]
In the study of queue networks one typically tries to obtain the equilibrium distribution of the network, although in many applications the study of the transient state is fundamental. Queueing theory is the mathematical study of waiting lines, or queues. [1] A queueing model is constructed so that queue lengths and waiting time can be ...
In probability theory and statistics, the exponential distribution or negative exponential distribution is the probability distribution of the distance between events in a Poisson point process, i.e., a process in which events occur continuously and independently at a constant average rate; the distance parameter could be any meaningful mono-dimensional measure of the process, such as time ...