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  2. Jackson network - Wikipedia

    en.wikipedia.org/wiki/Jackson_network

    A generalized Jackson network allows renewal arrival processes that need not be Poisson processes, and independent, identically distributed non-exponential service times. In general, this network does not have a product-form stationary distribution, so approximations are sought. [13]

  3. Burke's theorem - Wikipedia

    en.wikipedia.org/wiki/Burke's_theorem

    In queueing theory, a discipline within the mathematical theory of probability, Burke's theorem (sometimes the Burke's output theorem [1]) is a theorem (stated and demonstrated by Paul J. Burke while working at Bell Telephone Laboratories) asserting that, for the M/M/1 queue, M/M/c queue or M/M/∞ queue in the steady state with arrivals is a Poisson process with rate parameter λ:

  4. Queueing theory - Wikipedia

    en.wikipedia.org/wiki/Queueing_theory

    [6] [7] For an example of the notation, the M/M/1 queue is a simple model where a single server serves jobs that arrive according to a Poisson process (where inter-arrival durations are exponentially distributed) and have exponentially distributed service times (the M denotes a Markov process).

  5. M/G/1 queue - Wikipedia

    en.wikipedia.org/wiki/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 Markovian (modulated by a Poisson process), service times have a General distribution and there is a single server. [1]

  6. M/D/1 queue - Wikipedia

    en.wikipedia.org/wiki/M/D/1_queue

    Arrivals occur at rate λ according to a Poisson process and move the process from state i to i + 1. Service times are deterministic time D (serving at rate μ = 1/D). A single server serves entities one at a time from the front of the queue, according to a first-come, first-served discipline. When the service is complete the entity leaves the ...

  7. Renewal theory - Wikipedia

    en.wikipedia.org/wiki/Renewal_theory

    Renewal theory is the branch of probability theory that generalizes the Poisson process for arbitrary holding times. Instead of exponentially distributed holding times, a renewal process may have any independent and identically distributed (IID) holding times that have finite mean. A renewal-reward process additionally has a random sequence of ...

  8. M/M/c queue - Wikipedia

    en.wikipedia.org/wiki/M/M/c_queue

    In queueing theory, a discipline within the mathematical theory of probability, the M/M/c queue (or Erlang–C model [1]: 495 ) is a multi-server queueing model. [2] 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. [3]

  9. M/M/∞ queue - Wikipedia

    en.wikipedia.org/wiki/M/M/%E2%88%9E_queue

    An M/M/∞ queue is a stochastic process whose state space is the set {0,1,2,3,...} where the value corresponds to the number of customers currently being served. Since, the number of servers in parallel is infinite, there is no queue and the number of customers in the systems coincides with the number of customers being served at any moment.

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