M/M/1 QUEUING MODEL

The M/M/1 queuing model is a queuing model where the arrivals follow a Poisson process, service times are exponentially distributed and there is one server.

The assumption of M/M/1 queuing model are as follows:

  1. The number of customers arriving in a time interval t follows a Poisson Process with parameter λ.
  2. The interval between any two successive arrivals is exponentially distributed with parameter λ.
  3. The time taken to complete a single service is exponentially distributed with parameter μ.
  4. The number of server is one.
  5. Although not explicitly stated both the population and the queue size can be infinity.
  6. The order of service is assumed to be FIFO.

If , the steady state probabilities exist and Pn the number of customers in ...

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