Kendall's notation provides a method for representing a general queue system. Such a queue system will have a set of arrivals with a statistical model, a buffer for the arrivals, a number of servers that have a statistical model for their service time. Such a system might be a telephone call center with calls arriving on average every 10seconds, space for 100 calls to be queued in a buffer, and 20 operators ("servers") who take about 2minutes to deal with each call.

The notation expresses the key properties of the system in the form:



  • A = expresses the arrival time distribution, with M for Poisson arrivals, G for Gaussian arrivals.
  • S = expresses the service time distribution.
  • K = the number of servers.
  • N = system capacity, the number of items in the whole system at capacity. Equivalent to K + buffer size.
  • QD = expresses the queue discipline, LIFO, FIFO or whatever. Sometimes omitted, and assumed to be FIFO.

So a M/M/K/inf/FIFO queue system has Poisson arrivals, exponentially distributed service times, an infinitely large buffer and serves entries in arrival order. More typical is the Erlang Loss System, expressed as M/M/K/K. Here, if an arrival can't be dealt with, it is lost forever.

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