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.