Kendall notation
For the term Kendall notation are causally the works of the English mathematician David George Kendall, who defined a procedure for the classification of maintenance systems. Its characteristics are determined by the use of letters in a certain sequence of letters and numbers - separated by slashes.
The unified description of maintenance systems has the form:
A / B / C [/K /N /xxxx].
The first three parameters go back to Kendall himself and describe with A: Arrival process, distribution of inter-arrival times, which are the times between two arriving jobs or orders. B: operating process, distribution of processing times, neglecting waiting times. C: the number of operating units working in parallel.
For a more flexible description of possible queuing systems, the last three optional parameters were introduced: k: the capacity of the queue i.e. the number of waiting places. N: population for closed queuing systems i.e. the number of all possible orders. xxxx: service strategy, explains the order in which the orders are served.
Arrival process A and service process B are defined by stochastic processes. Regarding the characteristics of these processes, they can be described in different ways. Thereby mean: M, Exponentially distributed, Markov property, D, Deterministic, at regular intervals, general distribution, mean and variance are known respectively and E, Erlang distribution.
Possible operating strategies are: First In First Out( FIFO), Last In First Out( LIFO), Shortest Processing Time (SPT), and Random, random.
If no explicit value is specified for K and N, it is defined as infinite by default.
Example of the application of Kendall notation:
M/M/1: queueing system with 1 queueing unit, arrival and queueing process are exponentially distributed, queueing strategy = FIFO, the number of queues as well as the number of possible orders are each equal to infinity.
M/G/1: also a queueing system with 1 queueing unit, the arrival process is still exponentially distributed, but the queueing process can be specified more precisely as a general distribution with known mean and variance.