As per Little’s Theorem the average number of customers (N) that arrive can be determined form the equation:
N = λ T , where λ is the customer arrival rate and T is the average service time for a customer.
The queuing system can be classified as per the following convention:
A/S/n – A is the arrival process, S is the service process and n is the number of servers.
Examples of Queuing Systems are:
M/M/1 – This is the simplest type with only 1 server and the arrival and service times are exponentially distributed (Poisson Process). Eg: Arrival of telephone calls to a telephone exchange.
M/D/n – Here there are n servers, the arrival process follows Poisson distribution whereas the service time is deterministic and can be assumed to be fixed for all customers. Eg: Ticket booking counters in a railway station.
G/G/n – This system has n servers but the arrival and service times are both arbitrary.