The first and second parameters for the Kendall's notation may have a
G value, which stands for General distribution, see here.
But what does that mean? What is a general distribution?
Queueing theory uses Kendall's notation, as you described. There are three components describing the behavior of a queue:
Generally general case
In the most general case, the behavior of a queue would be described as G/G/c where G is an unknown rate of customer arrivals, with an unknown service time distribution, G, (which is NOT necessarily the same as the process that characterizes arrivals), and c is an integer value greater than or equal to one.
In such general terms, it doesn't make much sense! It is more accessible to start with a specific queue behavior, for example, the performance of a fixed hard disk-drive (i.e. DASD, or direct access storage device).
DASD performance is modeled most accurately as an M/G/1 queue. M means that customers, or requests for disk access, behave according to a Poisson process. This is referred to as a stochastic, or Markov process, thus the use of "M". The rate at which the disk drive is able to meet these requests for service is unknown. Since job service times can have an arbitrary distribution, this is designated by "G" for "general". Finally, if there is only one disk-drive, c = 1.
Let's consider another example, where customers arrive randomly (according to a Poisson process), with exponentially distributed service times. There are multiple servers. This would be described as an M/M/c queue.
This is the typical situation at Walmart, during the night shift (with few cashiers on duty), or at a bank with tellers, or when making a phone call for customer support. Customers arrive randomly (M). The time required to check out their groceries or answer their question is also random (M) e.g. when grocery queues don't have a "10 items or less" configuration for some checkers. Meanwhile, there are a fixed number of cashiers or telephone support staff on duty, we'll say five. This would be an M/M/5 queue.