The G/M/C/K,T queuing system in terms of queuing theory
Such a system is an advanced case of
M/M/C/K,T queuing system.
In some particular case, the
G/M/C/K,T queuing system can represent a retrial queuing system.
Entities also arrive at a common queue with
FIFO discipline as a Poisson process.
The queue capacity is limited with
K waiting places.
The queue timeout (maximum waiting time) is exponentially distributed with
T mean value.
Entities from the queue are distributed between
C servers.
The service time value of all servers is exponentially distributed.
Free server is selected randomly.
The considered queuing system model represents already real objects.
The difference from the
M/M/C/K,T queuing system is that the entities rejected from the queue due to a timeout are split into two flows.
The entities of the first one are destroyed.
This simulates the loss of clients that don't want to try again to get service again.
The second flow entities are delayed for a while before being sent back to the queue.
This simulates the attempt of clients to get service again.
After some delay, these entities are mixed with newly arrived entities and passed together to the queue.
So, the mixed flow entering the queue is non-Poisson process, and, therefore, the designation of this system is
G/M/C/K,T queue, where
G stands for the general distribution.
The characteristics under study are the
queue probability,
mean waiting time and
mean queue length.
Since free server selection rule does not affect these characteristics, the selection rule, in general, can be any.