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- TL;DR Summary
- What is the generator matrix for the following two different Queueing models?

Hello there,

If we have M/M/C/K = M/M/2/2 (where note that the first M stands for memoryless arrival times for the packets (thus described by a Poisson process(lambda)), the second M stands for memoryless service times (i.e. described by an exponentially distributed(mu)), the number 2 for C means that there are two servers handling the packets and the number 2 for K is the maximum size of the queue, which is 2. Note that arrivals to a full queue are simply rejected.

What is the generator matrix (Q) for a system of M/M/2/2? What about for M/M/2/4?

My attempt: I know what is it for M/M/2/4 given that K > C (just included it to explain what I am exactly after), but is there any way to have a canonical form of the generator matrix for M/M/C/C such as M/M/2/2? Any help would be appreciate it.

Thanks for your help in advance

If we have M/M/C/K = M/M/2/2 (where note that the first M stands for memoryless arrival times for the packets (thus described by a Poisson process(lambda)), the second M stands for memoryless service times (i.e. described by an exponentially distributed(mu)), the number 2 for C means that there are two servers handling the packets and the number 2 for K is the maximum size of the queue, which is 2. Note that arrivals to a full queue are simply rejected.

What is the generator matrix (Q) for a system of M/M/2/2? What about for M/M/2/4?

My attempt: I know what is it for M/M/2/4 given that K > C (just included it to explain what I am exactly after), but is there any way to have a canonical form of the generator matrix for M/M/C/C such as M/M/2/2? Any help would be appreciate it.

Thanks for your help in advance