The mathematical model of an two-phases-service M/M/1/N queuing system with the server breakdown and multiple vacations was realized and established in the Graduate Employment Services system. Secondly, equations of steady-state probability were derived by applying the Markov process theory. Then, we obtained matrix form solution of steady-state probability by using blocked matrix method. Final...

While vacation processes are considered to be ordinary behavior for servers, the study of queueing networks with server vacations is limited, interesting, and challenging. In this paper, we provide a unified and effective method of functional analysis for the study of a supermarket model with server multiple vacations. Firstly, we analyze a supermarket model of N identical servers with server m...

We investigate Gaver’s parallel system attended by a cold standby unit and a repairman with multiple vacations. By analysing the spectral distribution of the system operator and taking into account the irreducibility of the semigroup generated by the system operator we prove that the dynamic solution converges strongly to the steady state solution. Thus we obtain asymptotic stability of the dyn...