Single Server Queueing Model with Multiple Working Vacation and with Breakdown

In our model, we discussed about the queueing model where the server takes Multiple Working Vacation and also get breakdown during service. Customer get in to the organization with parameter λ comes off Poisson process. Service time during multiple working vacation epoch, normal service epoch and vacation epoch are all exponentially distribution with parameters μ
1
, μ
2
and γ respectively. If queue length increases during a working vacation epoch, the server goes to normal busy epoch. If there is no arrival the server takes another vacation is called Multiple Working Vacation. When a server can breakdown while providing service with rate α
0
and α
1
and become unavailable to the customers. After breakdown, it should be repaired with rate ß
0
and ß
1
. This type of model is analyzed by using Matrix Geometric Approach to device probability vectors. From that, we also obtain some performance measurements.