Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: ,  study a MAP/PH/1 queue with two classes of customers and discretionary priority. There are two stages of service for the low-priority customer. The server adopts the preemptive priority discipline at the first stage and adopts the nonpreemptive priority discipline at the second stage. Such a queueing system can be modelled into a quasi-birth-and-death (QBD) process. But there is no general solution for this QBD process since the generator matrix has a block structure with an infinite number of blocks and each block has infinite dimensions.  present an approach to derive the bound for the high-priority queue length. It guarantees that the probabilities of ignored states are within a given error bound, so that the system can be modelled into a QBD process where the block elements of the generator matrix have finite dimensions. Sojourn time distributions of both high and low priority customers are obtained.
['Ning Zhao', 'Yaya Guo', 'Zhaotong Lian', 'Mengchang Wang']
I am writing a research paper on a idea Analysis of a MAP/PH/1 queue with discretionary priority
[{"from": "human", "value": "I am writing a research paper on a idea Analysis of a MAP/PH/1 queue with discretionary priority"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: ,  study a MAP/PH/1 queue with two classes of customers and discretionary priority. There are two stages of service for the low-priority customer. The server adopts the preemptive priority discipline at the first stage and adopts the nonpreemptive priority discipline at the second stage. Such a queueing system can be modelled into a quasi-birth-and-death (QBD) process. But there is no general solution for this QBD process since the generator matrix has a block structure with an infinite number of blocks and each block has infinite dimensions.  present an approach to derive the bound for the high-priority queue length. It guarantees that the probabilities of ignored states are within a given error bound, so that the system can be modelled into a QBD process where the block elements of the generator matrix have finite dimensions. Sojourn time distributions of both high and low priority customers are obtained."}]