Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: For the M/G/1 model,  look into a preemptive priority scheme in which the priority level is decided by a lottery. Such a scheme has no effect on the mean waiting time in the non-preemptive case (in comparison with the First Come First Served (FCFS) regime, for example). This is not the case when priority comes with preemption.  derived the resulting mean waiting time (which is invariant with respect to the lottery performed) and show that it lies beten the corresponding means under the FCFS and the Last Come First Served with Preemption Resume (LCFS-PR) (or equivalently, the Egalitarian Processor Sharing (EPS)) schemes.  also derive an expression for the Laplace-Stieltjes transform for the time in the system in this model. Finally,  show how this priority scheme may lead to an improvement in the utilization of the server when customer decide whether or not to join.
['Moshe Haviv']
I am writing a research paper on a idea The M/G/1 queueing model with preemptive random priorities
[{"from": "human", "value": "I am writing a research paper on a idea The M/G/1 queueing model with preemptive random priorities"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: For the M/G/1 model,  look into a preemptive priority scheme in which the priority level is decided by a lottery. Such a scheme has no effect on the mean waiting time in the non-preemptive case (in comparison with the First Come First Served (FCFS) regime, for example). This is not the case when priority comes with preemption.  derived the resulting mean waiting time (which is invariant with respect to the lottery performed) and show that it lies beten the corresponding means under the FCFS and the Last Come First Served with Preemption Resume (LCFS-PR) (or equivalently, the Egalitarian Processor Sharing (EPS)) schemes.  also derive an expression for the Laplace-Stieltjes transform for the time in the system in this model. Finally,  show how this priority scheme may lead to an improvement in the utilization of the server when customer decide whether or not to join."}]