Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  develop an algorithm for computing the (exact) cumulative distribution function of the time-dependent workload in a piecewise-stationary Mt/Gt/1 queue with a work-conserving service discipline and general service-time distributions, where service times are determined at arrival instants. The t subscripts indicate that the arrival rate and the general service-time distribution may change with time, but  allow changes only at finitely many time points. The algorithm is based on numerical transform inversion, using the classical Takacs double-transform of the transient workload in an M/G/1 queue recursively over the successive stationary intervals. In particular,  apply our recently developed Fourier-series-based inversion algorithms for two-dimensional transforms and nested one-dimensional transforms.  also do additional work to greatly speed up the computation while tightly controlling the error. As a consequence, the computation time grows only quadratically with the number of intervals. The algo...
['Gagan L. Choudhury', 'David M. Lucantoni', 'Ward Whitt']
I am writing a research paper on a idea Numerical Solution of Piecewise-Stationary Mt/Gt/1 Queues
[{"from": "human", "value": "I am writing a research paper on a idea Numerical Solution of Piecewise-Stationary Mt/Gt/1 Queues"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  develop an algorithm for computing the (exact) cumulative distribution function of the time-dependent workload in a piecewise-stationary Mt/Gt/1 queue with a work-conserving service discipline and general service-time distributions, where service times are determined at arrival instants. The t subscripts indicate that the arrival rate and the general service-time distribution may change with time, but  allow changes only at finitely many time points. The algorithm is based on numerical transform inversion, using the classical Takacs double-transform of the transient workload in an M/G/1 queue recursively over the successive stationary intervals. In particular,  apply our recently developed Fourier-series-based inversion algorithms for two-dimensional transforms and nested one-dimensional transforms.  also do additional work to greatly speed up the computation while tightly controlling the error. As a consequence, the computation time grows only quadratically with the number of intervals. The algo..."}]