Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A class of stochastic processes known as semi-martingale reflecting Brownian motions SRBMs is often used to approximate the dynamics of heavily loaded queueing networks. In two influential papers, Bramson [Bramson M 1998 State space collapse with applications to heavy-traffic limits for multiclass queueing networks. Queueing Systems 30:89--148] and Williams [Williams RJ 1998b Diffusion approximations for open multiclass queueuing networks: Sufficient conditions involving state space collapse. Queueing Systems 30:27--88] laid out a general and structured approach for proving the validity of such heavy-traffic approximations, in which an SRBM is obtained as a diffusion limit from a sequence of suitably normalized workload processes. Hover, for multiclass networks it is still not known in general whether the steady-state distribution of the SRBM provides a valid approximation for the steady-state distribution of the original network.   study the case of queue-ratio disciplines and provide a set of sufficient conditions under which the above question can be ansred in the affirmative. In addition to standard assumptions made in the literature towards the stability of the pre-and post-limit processes and the existence of diffusion limits,  add a requirement that solutions to the fluid model are attracted to the invariant manifold at a linear rate. For the special case of static-priority networks such linear attraction is known to hold under certain conditions on the network primitives. The analysis elucidates interesting connections beten stability of the pre-and post-limit processes, their respective fluid models and state-space collapse, and identifies the respective roles played by all of the above in establishing validity of heavy-traffic steady-state approximations.
['Itai Gurvich']
I am writing a research paper on a idea Validity of Heavy-Traffic Steady-State Approximations in Multiclass Queueing Networks: The Case of Queue-Ratio Disciplines
[{"from": "human", "value": "I am writing a research paper on a idea Validity of Heavy-Traffic Steady-State Approximations in Multiclass Queueing Networks: The Case of Queue-Ratio Disciplines"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A class of stochastic processes known as semi-martingale reflecting Brownian motions SRBMs is often used to approximate the dynamics of heavily loaded queueing networks. In two influential papers, Bramson [Bramson M 1998 State space collapse with applications to heavy-traffic limits for multiclass queueing networks. Queueing Systems 30:89--148] and Williams [Williams RJ 1998b Diffusion approximations for open multiclass queueuing networks: Sufficient conditions involving state space collapse. Queueing Systems 30:27--88] laid out a general and structured approach for proving the validity of such heavy-traffic approximations, in which an SRBM is obtained as a diffusion limit from a sequence of suitably normalized workload processes. Hover, for multiclass networks it is still not known in general whether the steady-state distribution of the SRBM provides a valid approximation for the steady-state distribution of the original network.   study the case of queue-ratio disciplines and provide a set of sufficient conditions under which the above question can be ansred in the affirmative. In addition to standard assumptions made in the literature towards the stability of the pre-and post-limit processes and the existence of diffusion limits,  add a requirement that solutions to the fluid model are attracted to the invariant manifold at a linear rate. For the special case of static-priority networks such linear attraction is known to hold under certain conditions on the network primitives. The analysis elucidates interesting connections beten stability of the pre-and post-limit processes, their respective fluid models and state-space collapse, and identifies the respective roles played by all of the above in establishing validity of heavy-traffic steady-state approximations."}]