Steady-State Convergence of the Continuous-Time Routing System with General Distributions in Heavy Traffic
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917968613474304 |
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| author | Guang, Jin Xu, Yaosheng Dai, J. G. |
| author_facet | Guang, Jin Xu, Yaosheng Dai, J. G. |
| contents | This paper examines a continuous-time routing system with general interarrival and service time distributions, operating under the join-the-shortest-queue and power-of-two-choices policies. Under a weaker set of assumptions than those commonly found in the literature, we prove that the scaled steady-state queue length at each station converges weakly to an identical exponential random variable in heavy traffic. Specifically, our results hold under the assumption of the $(2 + δ_0)$th moment for the interarrival and service distributions with some $δ_0 > 0$. The proof leverages the Palm version of the basic adjoint relationship (BAR) as a key technique. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_10876 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Steady-State Convergence of the Continuous-Time Routing System with General Distributions in Heavy Traffic Guang, Jin Xu, Yaosheng Dai, J. G. Probability This paper examines a continuous-time routing system with general interarrival and service time distributions, operating under the join-the-shortest-queue and power-of-two-choices policies. Under a weaker set of assumptions than those commonly found in the literature, we prove that the scaled steady-state queue length at each station converges weakly to an identical exponential random variable in heavy traffic. Specifically, our results hold under the assumption of the $(2 + δ_0)$th moment for the interarrival and service distributions with some $δ_0 > 0$. The proof leverages the Palm version of the basic adjoint relationship (BAR) as a key technique. |
| title | Steady-State Convergence of the Continuous-Time Routing System with General Distributions in Heavy Traffic |
| topic | Probability |
| url | https://arxiv.org/abs/2405.10876 |