Retrials in Loss Systems: Mean-Field Analysis, Erlang Bounds, and Power-of-d Comparison
Abstract
We consider a system of N parallel, homogeneous servers, each with finite capacity C. Jobs requiring one unit of capacity arrive according to a Poisson process with total rate Nλ and have exponential service times with rate μ. We study a decentralized random--retrial policy with d attempts: upon arrival, a job is assigned to a uniformly chosen server; if the server is full, the job is reassigned to another uniformly chosen server, for at most d attempts; if all d attempts fail, the job is rejected. In the mean-field limit, we prove that the stationary blocking probability is characterized by the unique solution of a fixed-point equation involving the Erlang-B loss function, and we establish global convergence of the fluid model to this equilibrium. We also compare the mean-field stationary blocking probability with the analogous quantity in the power-of-d model under the same parameters (C,λ,μ). For the same d, we show, via coupling techniques, that the blocking probability under power-of-d is always less than or equal to the blocking under retrial-of-d; but if we consider d and d̃ with d̃>d, then the retrial-of-d̃ policy achieves a strictly lower blocking than the power-of-d policy when ρ=λ/μ is sufficiently large. Moreover we show that for some specific cases, like C=2, d=2 and d̃=3, it occurs for all ρ>0, not only for ρ sufficiently large. We complement the analysis with simulations that estimate the load level above which retrial-of-d̃ outperforms power-of-d in terms of blocking.
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BibTeX
@misc{cuesta2026retrials,
title = {{Retrials in Loss Systems: Mean-Field Analysis, Erlang Bounds, and Power-of-d Comparison}},
author = {D Cuesta and M Jonckheere and B J Prabhu and O Brun},
howpublished = {HAL},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.06267},
eprint = {2611.06267},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05852014v1},
}
RIS
TY - UNPB
TI - Retrials in Loss Systems: Mean-Field Analysis, Erlang Bounds, and Power-of-d Comparison
AU - D Cuesta
AU - M Jonckheere
AU - B J Prabhu
AU - O Brun
PY - 2026
DA - 2026/11/04
PB - HAL
DO - 10.48550/arxiv.2611.06267
UR - https://hal.science/hal-05852014v1
AB - We consider a system of N parallel, homogeneous servers, each with finite capacity C. Jobs requiring one unit of capacity arrive according to a Poisson process with total rate Nλ and have exponential service times with rate μ. We study a decentralized random--retrial policy with d attempts: upon arrival, a job is assigned to a uniformly chosen server; if the server is full, the job is reassigned to another uniformly chosen server, for at most d attempts; if all d attempts fail, the job is rejected. In the mean-field limit, we prove that the stationary blocking probability is characterized by the unique solution of a fixed-point equation involving the Erlang-B loss function, and we establish global convergence of the fluid model to this equilibrium. We also compare the mean-field stationary blocking probability with the analogous quantity in the power-of-d model under the same parameters (C,λ,μ). For the same d, we show, via coupling techniques, that the blocking probability under power-of-d is always less than or equal to the blocking under retrial-of-d; but if we consider d and d̃ with d̃>d, then the retrial-of-d̃ policy achieves a strictly lower blocking than the power-of-d policy when ρ=λ/μ is sufficiently large. Moreover we show that for some specific cases, like C=2, d=2 and d̃=3, it occurs for all ρ>0, not only for ρ sufficiently large. We complement the analysis with simulations that estimate the load level above which retrial-of-d̃ outperforms power-of-d in terms of blocking.
ER -