Abstract We present a heavy traffic analysis of a single-server polling model, with the special features of retrials and glue periods. The combination of these features in a polling model typically occurs in certain optical networking models, and in models where customers have a reservation period just before their service period. Just before the server arrives at a station there is some deterministic glue period. Customers (both new arrivals and retrials) arriving at the station during this glue period will be served during the visit of the server. Customers arriving in any other period leave immediately and will retry after an exponentially distributed time. As this model defies a closed-form expression for the queue length distributions, our main focus is on their heavy-traffic asymptotics, both at embedded time points (beginnings of glue periods, visit periods, and switch periods) and at arbitrary time points. We obtain closed-form expressions for the limiting scaled joint queue length distribution in heavy traffic. We show that these results can be used to accurately approximate the performance of the system for the complete spectrum of load values by use of interpolation approximations.

中文翻译：

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具有重试和粘合期的轮询模型的繁忙流量分析

摘要 我们提出了单服务器轮询模型的大流量分析，具有重试和粘合期的特殊特征。轮询模型中这些功能的组合通常出现在某些光网络模型中，以及客户在其服务期之前具有预订期的模型中。就在服务器到达站点之前，有一些确定性的粘合期。在此胶水期间到站的客户（新到站和重试）将在服务器访问期间得到服务。在任何其他时间段到达的客户会立即离开，并会在指数分布的时间后重试。由于该模型不符合队列长度分布的封闭形式表达式，因此我们主要关注它们的大流量渐近性，在嵌入时间点（粘合期、访问期和切换期的开始）和任意时间点。我们获得了繁忙交通中限制缩放联合队列长度分布的封闭形式表达式。我们表明，通过使用插值近似，这些结果可用于准确地近似系统在负载值的完整频谱上的性能。