Multiserver Loss Systems with Subscribers

• 成果类型: Article
• 署名作者: Randhawa, Ramandeep S.; Kumar, Sunil
• 署名单位: University of Texas System; University of Texas Austin; Stanford University
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.1080.0350
• 发表日期: 2009
• 页码: 142-179
• 关键词: diffusion approximations; networks; LIMITS

摘要

We study a multiserver loss system with two kinds of customers: subscribers and infrequent users. We model the infrequent users' requests for service by a Poisson process. However, noting that the Poisson process is unable to capture repeated interactions as well as retrials, we propose a Markovian on-off-hold model for the subscribers' requests for service that takes into account retrials by subscribers denied service. We analyze this system in an asymptotic regime where the number of subscribers and the arrival rate of the Poisson stream, and consequently the number of servers, grow without bound. In this regime, we identify and prove convergence to diffusion limits for the system. We also prove the convergence of the invariant distributions to the invariant distribution of the limiting diffusions.