Fluctuation analysis of debt based policies for wireless networks with hard delay constraints

Hou et al. have analyzed wireless networks where clients served by an access point require a timely-throughput of packets to be delivered by hard per-packet deadlines and also proved the timely-throughput optimality of certain debt-based policies. However, this is a weak notion of optimality; there might be long time intervals in which a client does not receive any packets, undesirable for real-time applications. Motivated by this, the authors, in an earlier work, introduced a pathwise cost function based on the law of the iterated logarithm, studied in fluctuation theory, which captures the deviation from a steady stream of packet deliveries and showed that a debt-based policy is optimal if the frame length is one. This work extends the analysis of debt-based policies to general frame lengths greater than one, as is important for general applications.