Dynamic circuits are well suited for applications that require predictable service with a constant bit rate for a prescribed period of time, such as cloud computing and e-science applications. Past research on upstream transmission in passive optical
networks (PONs) has mainly considered packet-switched traffic and has focused on optimizing packet-level performance metrics, such as reducing mean delay. This study proposes and evaluates a dynamic circuit and packet PON (DyCaPPON) that provides dynamic circuits along with packet-switched service. DyCaPPON provides $(i)$ flexible packet-switched service through dynamic bandwidth allocation in periodic polling cycles, and $(ii)$ consistent circuit service by allocating each active circuit a fixed-duration upstream transmission window during each fixed-duration polling cycle. We analyze circuit-level performance metrics, including the blocking probability of dynamic circuit requests in DyCaPPON through a stochastic knapsack-based analysis. Through this analysis we also determine the bandwidth occupied by admitted circuits. The remaining bandwidth is available for packet traffic and we conduct an approximate analysis of the resulting mean delay of packet traffic. Through extensive numerical evaluations and verifying simulations we demonstrate the circuit blocking and packet delay trade-offs in DyCaPPON.
We study the small deviation probabilities of a family of very smooth self-similar Gaussian processes. The canonical process from the family has the same scaling property as standard Brownian motion and plays an important role in the study of zeros o
f random polynomials. Our estimates are based on the entropy method, discovered in Kuelbs and Li (1992) and developed further in Li and Linde (1999), Gao (2004), and Aurzada et al. (2009). While there are several ways to obtain the result w.r.t. the $L_2$ norm, the main contribution of this paper concerns the result w.r.t. the supremum norm. In this connection, we develop a tool that allows to translate upper estimates for the entropy of an operator mapping into $L_2[0,1]$ by those of the operator mapping into $C[0,1]$, if the image of the operator is in fact a Holder space. The results are further applied to the entropy of function classes, generalizing results of Gao et al. (2010).
