Abstract-In this paper, we study the power efficiency and delay performance of the IEEE 802.3az Energy Efficient Ethernet (EEE) protocol. A new approach is proposed to analyze the M/G/1 queue with the vacation time that is governed by the arrival process and the parameter τ and N of the BTR strategy. Our key idea is to establish the connection between the vacation time and the arrival process to account for their dependency. We first derive the distribution of the number of arrivals during a vacation time based on an event tree of the BTR strategy, from which we obtain the mean vacation time and the power efficiency. Next, from the condition on the number of arrivals at the end of a vacation period, we derive a generalized P-K formula of the mean delay for EEE systems, and prove that the classical P-K formula of the vacation model is only a special case when the vacation time is independent of the arrival process. Our analysis demonstrates that the τ policy and N policy of the BTR strategy are compensating each other. The τ policy ensures the frame delay is bounded when the traffic load is light, while the N policy ensures the queue length at the end of vacation is bounded when the traffic load is heavy. These results, in turn, provide the rules to select appropriate τ and N . Our analytical results are confirmed by simulations.Index Terms-Ethernet, IEEE802.3az, EEE protocol, M/G/1 queue with vacation, P-K formula.

This paper studies an M/G/1 queueing system with a finite waiting room and with server vacation times consisting of periods of time that the server is away from the queue doing additional work. This model has been used in conjunction with a related model to analyze the performance of a processor with a cyclic scheduling algorithm and where, due to finite queueing capacities, losses are a primary concern. Service at the queue is exhaustive, in that a busy period at the queue ends only when the queue is empty. At each termination of a busy period, the server takes an independent vacation. The queue length process is studied using the embedded Markov chain. Using a combination of the supplementary variable and sample biasing techniques, we derive the general queue length distribution of the time continuous process, as well as the blocking probability of the system, due to the finite waiting room in the queue. We also obtain the busy period and waiting time distributions.

Abstract-The three-stage Clos networks remain the most popular solution to many practical switching systems to date. The aim of this paper is to show that the modular structure of Clos networks is invariant with respect to the technological changes. Due to the wavelength routing property of arrayed-waveguide gratings (AWGs), non-blocking and contention-free wavelengthdivision-multiplexing (WDM) switches require that two calls carried by the same wavelength must be connected by separated links; otherwise, they must be carried by different wavelengths. Thus, in addition to the non-blocking condition, the challenge of the design of AWG-based multistage switching networks is to scale down the wavelength granularity and to reduce the conversion range of tunable wavelength converters (TWCs). We devise a logic scheme to partition the WDM switch network into wavelength autonomous cells, and show that the wavelength scalability problem can be solved by recursively reusing similar, but smaller, set of wavelengths in different cells. Furthermore, we prove that the rearrangeably non-blocking (RNB) condition and route assignments in these AWG-based three-stage networks are consistent with that of classical Clos networks. Thus, the optimal AWG-based non-blocking Clos networks also can achieve 100% utilization when all input and output wavelength channels are busy.Index Terms-Clos network, rearrangeably non-blocking (RNB), wavelength-division-multiplexing (WDM), arrayedwaveguide grating (AWG), tunable wavelength converter (TWC)

No abstract

No abstract