Constraint-based scheduling algorithm with the non-adjacency requirement for multi-flow AWG switches
Introduction
Power density and dissipation are becoming the major bottleneck in next generation datacenters and routers (McKeown, 2003). People are turning to optics for solutions because sending and switching optical signals consumes significantly lower energy than electronic signals (Bonetto et al., 2009). An arrayed waveguide grating (AWG) (Takahashi et al., 1995; Dragone, 1991) has tremendous advantages in this regard because it is a passive device and consumes little power. For these reasons, AWGs have become the centerpiece of many optical switching architecture proposals (Kachris and Tomkos, 2012).
An N × N AWG operates on N different wavelengths, denoted by {λ0, λ1, …, λN−1}. It uses diffraction grating to route multi-wavelength signals from input ports to output ports. A flow in such a device is defined by a three-tuple−(i,w,o)−where i represents input, w wavelength, and o output (0 ≤ i,w,o ≤ N–1). The relationship among the three is given as follows:
Fig. 1 shows a matrix that characterizes the relationship given in Eq. (1) among the three parameters. This matrix is normally called the λ-matrix of an AWG device. Given any two of the three parameters (i,w,o), the third parameter is determined automatically. Therefore, there are only N2 flows in an N × N AWG. All N2 flows in an N × N AWG can pass through the device without blocking. We can also use (i,w,*) or (i,*,o) to represent a flow, where * represents the unspecified parameter which can be derived from the other two given parameters.
Although an N × N AWG can support N2 flows simultaneously, conventional AWG-based switches assume each input only transmits one flow at a time. This will simplify the receiver design where a wideband receiver will suffice (see Fig. 2a). Although many centralized and distributed scheduling algorithms (Anderson et al., 1993; Chen et al., 1994; McKeown et al., 1997; LaMaire and Serpanos, 1994; McKeown, 1999; Jiang and Hamdi, 2001) proposed for crossbar switches can be used for this switch, an AWG has an inherent crosstalk problem that does not exist in an electronic crossbar switch. When optical signals of the same wavelength pass through the device simultaneously, crosstalk will be generated, which will negatively affect the signal quality of each other. Fig. 3 (from (Takahashi et al., 1996)) shows the relationship between the power penalty and the total crosstalk, with the BER set at 10−9. As can be seen, the higher the crosstalk, the larger the power penalty. Crosstalk can also severely limit the size of an AWG-based optical switch. This crosstalk problem can be tackled with a system-level technique, wavelength constraint scheduling (Bianco et al., 2010; Fernandez Hermida et al., 2012), where each AWG-based switch has a scheduler to coordinate the transmissions from different ports. Its scheduler can limit the number of packets with the same wavelength simultaneously traversing the switch. It has been shown that these algorithms can reduce the crosstalk and achieve a reasonably good throughput. This also means that a larger AWG port count is achievable under a given crosstalk requirement.
However, conventional constraint-based scheduling algorithms have two limitations. First, they are for the single-transmitter design. Although this simplifies the design, this design severely limits the capacity of an AWG switch. Second, they ignore the physical characteristic of crosstalk in an AWG. They assume that the crosstalk impacts of all signals of the same wavelength are the same. This assumption, however, is false. Crosstalk created by signals of the same wavelength in an AWG can be divided into two categories: from adjacent channels and from non-adjacent channels (note that adjacency is defined in a modulo sense), and the strengths of each are significantly different.
In general, the crosstalk from (immediate) adjacent channels is much stronger than that from the remaining channels (Li et al., 2017; APSS Apollo, 2003; Rahman, 2011). Ignoring this effect can significantly degrade the performance of the scheduling algorithms, as will be shown in the paper. In this paper, we exploit this insight and show how it can improve the performance of an AWG-based optical switch. Our main contributions can be summarized as follows.
- 1.
We describe a new type of constraint-based scheduling algorithm which exploits the physical crosstalk characteristic of an AWG, namely that the crosstalk from (immediate) adjacent channels is much stronger than that from the remaining channels.
- 2.
We design the algorithm for a multi-flow case where each input is equipped with multiple transmitters and can transmit multiple packets of different wavelengths simultaneously. Prior work on wavelength constraint-based scheduling only focuses on single-transmitter cases. The maximum throughput and the delay/throughput analysis of the proposed new algorithm are also given in the paper.
The rest of the paper is organized as follows. In Section 2, we briefly review conventional crosstalk-constraint-based scheduling algorithms. In Section 3, we investigate the properties for the crosstalk in an AWG and propose a new type of constraint-based scheduling algorithm. We design an RDSRR-type scheduling algorithm for the multi-flow case. Prior works only consider the single-transmitter case. In Section 4, we use analysis and simulation to study the performance gain of the new approach over the conventional constraint-based scheduling algorithm under the multi-flow scenario. We conclude our discussion in Section 5.
Section snippets
Prior work
In this section, we briefly review prior works related to the constraint-based scheduling.
Co-channel interference limits the size and scalability of an AWG-based optical switch. Ref (Rodelgo-Lacruz et al., 2009) first proposes the idea of wavelength constraint-based scheduling. By limiting the number of flows using the same wavelength to at most k times in each slot, where k is given and its value determines the crosstalk level in the switch, we can control the overall crosstalk level added to
Proposed constraint-based scheduling: multi flows and non-adjacency requirement
A multi-flow AWG-based switch is shown in Fig. 2b, where each input port is equipped with m transmitters and each output port with m receivers (note that the i-th input port and the i-th output port are co-located). Due to the cost issue, m cannot be too large. In Fig. 2b, we assume m = 3. Both the transmitters and receivers need to be tunable in this design. Currently, the tuning speed of a tunable receiver is in the μs range (Tao and Ye, 2014). If this is an issue, the design in Fig. 2c,
Performance evaluations
In this section, we evaluate the performance of the proposed scheduling algorithms for multi-flow AWG switches. As mentioned in the beginning, an AWG has the capability of transmitting multiple flows from each input simultaneously without blocking. This has not been explored in prior works on constrained-based scheduling. Combining analysis and simulation, our study will focus on the important feature of our algorithm: the non-adjacency requirement. We will show the performance gain by adding
Conclusion
By exploiting the insight that crosstalk from non-adjacent channels is much weaker than from adjacent channels, we proposed a new type of constraint-based scheduling algorithm in the paper for AWG-based optical switches. We showed how to use the idea to design routing and scheduling algorithms for multi-transmitter switches, while conventional routing and scheduling algorithms for AWGs are for single-transmitter systems. We showed that a significant performance gain can be achieved by the
Acknowledgment
Prof. Lea's research is supported by HK ITF [grant number UIM338] and HK RGC [grant number 16206015].
Shuyue Chen received the B.S. degree in information engineering (optoelectronics) from Zhejiang University, Hangzhou, China, in 2014. He is currently working toward the Ph.D. degree in electronic and computer engineering at Hong Kong University of Science and Technology, Hong Kong. His research interests include optical routing and switching.
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Shuyue Chen received the B.S. degree in information engineering (optoelectronics) from Zhejiang University, Hangzhou, China, in 2014. He is currently working toward the Ph.D. degree in electronic and computer engineering at Hong Kong University of Science and Technology, Hong Kong. His research interests include optical routing and switching.
Chin-Tau Lea received the B.S and M.S. degrees from National Taiwan University, Taipei City, Taiwan, in 1976 and 1978, respectively, and the Ph.D. degree from the University of Washington, Seattle, WA, USA, in 1982, all in electrical engineering. He is currently a Professor in the Department of Electronic and Computer Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, which he joined in 1996. Prior to that, he was with AT&T Bell Labs from 1982 to 1985, and with the Georgia Institute of Technology from 1985 to 1995. His research interests are in the general area of switching and networking. His research contributions include the invention of Multi-Log2 N networks and the associated crosstalk-free photonic switching theory. He also holds fifteen U.S. patents.