Spatio-temporal fragmentation-aware time-varying service provisioning in computing power networks based on model-assisted reinforcement learning

Huangxu Ma; Jiawei Zhang; Zhiqun Gu; Daniel C. Kilper; Yuefeng Ji; Yuefeng Ji

doi:10.1364/JOCN.498951

Journal of Optical Communications and Networking
Vol. 15,
Issue 11,
pp. 788-803
(2023)
•https://doi.org/10.1364/JOCN.498951

Spatio-temporal fragmentation-aware time-varying service provisioning in computing power networks based on model-assisted reinforcement learning

Huangxu Ma, Jiawei Zhang, Zhiqun Gu, Daniel C. Kilper, and Yuefeng Ji

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Huangxu Ma, Jiawei Zhang, Zhiqun Gu, Daniel C. Kilper, and Yuefeng Ji, "Spatio-temporal fragmentation-aware time-varying service provisioning in computing power networks based on model-assisted reinforcement learning," J. Opt. Commun. Netw. 15, 788-803 (2023)

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Abstract

Widespread application of AI with high computing requirements has promoted the rapid development of cloud and edge computing. Ubiquitous computing resources need to be interconnected through high-performance IP and optical networks. Computing power networks (CPNs) have been studied as an IP/optical cross-layer architecture to provide on-demand computing services. The service provisioning in CPNs can be modeled as a virtual optical network embedding problem; however, the time-varying characteristics of service requirements increase the complexity. In particular, there can be stranded computing or bandwidth resources that are isolated in the spatio-temporal dimension and therefore difficult for other requests to utilize. This phenomenon is referred to as spatio-temporal resource fragmentation, which will lead to inefficient use of resources and higher energy consumption. To meet the time-varying requirements and achieve an energy-efficient CPN, in this paper, we first analyze the main reason for spatio-temporal resource fragmentation and excess energy consumption in cross-layer CPNs, which is the mismatched embedding scheme and the inappropriate scheduling order. Therefore, an auxiliary-graph-model-assisted edge-featured graph-attention-network-enabled DRL algorithm, DeepDefrag, is studied to solve the problem. Its core highlight is co-optimizing the scheduling and embedding of time-varying virtual networks along with the awareness of resource fragmentation. In addition, an integer linear programming algorithm is developed to determine the performance bounds. We validate DeepDefrag through a series of ablation studies and comparison algorithms under different numbers of requests. The results show that DeepDefrag can achieve ${\gt}{26.4}\%$ lower energy consumption for CPNs compared with the DRL-based baseline. Moreover, it is shown to generalize well across requests and networks.

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Category	Constant	Description
CPN	$G^{S}$	CPN topology
	$N^{S}$	Set of computing nodes
	$W$	Set of wavelengths
	$Λ_{i, j}$	Binary, 1 if node $i$ is connected to node $j$ in $G^{S}$ , $i, j \in N^{S}$
	$C_{n}^{N}$	Computing capacity of node $n$ , $n \in N^{S}$
	$C_{i, j, w}^{L}$	Bandwidth capacity of wavelength $w$ of link $(i, j)$ , $i, j \in N^{S}$ , $w \in W$
	$P^{α}$	Energy consumption when activating a new server
	$P^{β}$	Energy consumption when activating a new lightpath
	$P^{γ}$	Energy consumption when activating a new ROADM degree
TVNR	$R$	Set of TVNRs
	$T$	Time period of one optimization cycle
	$G_{r}^{V}$	Topology for request $r$ , $r \in R$
	$N_{r}^{V}$	Set of virtual nodes for request $r$ , $r \in R$
	$L_{r}^{V}$	Set of virtual links for request $r$ , $r \in R$
	$D_{r, k, t}^{N}$	Computing demand of virtual node $k$ for request $r$ at time $t$ , $k \in N_{r}^{V}$ , $r \in R$ , $t \in T$
	$D_{r, q, t}^{L}$	Bandwidth demand of virtual link $q$ for request $r$ at time $t$ , $q \in L_{r}^{V}$ , $r \in R$ , $t \in T$
	$E_{r, q}$	Source virtual node of virtual link $q$ for request $r$ , $r \in R$ , $q \in L_{r}^{V}$
	$F_{r, q}$	Destination virtual node of virtual link $q$ for request $r$ , $r \in R$ , $q \in L_{r}^{V}$
Others	$Δ$	A sufficiently large number

Variable	Description
$Θ_{n}$	Binary, 1 if node $n$ is activated
$Ω_{r, k, n}$	Binary, 1 if virtual node $k$ of request $r$ is deployed in node $n$
$L^{S}$	Set of established lightpaths
$H_{i, n, j, w}$	Binary, 1 if there exists an established lightpath in $L^{S}$ that passes through three adjacent nodes $i, n, j$ with wavelength $w$
$A_{i, j}$	Binary, 1 if link $(i, j)$ is occupied
$Y_{i, j, w}$	Binary, 1 if wavelength $w$ of link $(i, j)$ is occupied
$X_{r, q, i, j, w}$	Binary, 1 if virtual link $q$ of request $r$ is carried on wavelength $w$ of link $(i, j)$
$Z_{i, j, w}^{D}$	Binary, 1 if wavelength $w$ enters node $j$ from node $i$ and experiences the “drop” operation at node $j$
$Z_{i, j, w}^{A}$	Binary, 1 if wavelength $w$ leaves node $i$ to node $j$ and experiences the “add” operation at node $i$
$S_{r, q, i, j, w}^{D}$	Binary, 1 if virtual link $q$ of request $r$ is carried on wavelength $w$ of link $(i, j)$ and experiences the “drop” operation at node $j$
$S_{r, q, i, j, w}^{A}$	Binary, 1 if virtual link $q$ of request $r$ is carried on wavelength $w$ of link $(i, j)$ and experiences the “add” operation at node $i$

Symbol	Description	Power
$P^{server}$	Basic power of a 100 TFLOPS server with a 100 Gbps Ethernet adapter	84.5 W [30]
$P^{eport}$	Power of a 100 Gbps E-switch port	8.25 W [31]
$P^{degree}$	Power of a ROADM node degree	20 W [28]
$P^{sr}$	Power of a 100 Gbps QSFP28 SR4 optical module	3.5 W [32]
$P^{zr}$	Power of a 100 Gbps QSFP28 ZR4 optical module	5.5 W [32]

Category	Constant	Description
CPN	$G^{S}$	CPN topology
	$N^{S}$	Set of computing nodes
	$W$	Set of wavelengths
	$Λ_{i, j}$	Binary, 1 if node $i$ is connected to node $j$ in $G^{S}$ , $i, j \in N^{S}$
	$C_{n}^{N}$	Computing capacity of node $n$ , $n \in N^{S}$
	$C_{i, j, w}^{L}$	Bandwidth capacity of wavelength $w$ of link $(i, j)$ , $i, j \in N^{S}$ , $w \in W$
	$P^{α}$	Energy consumption when activating a new server
	$P^{β}$	Energy consumption when activating a new lightpath
	$P^{γ}$	Energy consumption when activating a new ROADM degree
TVNR	$R$	Set of TVNRs
	$T$	Time period of one optimization cycle
	$G_{r}^{V}$	Topology for request $r$ , $r \in R$
	$N_{r}^{V}$	Set of virtual nodes for request $r$ , $r \in R$
	$L_{r}^{V}$	Set of virtual links for request $r$ , $r \in R$
	$D_{r, k, t}^{N}$	Computing demand of virtual node $k$ for request $r$ at time $t$ , $k \in N_{r}^{V}$ , $r \in R$ , $t \in T$
	$D_{r, q, t}^{L}$	Bandwidth demand of virtual link $q$ for request $r$ at time $t$ , $q \in L_{r}^{V}$ , $r \in R$ , $t \in T$
	$E_{r, q}$	Source virtual node of virtual link $q$ for request $r$ , $r \in R$ , $q \in L_{r}^{V}$
	$F_{r, q}$	Destination virtual node of virtual link $q$ for request $r$ , $r \in R$ , $q \in L_{r}^{V}$
Others	$Δ$	A sufficiently large number

Variable	Description
$Θ_{n}$	Binary, 1 if node $n$ is activated
$Ω_{r, k, n}$	Binary, 1 if virtual node $k$ of request $r$ is deployed in node $n$
$L^{S}$	Set of established lightpaths
$H_{i, n, j, w}$	Binary, 1 if there exists an established lightpath in $L^{S}$ that passes through three adjacent nodes $i, n, j$ with wavelength $w$
$A_{i, j}$	Binary, 1 if link $(i, j)$ is occupied
$Y_{i, j, w}$	Binary, 1 if wavelength $w$ of link $(i, j)$ is occupied
$X_{r, q, i, j, w}$	Binary, 1 if virtual link $q$ of request $r$ is carried on wavelength $w$ of link $(i, j)$
$Z_{i, j, w}^{D}$	Binary, 1 if wavelength $w$ enters node $j$ from node $i$ and experiences the “drop” operation at node $j$
$Z_{i, j, w}^{A}$	Binary, 1 if wavelength $w$ leaves node $i$ to node $j$ and experiences the “add” operation at node $i$
$S_{r, q, i, j, w}^{D}$	Binary, 1 if virtual link $q$ of request $r$ is carried on wavelength $w$ of link $(i, j)$ and experiences the “drop” operation at node $j$
$S_{r, q, i, j, w}^{A}$	Binary, 1 if virtual link $q$ of request $r$ is carried on wavelength $w$ of link $(i, j)$ and experiences the “add” operation at node $i$

Abstract

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Equations (38)

Journal of Optical Communications and Networking