Hose-model network virtualization in flexgrid optical networks

Fengqing Liu; Weiguang He

doi:10.1364/JOCN.374220

Journal of Optical Communications and Networking
Vol. 12,
Issue 3,
pp. 13-23
(2020)
•https://doi.org/10.1364/JOCN.374220

Hose-model network virtualization in flexgrid optical networks

Fengqing Liu and Weiguang He

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Fengqing Liu and Weiguang He, "Hose-model network virtualization in flexgrid optical networks," J. Opt. Commun. Netw. 12, 13-23 (2020)

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Abstract

Network virtualization, which can flexibly and efficiently embed multiple client networks to a substrate network, is one of the most promising technologies to address the ossification problem of Internet infrastructure. This work focuses on studying the problem of hose-model network virtualization in general topology flexgrid optical networks. A mathematical model for this problem is presented, which integrates hose-model traffic routing and virtual network mapping into a unified integer linear programming (ILP) formulation. Considering the computational difficulty of an ILP algorithm, four heuristic algorithms are presented. They first optimize and allocate link bandwidths to transport hose-model traffic in the virtual network; second, the derived virtual network is mapped in a substrate flexgrid optical network, in which a virtual link is mapped to one or multiple optical connections with or without grooming being allowed. The performance of the mapping success rate and time-average revenue for these algorithms is assessed by extensive simulation.

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Constants
$h_{c}$	Hop number of connection $c$
$n s_{c}$	Number of FSs used by connection $c$
$r_{c}$	Residual bandwidth of connection $c$
$c p_{v}$	Amount of computing resources required by virtual node $v$
$b_{v}$	Amount of hose bandwidth required by virtual node $v$
$c p_{s}$	Available computing resources of substrate node $s$
$M$	A big integer
$θ_{v, s}^{c}$	1 if connection $c$ goes through auxiliary edge $(v, s)$ , 0 otherwise
$θ_{l}^{c}$	1 if connection $c$ goes through optical link $l$ , 0 otherwise
$λ_{i}^{c}$	1 if connection $c$ uses FS $i$ , 0 otherwise
$C^{S}$	Set of all candidate connections, including potential and already established connections, index $c$
$C_{p o t}^{S}$	Set of potential connections
$C_{e}$	Set of candidate connections for virtual link $e$
$C_{v}$	Set of connections that originate from or terminate at virtual node $v$
$N^{V}$	Set of virtual nodes, index $v$
$E^{V}$	Set of virtual links, index $e$
$E_{+}^{V} (k)$	Set of virtual links originating from virtual node $k$
$E_{-}^{V} (k)$	Set of virtual links terminating at $k$
$A_{v}$	Set of optical nodes that virtual node $v$ can be attached (mapped) to, index $s$
$N^{S}$	Set of optical nodes in a substrate FGON, index $s$
$L^{S}$	Set of optical links in a substrate FGON, index $l$
$F S^{S}$	Set of frequency slots in an optical link, index $i$
Decision Variables
$δ_{c}$	1 if connection $c$ needs to be established, 0 otherwise
$m_{v, s}$	1 if virtual node $v$ is mapped to substrate optical node $s$ , 0 otherwise
$x_{e}^{u}, y_{e}^{v}$	Dual variables derived by hose-model traffic routing
$f_{e}^{u, v}$	Fraction of traffic from virtual node $u$ to $v$ that goes through virtual link $e$

	5		10		15		20
Load (Erlang)	ILP	MCGr	ILP	MCGr	ILP	MCGr	ILP	MCGr
$P_{m a p}^{t}$	100	99.7	89.3	83	84	79	70	64.7
$R_{t}$	1607	1592	2356	2257	2831	2569	2881	2836
$T$ (ms)	943	12.0	411	11.5	323	11.6	217	11.5

$\| F S^{S} \|$	10	20	30	40	50	60	70
T (s)	1	33	78	241	351	694	not solvable

Constants
$h_{c}$	Hop number of connection $c$
$n s_{c}$	Number of FSs used by connection $c$
$r_{c}$	Residual bandwidth of connection $c$
$c p_{v}$	Amount of computing resources required by virtual node $v$
$b_{v}$	Amount of hose bandwidth required by virtual node $v$
$c p_{s}$	Available computing resources of substrate node $s$
$M$	A big integer
$θ_{v, s}^{c}$	1 if connection $c$ goes through auxiliary edge $(v, s)$ , 0 otherwise
$θ_{l}^{c}$	1 if connection $c$ goes through optical link $l$ , 0 otherwise
$λ_{i}^{c}$	1 if connection $c$ uses FS $i$ , 0 otherwise
$C^{S}$	Set of all candidate connections, including potential and already established connections, index $c$
$C_{p o t}^{S}$	Set of potential connections
$C_{e}$	Set of candidate connections for virtual link $e$
$C_{v}$	Set of connections that originate from or terminate at virtual node $v$
$N^{V}$	Set of virtual nodes, index $v$
$E^{V}$	Set of virtual links, index $e$
$E_{+}^{V} (k)$	Set of virtual links originating from virtual node $k$
$E_{-}^{V} (k)$	Set of virtual links terminating at $k$
$A_{v}$	Set of optical nodes that virtual node $v$ can be attached (mapped) to, index $s$
$N^{S}$	Set of optical nodes in a substrate FGON, index $s$
$L^{S}$	Set of optical links in a substrate FGON, index $l$
$F S^{S}$	Set of frequency slots in an optical link, index $i$
Decision Variables
$δ_{c}$	1 if connection $c$ needs to be established, 0 otherwise
$m_{v, s}$	1 if virtual node $v$ is mapped to substrate optical node $s$ , 0 otherwise
$x_{e}^{u}, y_{e}^{v}$	Dual variables derived by hose-model traffic routing
$f_{e}^{u, v}$	Fraction of traffic from virtual node $u$ to $v$ that goes through virtual link $e$

	5		10		15		20
Load (Erlang)	ILP	MCGr	ILP	MCGr	ILP	MCGr	ILP	MCGr
$P_{m a p}^{t}$	100	99.7	89.3	83	84	79	70	64.7
$R_{t}$	1607	1592	2356	2257	2831	2569	2881	2836
$T$ (ms)	943	12.0	411	11.5	323	11.6	217	11.5

Abstract

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Equations (18)

Journal of Optical Communications and Networking