Geun-soo Kim,Jae-Hoon Kim,Limei Peng＊

1 Department of Industrial Engineering,Ajou Univerisy,Suwon 16499,Korea

2 School of Computer Science and Engineering,Kyungpook National University,Daegu 41566,Korea

Abstract:To accommodate the asymmetric characteristic of Internet traffic,we propose a flexible node architecture based on multiflow optical transponders (MF-OTP) under the integrated Cloud-Fog framework.The proposed MF-OTP architecture is flexible in the following two degrees.Firstly,it can be flexibly adjusted to transmit either downstream or upstream traffic according to the timely traffic demand distribution.Secondly,it allows multiple sub-channels using flexible (i.e.,same/different) modulation formats to serve the same traffic demand.To evaluate the efficiency of the flexible MT-OTP in serving asymmetric traffic,we propose two integer linear programming (ILP) models to address the routing,modulation and spectrum assignment (RMSA),with one aiming at minimizing the required number of sub-channels and another aiming at maximizing the volume of traffic transmission.Numerical simulations are conducted and the results show that the proposed models based on the flexible MF-OTP architecture requires less number of sub-channels and can serve more traffic demands.

Keywords:fog computing; traffic asymmetric; flexible MF-OTP; ILP

I.INTRODUCTION

Different from the traditional Internet traffic which are mainly from the Cloud,nowadays Internet traffic are also featured by the Fog that generates a huge volume of daily IoT data with the fast development of IoT technologies.One of the most important features of the current Internet traffic is timely and geographically asymmetric,due to the intensive traffic demands geographically generated at the IoT ends instantly [1-5].One example on the traffic asymmetry can be a small text upstream traffic demand requiring a huge video download from the downstream.To accommodate the asymmetric feature of Internet traffic efficiently,elastic and flexible traffic provisioning schemes are required under the fixed deployed physical carrier networks.Even though great research progress on traffic provisioning of the Cloud has been witnessed in the past decade,most of them have assumed symmetric traffic demands between the upstream and downstream links [6].

Since the development of Cloud computing,Fog computing,IoT,etc.,shows no sign of stopping,the asymmetric characteristic of Internet traffic becomes non-negligible and would affect the overall network performance if not being well addressed.The asymmetric feature naturally prefers a more dynamic network infrastructure which would support both symmetric and asymmetric Internet traffic efficiently and elastically.Nonetheless,most of the current networks are symmetrically constructed under the assumption of asymmetric traffic demands,say,the transmission capacity of the upstream and downstream links are symmetric.Serving the asymmetric traffic demands above the symmetric network infrastructure would lead to inferior service quality as well as poor network performance.

Multi-flow optical transponder (MF-OTP) has been developed as the one of the key enablers in the optical networks due to its efficient router-bypass capability in the optical layer [8].It was proposed to overcome the shortcomings of the bandwidth variable transponder (BVT).The BVT has limitations in transmitting traffic to multiple destinations due to the limited number of ports that corresponds to sub-channels as well as the coarse transmission granularity of each port/sub-channel.As an improvement,more ports/sub-channels with finer granularities equipped with low-rate transponders are proposed in MF-OTP.Since there are more sub-channels with finer granularity in each link,traffic from the same source node can be transmitted to multiple destinations using one or more sub-channels [8].

Similarly,most existing studies on MF-OTP by default assume that the network infrastructure is symmetric,which implies that MF-OTP is short of handling asymmetric traffic.To serve the asymmetric traffic more efficiently in MF-OTP EONs,we propose an improved MF-OTP architecture which is flexible in two degrees.Firstly,the transmission direction (i.e.,upstream and downstream) of each sub-channel is not fixed but flexible [7].The transmission direction of each sub-channel can be flexibly adjusted based on the timely traffic distribution.Secondly,the modulation formats of sub-channels can be flexibly set even for the same traffic demand,with the objective of maximizing the volume of served traffic while optimizing the network performance.More specifically,for each traffic demand of a source-destination (SD) node pair,we assume that all the sub-channels that are selected for serving this traffic demand of the SD node pair can be flexibly (i.e.,same or different) modulated,therefore allowing more efficient traffic transmission.

With the flexible MF-OTP architecture,we propose two integer linear programming (ILP) models to address the routing,modulation and spectrum assignment (RMSA) issue and evaluate the efficiency of the proposed models when serving asymmetric traffic under the integrated Cloud-Fog framework [11].Specifically,the first ILP model aims to minimize the number of sub-channels needed to serve a given number of traffic demands and the second one aims to maximize the volume of successfully transmitted traffic under the fixed amount of overall channel transmission capacity.The major contributions of this paper are as follows:

1) we review a flexible MF-OTP node architecture,where each sub-channel is flexible in transmitting timely bidirectional traffic.

2) we propose to flexibly modulate all the sub-channels so as to optimize the overall network performance.

3) we propose two theoretical integer linear programming (ILP) models to evaluate the proposed architecture when serving asymmetric traffic in integrated Cloud-Fog framework.

4) In addition,to the best of our knowledge,there are very few,if any,literatures have addressed the spectrum continuity and spectrum contiguity simultaneously in numerical ILP models.In this paper,we consider the two constraints simultaneously in our ILP models.

The rest of this paper is organized as follows.Section II introduces the related works.In Section III,we introduce the original dedicated MF-OTP architecture and the proposed flexible MF-OTP architecture,respectively.In Section IV,we state the problems in addressing the RMSA issue in integrated Cloud-Fog architecture.In Section V,we introduce the proposed ILP models.In Section VI,we conduct numerical simulations and presents the evaluation results.Section Ⅶ concludes this paper.

II.RELATED WORK

In this part,we introduce the existing studies that are related to our work mainly in three aspects,say Fog computing and IoT,asymmetric traffic,MF-OTP,and flexible modulation format,respectively.

The authors in [12] proposed an integrated Cloud-Fog (iCloudFog) architecture with the objective of integrating the resources from both of the wired nodes in the Cloud and the wireless nodes in the access/edge to provision the IoT data efficiently.Three different types of Fogs have been proposed,i.e.,wired Fog which consists of only wired nodes,mixed Fog which consists of both wired and wireless nodes,and wireless Fog which consists of only wireless node are proposed.Note that,the work in this paper was conducted based on the wired Fog architecture.

Y.Sheng,et.al.proposed to employ unidirectional design to alleviate the impact of traffic asymmetry on EONs performance [10].Specifically,they decouple a bidirectional transponder into an isolated unidirectional transmitter (Tx) and an isolated unidirectional receiver (Rx).K.Walkowiak,et.al.experimentally evaluated the impact of service request asymmetry on the performance of EONs by investigating two different scenarios,i.e.,a reference one that assumes symmetric lightpaths and the one that makes use of flexible spectrum allocation to support asymmetric traffic demands [11].Authors studied asymmetric service requests in EON based on virtual asymmetric network construction[13] and proposed a flexible MF-OTP architecture which supports directional transmission of sub-channels [9].

M.Jinno,et al.proposed the multi-flow OTP (MF-OTP) to offload IP traffic to a lower layer yielding benefits that are potentially cost-effective and power efficient in [8].It introduced that the objective of MF-OTP is to allow client data flows that arrive from a single client interface to be mapped to multiple optical flows.J.Zhang,et al.proposed a sliceable-transponder and evaluated it in terms of energy efficiency [14].Three bandwidth-variable transponders (BVTs) based on their sliceability,namely,non-sliceable BVTs,fully sliceable BVTs,and partially sliceable BVTs,were proposed and investigated.R.Martinez,et al.focused on the automatic control and management of MF-OTPs when dynamically setting up flex-grid LSPs with different bitrate demands [15].Specifically,they designed an on-line distance-adaptive routing,spectrum,and modulation assignment (RSMA) algorithm that can dynamically serves flex-grid LSPs with the objective of optimizing the use of both the network's optical spectrum as well as the MF-OTP's resources.

Y.Zhao,et al.aimed at addressing the energy efficiency issue in survivable VONs with the sliceable multi-flow transponders and the elastic regenerators [16].ILP models and virtual optical network (VON) mapping approaches are developed to minimize the power consumption,improve the energy efficiency,and reduce the spectrum usage for different line rates,as well as the baseline VON mapping approach.K.Walkowiak,et al.focused on dynamic lightpath provisioning in translucent spectrally spatially flexible optical networks operating with multi-core fibers and realizing spectral super-channel transmission [17].M.Klinkowski,et.Al.studied potential performance gains resulting from deliberate use of signal regeneration along with modulation and spectrum conversion in translucent elastic optical networks,realizing super-channel transmission [18].

III.OVERVIEW

In this part,we give an overview on the proposed flexible MF-OTP node architecture and the representation of the asymmetric traffic model.

3.1 Node architecture based on MFOTP

Figure 1 and 2 show the original dedicated MF-OTP and the proposed flexible MF-OTP architecture,respectively.In the original dedicated MF-OTP,we assume two fiber links are deployed between any adjacent node pair,one for upstream direction and another for downstream direction.Each directional fiber link is divided into several directional sub-channels as shown.Fixed transmitter (Tx) or receiver (Rx) are equipped for each directional sub-channel [9].

Fig.1.Original dedicated MF-OTP with fixed subchannel direction.

As an alternative,we propose to use the MT-OTP in a more flexible manner as shown in figure 2,which can serve the asymmetric traffic more efficiently [9].Specifically,we assume that the two fiber links between any adjacent node pair is directionless,and so does the sub-channels.Each sub-channel connecting to a node is equipped with both a low-rate Tx and Rx,and thus the transmission direction can be flexibly decided based on the timely distribution of directional traffic demands.

For example,to serve a traffic demand of 150 Gbps by assuming BPSK for each sub-channel (where the modulation spectrum efficiency is 12.5Gbps per sub-channel),a total of 12 (=150Gbps/12.5Gbps) sub-channels is required.In this case,if we use the original dedicated MF-OTP architecture as shown in figure 3(a),this traffic demand would either be blocked or only a part of it,say 125Gbps (=12.5Gbps *10 channels),can be served.In contrast,if we serve the same traffic demands under the proposed flexible MF-OTP architecture,we can serve the whole traffic demand using 12 sub-channels in the same direction,and the rest 8 channels in the other direction as shown in figure 3(b).

3.2 Flexible sub-channels using different modulation formats

In this part,we introduce a flexible modulation scheme for the sub-channels that are selected for serving the traffic demand of a given SD node pair,as shown in figure 4(b).The fixed modulation scheme is also introduced in figure 4(a).In figure 4 (a),all sub-channels use the same modulation format to serve the traffic demand of a given SD node pair,for example BPSK.In contrast,Fig.4(b) shows that sub-channels can use different modulation format to transmit traffic of a given SD node pair,such as BPSK,QPSK,and 8QAM.

The flexible modulation scheme in figure 4(b) is expected to transmit more traffic as well as using the network resources more effi-ciently.For example,to serve a traffic demand of 50Gbps,the fixed scheme must use four sub-channels when using BPSK.In contrast,under the flexible modulation scheme,we have multiple options,such as using only two QPSK sub-channels,two BPSK sub-channels plus one QPSK sub-channel,etc.

3.3 Asymmetric traffic representation

For the asymmetric traffic demands from upstream and downstream links,we use a parameter called asymmetric ratio (AR) to demonstrate the difference in the amount of service requests between the upstream and downstream links.

We define the direction from client to datacenter as downstream,and the direction from datacenter to client as upstream.The difference in the amount of service requests between downstream and upstream is mathematically expressed asmax(hdown,hup)/min(hdown,hup),wherehupandhdownrepresent the amounts of upstream and downstream data demands,respectively [13].Therefore,AR=1 indicates the symmetric traffic model.AR=2 indicates the upstream/downstream traffic demands is twice of that from the other side,which indicates a asymmetric traffic model.

IV.PROBLEM STATEMENT

In addressing the routing,spectrum,and modulation assignment (RSMA) issues under the proposed flexible MF-OTP architecture,there are a serious of constraints need to be considered.In addition to the well discussed constraints on routing and flow conservation,we also consider the two important constraints of spectrum continuity and spectrum contiguity.Note that there exist a lot of literatures discussing either spectrum continuity or contiguity,few of them,if any,have addressed them simultaneously.In addition,constraints of using the flexible bidirectional sub-channel and using flexible modulation formats for sub-channels of the same traffic demand are also discussed.Details are introduced as follows.

Fig.3.Traffic transmission situation in Original dedicated and Flexible MF-OTP:(a) original dedicated MF-OTP (b) flexible MF-OTP.

Fig.4. Fixed and Flexible sub-channels: (a) fixed sub-channels (b) flexible sub-channels

4.1 Constraints of spectrum continuity and contiguity

Figure 5 shows spectrum continuity and contiguity constraints.Spectrum contiguity constrains that a consecutive set of sub-channels on a link should be selected for serving a traffic demand as shown in Fig.5(a),where Fig.5(b) shows a case which does not obey with this constraints and is not allowed.Spectrum continuity constrains that all links for serving the same traffic demand should use the same set of sub-channels as shown in Fig.5(c).Fig.5(c) shows a traffic demand from source nodesto destination nodedwould traversing an intermediated noded.We can see that the set of sub-channels used on links-ishould be the same with that on linki-d.

4.2 Constraints from the flexibility of MF-OTP

As introduced before,the sub-channel flexibility of the proposed MF-OTP architecture are two degrees,say on the transmission directions and the modulation formats.

The first flexibility degree constrains that the sub-channel should be in either the Tx mode or the Rx mode,and the total number of sub-channels of both directions should not exceed the permitted number of sub-channels,since each sub-channel can be set to transmit traffic in either directions.For the second flexibility degree,we consider the constraints of transmission distance when using different modulation formats.

There are some other general constraints,such as the transponders are switched on at source and destination nodes,but not at the intermediate nodes,the transmission bandwidth limitations,etc.,which will be introduced in the following section.

V.PROPOSED ILP MODELS

In this section,we introduce the two proposed ILP models for addressing the RMSA issue.The two proposed models solve routing,modulation and spectrum assignment (RMSA) problems in EON based on MF-OTP with flexible sub-channels.The first ILP model aims at minimizing the total number of sub-channels needed to serve a given number of the traffic demands,named asILP-MinSubc.The second ILP model aims at maximizing the total number of successfully served traffic demands under given network transmission capacity,named asILP-MaxTrf.They are described in details as follows

Fig.5.Spectrum Continuity and Contiguity :(a) Spectrum contiguity (b) Non spectrum contiguity (c) Spectrum continuity (d) Non spectrum continuity.

5.1 ILP-MinSubc

1)Set and Parameters:

N:Set of network nodes

L:Set of network links

NP:Set of SD pairs in the network

Lii:Set of links that start or end at nodei

MF:Set of modulation formats.

MF={1,2,3,…},r∈MF

TDsd:Traffic demand between node pairsd

SC:Total number of sub-channel

CP:Base capacity of sub-channel (BPSK)

Dmn:Distance between linkmn

Dr:Maximum optical transmission reach of a lightpath adoption modulation levelr

Rr:Bit per symbol of modulation formatr

2)Variables:

Binary variable that is 1 if the lightpath established for node pairsdtraverses linkij; otherwise 0

Binary variable that is 1 if the lightpath established for node pairsduses thetthsub-channel using modulation levelron linkij; otherwise 0

Binary variable that is 1 if the ligthpath established for node pairsduses thetthsub-transmitter using modulation levelrof nodeiand traversed linkij; otherwise 0

Binary variable that is 1 if the ligthpath established for node pairsduses thetthsub-receiver using modulation levelrof nodejand traversed linkij; otherwise 0

DLsd:distance between node pairsd

3)Objective function:

The objective is to minimize the total number of channels used to transmit the traffic.

4)Constraints:

i) Routing and Flow conservation:

Constraints (1) and (2) ensure that the lightpath established for node pairsdstarts from the source nodesand end at destination noded[19].Constraint (3) ensures that for any intermediate node traversed by a lightpath,two links are associate with the node,i.e.,one ends at the node and the other starts from the node [19].Constraint (4) ensures that if the lightpath for the traffic of node pairsdtraverses a physical linkmn,it should also traverse physical nodemandn[19].

ii) Directional Sub-channels with MF-OTP allocation:

Constraint (5) ensures that the total amount of the served traffic demands should be no larger than the available link transmission capacity.Constraint (6) ensures that a lightpath should be established before a sub-channel can be modulated to transmit traffic on this lightpath.

Constraints (7) to (11) ensure that a) only transmitters/receivers of the source/destination nodes are tuned to transmit/receive traffic,b) traffic traversing the intermediate nodes are bypassed,and c) a transmitter/receiver can be used to transmit traffic for only one SD node pair at one time.

iii) Related Original/Flexible Transponder:

Constraints (12) and (13) are for the original dedicated MF-OTP architecture.They ensure that the total number of transmitters or receivers used to transmit or receive traffic demands of all thesdnode pairs on linkijdoes not exceed the total number of sub-channels of each directional fiber link,say 10.

Constraints (14) is for the proposed flexible MF-OTP architecture.It ensures that the sum of the total numbers of transmitters on linkijand receivers on linkjiused to transmitting/receiving traffic of all thesdnode pairs does not exceed the total number of sub-channels,say 20.

iv) Transmission Distance constraints:

Constraint (15) guarantees that the sum of sub-channels used on linkijcannot exceed the total available number of sub-channels.Constraint (16) guarantees that each sub-channel of a link can only be used to serve the traffic from one SD node pair.Constraint (17) ensures that one sub-channel uses one modulation format.Constraint (18) guarantees that the sub-channel using any modulation format does not exceed its maximum transmission distance of the modulation format.

v) Spectrum continuity and contiguity:

Constraint (19) guarantees spectrum contiguity.Constraints (20) and (21) guarantee spectrum continuity.

5.2 ILP-MaxTrf

The second ILP model was proposed to maximize the total amount of successfully transmitted traffic demands.Most of the set,parameters,and constraints are the same with that of the first ILP model,which will not be repeated.Instead,we introduce the additional ones as follows.

1) Additional Variables:

LDsdThe amount of traffic successfully transmitted betweensdnode pair.

2) Objective function:

The objective is to maximize the total amount of served traffic demand.

3)Constraints:

The ILP-MaxTrf model shares most of the constraints with that of the ILP-MinSubc model.Specifically,constraints (1) ～ (4) are for routing and flow conservation.Constraints (6) ～ (11) are for sub-channels with MF-OTP allocation.Constraints (12) ～ (14) are related to original/flexible transponder.Constrains (15) ～ (18) are related to transmission distance.Constraints (19) ～ (21) are for spectrum continuity/contiguity.However,constraint (5) is not used.Instead,the following two new constraints are added.

Constraint (22) guarantees that traffic to be sent by thesdpair is assigned to the sub-channel.Constraint (23) ensures that the traffic that thesdpair is sending does not exceed the total required traffic volume.

VI.CASE STUDY AND NUMERICAL RESULTS

In this part,we numerically evaluate the proposed ILP models for provisioning the asymmetric traffic in EONs using flexible MF-OTP with flexible sub-channels (F-MF) and original MF-OTP with original dedicated sub-channels (D-MF),respectively.F-MF indicates that each sub-channel can be used to transmit traffic in both directions using flexible modulation format.In D-MF,each sub-channel is fixed in either the upstream or downstream direction,but can use flexible modulation format.The simulation environments and results will be described as follows.

6.1 Simulation environments

The case study is implemented on a six-node nine-link (6N9L) mesh network,and an eightnode (8N12L) mesh network as shown in figure 6 and figure 7,respectively.All node apply either the F-MF architecture or the D-MF architecture.

We assume the distance of all links between two adjacent nodes is 500 km and the total number of sub-channels (i.e.,upstream plus downstream) is 20 with a channel capacity of 12.5Ghz per sub-channel.In addition,we set the asymmetric ratio (AR) to 2,and 3,respectively.The traffic offered load is denoted as TR,where TR=(total number of average traffic demands/total network transmission capacity).TR is set to 0.5,0.6,1.0 and 1.2 respectively.

For the above network model,we use AMPL's Gurobi to solve the proposed ILP models by considering three modulation formats,say BPSK,QPSK,and 8QAM as shown in table 1.The parameters for different modulation formats are summarized in table 1 [5].

6.2 Numerical results

1) Numerical results of the ILP model for minimizing the total number of required sub-channels

Figure 8 shows the number of required sub-channels used to serve traffic demands in N6L9 and N8L12 network topologies,respectively,under different values of AR and TR.In the figures,D-BPSK and D-MF indicates the original dedicated MF-OTP with BPSK and flexible modulation formats being used for all the sub-channels respectively.Similarly,F-BPSK and F-MF indicates the proposed flexible MF-OTP with BSPK and flexible modulation formats being used for all the sub-channels,respectively.

From the numerical results shown in Figs.8 and 9,we can obtain the following observations:1) to serve the same amount of traffic demands,MF-OTP with flexible sub-channel modulation formats,i.e.,F-MF and D-MF requires about 20% ～ 30% fewer sub-channels when compared to MF-OTP with fixed sub-channel modulation format scheme,i.e.,F-BPSK and D-BPSK.This is because MFOTP with flexible sub-channel modulation formats can use higher level modulation format to accommodate large traffic demands when the low-rate BPSK possibly cannot; 2) There is almost no difference between flexible directional scheme and fixed directional scheme under the same modulation schemes,say D-BPSK and F-BPSK,and D-MF and F-MF.The main reason is that the objective here is to minimize the number of required sub-channels in this model,where the sub-channel transmission capacity for all schemes are assumed to be the same.Under this assumption,to serve the same amount of overall traffic demands under all schemes using the same modulation schemes,as a matter of course,the numbers of required sub-channels must be the same.

Fig.6.N6L9 Networks topology.

Fig.7.N8L12 Networks topology.

Table I.Parameters for difference modulation format [7].

2) Numerical results of ILP model for maximizing the total number of successfully served traffic amount

Fig.8.Number of sub-channels used to serve traffic in N6L9.

Fig.9.Number of sub-channels used to serve traffic in N8L12.

Fig.10.Amount of traffic transmitted in N6L9.

Figure 10 and figure 11 shows the amount of traffic that is successfully transmitted on the N6L9 and N8L12 network topologies,respectively,under different values of AR and TR.From the results,we can obtain the following observations:1) flexible directional schemes performs better than the fixed directional scheme.Specifically,F-BPSK and F-MF can transmit about 7% to12% more traffic demands than D-BPSK and D-MF under almost different ARs and TRs; 2) Using flexible modulation formats for sub-channels can significantly improve the network performances when compared to the fixed modulation formats.Specifically,i.e.,D-MF and F-MF,where higher modulation levels are available,can transmit 25% to 40% more traffic demands than that of the schemes using a single modulation level,i.e.,D-BPSK and F-BPSK; 3) The heavier the traffic demands,the greater the difference is,and the higher the asymmetry ratio,the greater the difference is.

From the above results,we can conclude that the proposed MF-OTP architecture which is flexible in the sub-channel transmission direction and the modulation formats can serve the asymmetric traffic much better than the dedicated MF-OTP using just one single modulation format.

VII.CONCLUSION

In this paper,we proposed an improved MFOTP node architecture in EONs,which is flexible in both of the sub-channel transmission directions and the modulation formats.To evaluate the original dedicated and flexible MF-OTP schemes,two ILP models have been proposed for EONs using the proposed flexible architecture with objectives of minimizing the number of sub-channels required to serve a given number of traffic demands and maximizing the amount of served traffic under a fixed number of sub-channels Simulation results showed that our proposed architecture with two-degree flexibility can serve the asymmetric traffic much better than the original fixed MF-OTP does in terms of requiring fewer network resources,say number of sub-channels,and serving more traffic demands.

Fig.11.Amount of traffic transmitted in N8L12.

ACKNOWLEDGEMENT

This study was supported in part by the BK21 Plus project (SW Human Resource Development Program for Supporting Smart Life) funded by the Ministry of Education,School of Computer Science and Engineering,Kyungpook National University,Korea (21A20131600005),in part by the National Research Foundation of Korea grant funded by the Korean Government (2018R1D-1A1B07051118),and in part by Institute for Information& communications Technology Promotion (IITP) grant funded by the Korea government (MSIP) (No.2016-0- 00151,Development of LTE Small Cell supporting LWA/LAA dual mode).