An Adaptive Traffic Distribution Scheme for CMT based on Lotka-Volterra Model in Multihomed Networks

Weibing Gong, Xiaolong Yang, Min Zhang, Keping Long

School of Computer & Communication Engineering, University of Science and Technology Beijing, China

* The corresponding author, Email: yangxl@ustb.edu.cn.

I. INTRODUCTION

In current Mobile Internet, almost each host is equipped by multiple interfaces to be capable for connecting multiple access networks, and the multi-access function is called multihoming[1-8]. Then, multiple these hosts and simultaneous access networks form a multihomed network. Here, the host can be smartphone, PDA,laptop, and fixed PC with multiple network cards. Then, access networks are composed of some heterogeneous networks, for example,Wi-Fi, wired networks and 2G/3G/4G. Also, it is possible that each kind of the heterogeneous networks is formed by multiple simultaneous homogeneous networks, for example, multiple Wi-Fi access networks, and multiple wired networks for fixed PC with multiple network cards. Consequently, if each access network can transmit data for each multihomed host, it can effectively increase bandwidth utilization,traffic throughput, and transmission resiliency.However, nowaday network systems can’t sup-port this concurrent multihomed transmission,which is prevalently called concurrent multipath transfer (CMT)[1-4].

To exploit potential capacity of multihomed networks, some emerging multipath protocols,for example, CMT stream control transmission protocol (CMT-SCTP)[1, 3, 4, 8], multipath TCP (MPTCP)[5-7], and MPSCTP[3] have been introduced to modify the traditional single path transmission protocol to be capable for simultaneous multipath transmission.

Population dynamics is an important branch of mathematical biology, which studies dynamic population variations of each species in an ecosystem with changing time and space. Actually, with the increasing traffic demands in current Internet, the competition for network shared resources (bandwidth,connections, computation, storage, and so on)is growing. Then, population dynamics has been studied as an effective method to improve network resource utilization. To support service differentiation and guarantee QoS for heterogeneous network traffic in WLAN, literature[10] proposed a self-adaptive rate control approach based on LV (Lotka-Volterra) model for multi-priority traffic in a bottleneck node.Through classifying the traffic as four categories and arranging different priorities for them,the approach can allocate different bandwidth for traffic in different priorities. Regarding a converged heterogeneous network as an ecosystem, Literature[11] analyzed a resource diminishing system can keep stable over a period of time in the case of the resources fairly allocated at the time of admission. Also,they proposed a policy that is capable of assisting an admission control technique to ensure stable coexistence among competitors at bottleneck gateways. Literature[12] presented a LV-based congestion control approach for WSNs streaming applications to control the competition for buffer in bottleneck nodes,where congestion in WSNs could basically be prevented by regulating the rate of each traffic flow. However, these studies only regulate the resource competition in bottleneck nodes using LV model, but it is ignored about traffic distribution in the case that multiple bottleneck nodes exists in a network scenario together.

Obviously, if the number of transmission paths increases, CMT is indeed able to increase network bandwidth of each multihomed host. However, it is very possible to snatch bandwidth of other multihomed hosts, and decrease their transmission efficiency. So,it is necessary to propose an adaptive traffic distribution scheme for CMT in multihomed networks. In the paper, inspired by adaptive population variation characteristics of predator and prey in ecosystem, we propose an adaptive CMT traffic distribution scheme based on the LV model which is called CMT-LV for short. In the scheme, the LV model isfirst introduced to optimize multipath transmission for multihomed hosts. Moreover, we not only consider the resource competition in bottleneck paths, but also the competition for traffic among different paths. Then, we summarize two competition models in CMT multihomed transmission, which are respectively multiple S-D streams competition for one path and multipath competition for traffic between each multihomed S-D host pair. Also, two LV-based models are built to concretely modify the traffic distribution of the two competition modes.Subsequently, to apply our models into network systems, a traffic distributor is designed.So, the proposed scheme CMT-LV can be embedded into TCP/IP layer to optimize the multipath traffic distribution.

The rest of this paper is organized as follows. Section II introduces general LV model.And in section III, the proposed traffic distribution scheme CMT-LV is put forward, which is composed of two competition models. At last, the simulation setup and results are discussed in Section IV and conclusion of the paper is presented in Section V.

II. GENERAL LV MODEL

In nature, due to limited environment resources, population of each species is restricted.Also, population of various species of each ecosystem always dynamically approaches equilibrium. The LV competition model [9] is used to describe the population evolution of different species in an ecosystem, and an extended LV model with n species is presented as follows:

For species , the competition coefficientsand, intrinsic growth rate, and carrying capacityare positive constants. Subsequently, according to (1), we can obtain the following theorem.

Theorem.Supposedi fa n dwhereandare positive constants, equation (1) has one stable solution,(x1(t),x2(t), ... ,xn(t)), each component of which can be expressed as follows:

Proof.According to the supposedand(1), following equation can be obtained,

Now, we can solve the equation above as follows:

Then,

Through (2) in the theorem, we can present dynamic variations of species population in an ecosystem, and Figure 1 shows the population variations because of new invasive species.In thefigure, from time 0 to time 39, the ecosystem has only one species, species 1, whose population keeps stable. However, four new species come into the ecosystem respectively at time 40, 80, 120, and 160. Though new spe-cies instantaneously break the original equilibrium state, the ecosystem always approaches new equilibrium including the population of new species. It can be seen form the Figure 1,the population of the original species always declines, and that of new species increases.Finally, they go to the equilibrium.

III. A CMT TRAFFIC DISTRIBUTION SCHEME BASED ON LV MODEL

3.1 Competition behaviors analysis on CMT of multihomed networks

In multihomed networks, each multihomed S-D (source and destination) host pair can usually establish multiple transmission paths through multiple connectable access networks.Figure 2 shows multipath transmission process of multihomed equipment, for example, smartphone, notebook computer, and fixed host with multiple network cards. Here, multihomed networks can include Ethernet, Wi-Fi, and 2G/3G/4G networks, and these networks connect to Internet by ABR (Area Border Router).

CMT is introduced to increase transmission bandwidth of each multihomed host in multihomed networks. However, if each multihomed host uses CMT to transmit data, they compete for network bandwidth. Here, we conclude two competition modes respectively for multiple S-D streams and multipath. One is that multiple S-D streams compete for bandwidth in one path, the other one is that multiple paths compete for traffic between one multihomed S-D host pair. And, they correspond to Case 1 and Case 2 in Figure 2. Because LV model in (1) can adaptively adjust population of several competitors with shared resource,we propose two modified competition models respectively for two modes.

3.2 Multiple S-D streams competition for bandwidth of one shared path

Fig.1 Equilibrium state approaching demonstration of species population

Table I Analogy between predator-prey system and multiple S-D streams competition case

In this subsection, we present a redesigned LV model about multiple S-D streams competition for one path, which expresses competition behaviors of multiple S-D streams by (1).Here,is sending rate of traffic from-th S-D streams at time.andis inter-SD-streams and intra-SD-streamcompetition coefficients. And,is intrinsic traffic growth rate of each S-D stream. Subsequently,is maximum sending rate of traffic from the-th S-D stream i.e., the maximum sending rate that can be sustained by the S-D stream in the absence of all other S-D streams competing for same path bandwidth. Furthermore, Table I expresses an analogy between predator-prey system and multiple S-D streams competition case.

Without the loss of generality, we give four assumptions for Case 1 of Figure 2:

1. The effects of inter-SD-streams competition on each other for one path are identical,i.e. the coefficient

2. The effects of intra-SD-stream competition are identical, i.e. the coefficientwhereis occupancy ratio of the shared path, that is the number of S-D streams through the path.

Fig.2 Two Competition modes in multihomed networks

Table II Analogy between predator-prey system and multipath competition for traffic of each multihomed S-D pair

3. The intrinsic traffic growth rate of each S-D stream is identical, i.e. the coefficient

4. There is only one shared resource, i.e.physical bandwidth of the shared path. If the shared path is used by only one S-D stream,maximum sending rate of traffic from this S-D stream is as follows:

where path_BDW denotes the physical bandwidth of the shared path, receiver_WND denotes the maximum acceptable sending rate for receiver buffer, and max_rate denotes the maximum sending rate allocated by the S-D stream.

Here, we present a redesigned LV model about multipath competition for traffic between each multihomed S-D host pair, which expresses competition behaviors of multiple paths by(1). Then,is traffic sending rate of-th path at time, andis intrinsic traffic growth rate of each path. Subsequently,andis inter-paths and intra-path-competition coefficients. Alsois maximum traffic sending rate of the-th path i.e., the maximum sending rate that can be sustained by the path in the absence of all other paths competing for the same traffic. Furthermore, TABLE II makes an analogy between predator-prey system and multipath competition for traffic of each multihomed S-D pair.

Similarly, for the Case 2 in Figure 2, we present following four assumptions and definitions:

1. The effects of inter-paths competition for traffic between each multihomed S-D host pair are identical, i.e. the coefficient

3.3 Multipath competition for traffi c between each multihomed S-D host pair

2. To distribute the traffic into each path fairly, the intra-path competition coefficient is set according to occupancy ratio of each path,that is, the number of S-D streams through the path.

Otherwise, if there are more than one S-D stream passing through the path , the intra-path competition coefficient of the path is set according to the second assumption in last subsection.

3. The intrinsic traffic growth rate of each path is identical, i.e. the coefficient.

4. There is only one shared resource, i.e.total traffic sending rate between the corresponding S-D pair. If the S-D pair has only one path, the total traffic sending rate is also physical bandwidth of the path.

3.4 Traffi c distributor

In the last two subsections, we introduce two competition models about multiple S-D streams competition for one path and multipath competition for traffic between each multihomed S-D host pair. Here, we present a concrete traffic distribution scheme according to two models, which is called an adaptive CMT traffic distribution scheme based on LV model, CMT-LV for short.

When some data from application layers arrives at TCP/IP layer, it is buffered in a memory pool. Then, data is divided into many segment data according to TCP/IP protocol.Subsequently, each segment data is encapsulated in an IP packet and sent to destination host. However, it is important to improve transmission efficiency how the TCP/IP layer adaptively distributes these IP packets with segment data into different paths. Here, we setup a traffic distributor in the TCP/IP layer to embed our proposed traffic distribution scheme (CMT-LV). Furthermore, other comparison schemes can also be embedded into TCP/IP by the distributor, for example, greedy path selection, random path selection, and uniform traffic distribution.

The distributor can be seen in Figure 3.Here, each multihomed host has a traffic distributor in its TCP/IP layer, and then the distributor can probe path-related information by path feedback mechanism, e.g., path bandwidth, the number of S-D streams in one path, and path ETE (end-to-end) delay[13].According to the path-related information, the distributor can distribute traffic into multipath by a specified traffic distribution scheme.

Fig.3 A traffic distributor in TCP/IP layer

Fig.4 Traffic distribution flow of the proposed scheme CMT-LV

Figure 4 presents traffic distribution flow of our proposed scheme (CMT-LV). Here, we set a variable for each path to determine its traffic transmission time, which is called next packet sending time. When data for application layer arrives in traffic distributor, data is buffered in memory pool. Then, the distributor checks in turn if the next packet sending time of each path expires. If it expires, one IP packet with application segment data will be sent to this path. Otherwise, the distributor will check next path. Subsequently, the next packet sending time of the path sent one IP packet will be updated by our proposed scheme.Concretely, if the number of S-D streams that occupy the path is greater than 1, its sending rate is calculated by the model in Subsection 3.2. Otherwise, its sending rate is calculated by the model in Subsection 3.3. Here, the sending rates are calculated by the two models with (2). Consequently, the interval between current time and next packet sending time is obtained as inverse of the sending rate. So, the next packet time is summary of current time and the interval.

3.5 Complexity analysis

In the traffic distributor, we don’t basically create additional packets except in the process of the path-related information probe. When probing the path information, a probe packet can be a data packet to be sent. With the aid of a flag that is set in the data packets, the destination can identify it and send a corresponding feedback packet. Then the feedback packet can be a data packet to be sent or a high layer(TCP) ACK packet. But if there is no ACK packet or data packet to be sent timely, a feedback packet only including path and destination related information can be created for the source. Actually, the feedback packets generated occasionally increase traffic throughput very few.

Besides, to obtain the next packet sending time, the proposed scheme calculates the sending rate of each path through (2). Here, if one multihomed S-D host pair haspaths, computational complexity of (2) is. Actually,the computations ofand the intra-SD-stream or intra-paths competition coefficientare arranged in the same loop statement. In other places, there don’t have complex computations.

3.6 Stability analysis

To satisfy QoS requirements and ensure stability of multipath transmission, the proposed CMT-LV scheme is required to be able to make the sending rate of each path or S-D stream rise rapidly. According to the Theorem in Section II, the model of (1) has one stable solution, which isAlso, for fixed constants,is sufficiently great, the growth speed of the sending rate must be fast enough.

Subsequently, we test traffic variations of four paths in Figure 2 by the proposed CMTLV scheme. Figure 5 presents the sending rate variations of each path in the scenario of Figure 2, where “●” mark denotes the real-time sending of each path. Here, we set three cases for carry capacity (physical bandwidth) of four paths, which are respectively (150, 200,250, 300) marked by symbol “x” in time interval [0, 50], (250, 300, 350, 400) marked by symbol “*” in time interval [51, 100], and(100, 150, 200, 350) marked by symbol “+” in time interval [101, 150]. It can be seen from the Figure 5, the proposed scheme can always make the sending rate of each path rapidly approach the capacity no matter how path physical bandwidth changes. Meantime, it validates the stability of our scheme. Then, we will test whether the proposed scheme can improve data transmission efficiency of FTP service in multihomed networks.

Subsequently, we test traffic variations of four paths in Figure 2 by the proposed CMTLV scheme, as shown in Figure 5, where “●”mark denotes the real-time sending rate of each path. Here, we set three cases for carry capacity (physical bandwidth) of four paths,which are respectively (150, 200, 250, 300)marked by symbol “x” in time interval [0, 50],(250, 300, 350, 400) marked by symbol “*”in time interval [51, 100], and (100, 150, 200,350) marked by symbol “+” in time interval[101, 150]. It can be seen from the Figure 5,the proposed scheme can always make the sending rate of each path rapidly approach the capacity no matter how path physical bandwidth changes. Meantime, it validates the stability of our scheme. Then, we will test whether the proposed scheme can improve data transmission efficiency of FTP service in multihomed networks.

IV. SIMULATIONS

4.1 Simulation con figuration

To evaluate performance of our proposed traffic distribution scheme CMT-LV in multihomed network environments, we perform simulations in OPNET simulator. Simulation scenario is composed of 24 nodes, and those nodes are homogeneously distributed in a 10km12km area, including 6 multihomed hosts and 18 routers. Its basic layout uses the Figure 2 for reference. Without the loss of generality, three multihomed S-D host pairs are set in the scenario to facilitate testing of traffic distribution into different paths. Also,each S-D pair has three paths between them at least.

Fig.5 Sending rate variations of four paths in the scenario of Figure 2

Particularly, FTP service is configured in our scenario as an application, and each multihomed host can upload/download files to/from its corresponding destination multihomed host through multipath. The particular scenario parameters are showed in TABLE III except the defaults. Additionally in the FTP service, each client uploads or downloads files by sending the control messages with PUT and GET commands to the corresponding servers, where the PUT command denotes the corresponding client requires to upload files to its server, and the GET command denotes the corresponding client requires to download files from the server.Then the servers determine to receive or transmit thefiles in conformity to the commands in the control messages. In TABLE III, command mix (GET/Total) specifies the percentage of thefile-download requests of each client in its total requests, and inter-request time specifies the distribution function about the interval between two continuous file requests. Then,in the simulation, each multihomed host is set to send each file with an exponential distribution time for inter-request time (seconds),and the size of each file is set with a constant distribution. To validate the adaptation of the proposed scheme to the dynamic multihomed network environments, thefile sending is performed with 8 different expectation values in the exponential inter-request time. And, they are respectively Exponential(10), Exponential(20), …, Exponential(80), where 10, 20,…, 80 are the expectation values of the exponential inter-request time distribution. Finally,the simulation will be executed for an hour,and some other particular parameters can also be seen in Table III.

4.2 Simulation results and performance evaluation

As a comparison, we also implement a uniform traffic distribution scheme, and two path selection schemes. Here, the uniform scheme is to distribute the traffic into different pathswith a uniform distribution. And, the two path selection schemes are respectively greedy path selection and uniform random path selection,which can send packets only by one path and periodically select the transmission path greedily and at uniform random[14, 15]. Concretely,the greedy scheme selects the path with lowest path ETE delay as the transmission path of corresponding S-D pair each regular time. Actually, these three compared schemes can be performed easily through our designed traffic distributor presented in last section. Finally by applying the traffic distributor in the OPNET simulator, we compare the three schemes with our proposed scheme CMT-LV on improving the performance of the FTP service.

Table III Scenario parameters

Fig.6 The averagefile-load time comparison about various traffic intensity

Figure 6, Figure 7 and Figure 8 show the comparisons of four schemes on improving the transmission performance of the FTP service with the increasing expectation values of the inter-request time exponential distribution.They respectively shows average file download and upload (down-upload) time and average traffic throughput (average traffic received and average traffic sent) comparison for four schemes, i.e., CMT-LV, CMT-Uniform (uniform traffic distribution), Greedy (greedy path selection) and Random (uniform random path selection). Here, the average about down-upload time and traffic throughput denotes the average in the whole simulation.

Then, it can be seen from the Figure 6 the effect of different inter-request time distribution on the average down-upload time. As a result, the proposed scheme (CMT-LV) can basically perform better on reducing average down-upload time than the other three scheme except about the expectation values 40 and 50.It is reasonable because the exponential traffic distribution has characteristics of burstiness and intermittency.

Besides, the Figure 7 and Figure 8 present the comparison of four schemes about the traffic throughput. Here, the Figure 8 shows variations of the traffic sent are identical for the four schemes on the whole with the increasing of the distribution expectation.Expectedly, from the Figure 7, it can be seen that the proposed scheme increases the traffic received more than the other schemes. At the same time, it is evident that the proposed scheme can actually balance network load and reduce the number of queuing packets. However, when the distribution expectation value is greater than 60, the average traffic received of the proposed scheme declines. Because the distribution expectation value is greater, the inter-request time is longer. So, it leads to the less traffic sent. Naturally, the less traffic will make the performance of the different schemes approach identical. But, the Figure 6 shows the proposed scheme still effectively reduces the file transmission time with more than 60 distribution expectation values. Thence, compared with the three schemes, the proposed scheme CMT-LV can perform better about reducing file transmission time and increasing traffic throughput.

V. CONCLUSIONS

Inspired by the predator-prey competition mechanism of the ecosystem, we propose an adaptive traffic distribution scheme for CMT in multihomed networks, which can increase the traffic throughput and reduce thefile transmission time of the FTP service. In the future work, we will discuss the other performance of the proposed scheme CMT-LV, for example,load balancing and transmission reliability.Also, we expect to improve the efficiency of other services by the proposed scheme, e.g.,multimedia service, including video and voice transferring.

Fig.8 The average traffic sent comparison about various traffic intensity

ACKNOWLEDGEMENTS

This work was supported by National Basic Research Program of China (Grant No.2012CB315905), National Natural Science Foundation of China (Grant No. 60932005,61172048, 61100184, 61201128), and National High-tech R&D Program (Grant No.2013AA01A209).

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