electronics
Article The Yellow Active Queue Management Algorithm in ICN Routers Based on the Monitoring of Bandwidth Competition
Li Zeng 1,2 , Hong Ni 1,2 and Rui Han 1,2,*
1 National Network New Media Engineering Research Center, Institute of Acoustics, Chinese Academy of Sciences, No. 21 North Fourth Ring Road, Haidian District, Beijing 100190, China; [email protected] (L.Z.); [email protected] (H.N.) 2 School of Electronic, Electrical and Communication Engineering, University of Chinese Academy of Sciences, No. 19A Yuquan Road, Shijingshan District, Beijing 100049, China * Correspondence: [email protected]; Tel.: +86-1-381-107-7380
Abstract: Deploying the active queue management (AQM) algorithm on a router is an effective way to avoid packet loss caused by congestion. In an information-centric network (ICN), routers not only play a role of packets forwarding but are also content service providers. Congestion in ICN routers can be further summarized as the competition between the external forwarding traffic and the internal cache response traffic for limited bandwidth resources. This indicates that the traditional AQM needs to be redesigned to adapt to ICN. In this paper, we first demonstrated mathematically that allocating more bandwidth for the upstream forwarding flow could improve the quality of service (QoS) of the whole network. Secondly, we propose a novel AQM algorithm, YELLOW, which predicts the bandwidth competition event and adjusts the input rate of request and the marking
probability adaptively. Afterwards, we model YELLOW through the totally asymmetric simple exclusion process (TASEP) and deduce the approximate solution of the existence condition for each
Citation: Zeng, L.; Ni, H.; Han, R. stationary phase. Finally, we evaluated the performance of YELLOW by NS-3 simulator, and verified The Yellow Active Queue the accuracy of modeling results by Monte Carlo. The simulation results showed that the queue Management Algorithm in ICN of YELLOW could converge to the expected value, and the significant gains of the router with low Routers Based on the Monitoring of packet loss rate, robustness and high throughput. Bandwidth Competition. Electronics 2021, 10, 806. https://doi.org/10.3390 Keywords: ICN; active queue management; congestion control; TASEP; QoS; content router /electronics10070806
Academic Editor: Francisco Falcone 1. Introduction Received: 5 March 2021 According the statistics from Cisco, global IP traffic has quadrupled over the past Accepted: 24 March 2021 Published: 29 March 2021 5 years. From 2017 to 2022, IP traffic will continue to grow at an average annual compound growth rate of 26% [1]. The existing end-to-end communication mode of TCP/IP has
Publisher’s Note: MDPI stays neutral been unable to meet the needs of massive content distribution. The traditional TCP/IP with regard to jurisdictional claims in network is facing a series of problems such as scalability, mobility, security. Therefore, published maps and institutional affil- a promising future network architecture named information-centric networking (ICN) iations. has attracted researchers’ attention, such as Data-Oriented (and Beyond) Network Ar- chitecture [2], Content-Centric Network (CCN) [3], Network of Information (NetInf) [4], Publish-Subscribe Internet Routing Paradigm (PSIRP) [5]. Rather than gradually patching on the existing network like Content Delivery Network (CDN) [6] or IPv6 [7], ICN attempts to clean-state update the traditional network. In ICN, ubiquitous cache nodes reduce the Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. user’s download latency of content and the drain of network bandwidth, which enables This article is an open access article efficient content distribution. Adding a new content store (CS) module with complete ICN distributed under the terms and protocol stack in each router makes the router become a content provider. conditions of the Creative Commons In the early research, the high cost Static Random-Access Memory (SRAM) limited the Attribution (CC BY) license (https:// cache capacity of router to multi hundreds of megabytes (MB) [8]. Nowadays, researchers creativecommons.org/licenses/by/ have carried out extensive studies on how to design content router with cache capacity 4.0/). of multi terabytes (TB) [9–11]. For example, in our previous study, in order to make
Electronics 2021, 10, 806. https://doi.org/10.3390/electronics10070806 https://www.mdpi.com/journal/electronics Electronics 2021, 10, 806 2 of 23
the IP network evolve to ICN smoothly, we designed and implemented a router with huge cache capacity [11] through the latest storage performance development kit (SPDK) technology [12]. Chunk is the basic transmission unit in ICN. Some studies believe that link utilization can be improved by setting the size of chunk up to a few MBs due to the substantial overhead brought from small-sized chunks [13]. Owing to the limitation of the network maximum transmission unit (MTU), the content chunk will be cut into many segments to transmit in the network. Routers along the data transmission path collect and assemble these segments into complete chunks, and verify the integrity and correctness of this chunk. The receiver-driven ICN transport protocol ensures the reliable transmission of data chunks, including request loss and timeout retransmission, and traffic congestion control by adjusting the request sending rate in a receiver end system. As the limit of the ICN router’s cache capacity is broken [9], that is, the percentage of cache entries in the total content catalog becomes larger, the cache-hit ratio of the router will naturally increase. With the increase of concurrent services, the throughput requirement of internal cache service traffic will also increase, which will seize port bandwidth and buffer resources of the router against with the external forwarding traffic. Excessive competition will cause congestion, packet loss and may make the Quality of Service (QoS) of the whole ICN network drop sharply. Once any packet is dropped in one node, the chunk that loss packet belongs to will be unable to cache in all the subsequent nodes on the transmission path with high probability, which reduces the utilization of router memory and link. Although the ICN transport protocol contains fast retransmission mechanism, in the heavy load network environment, the round-trip time (RTT) and the queuing delay in each router are enough to release the assembling space allocated from the router memory for this chunk in advance [11]. Many studies [14,15] believe that caching content as close to the network centric node with high betweenness as possible could achieve a large amount of benefit, such as high cache hit rate, lower traffic on link and cache eviction rate. We refute this viewpoint here, because increasing the cache-hit ratio in such a high throughput node will only aggravate the bandwidth competition. There are two typical congestion control mechanisms in a traditional TCP/IP network, which are both effective methods to improve QoS. One is based on end to end. However, only relying on the source end to reduce the sending window cannot relieve the buffer over- flow caused by burst flow effectively, which is the design defect of loss-based transmission protocol [16]. Since the router is the closest congestion perceiver in the network, various network metrics contribute to measure the congestion in real time. Therefore, the other is deploying an active queue management (AQM) algorithm on router, which discards packets adaptively. Afterwards, congestion information will be implicitly or explicitly notified (ECN) to the source for further adjustment, which improves the transmission efficiency of the network [17]. In ICN, most of the congestion control research is carried out around with end-to-end [18–20], which imitates the window-based congestion control mechanism in TCP. Considering the content characteristics of multi-source and multi-path in ICN, these methods usually maintain multiple timeout values and multiple windows to judge and control congestion, which makes the content router maintain a large number of flow states and increases the complexity of congestion control. There are also some research works [21,22] that judge congestion through the assistance of intermediate router nodes. Like some AQM algorithms in IP networks, these methods judge congestion by queue occupancy or packet input rate. Nevertheless, they do not perform packet loss operation on the router, they just inform the receiver to adjust the sending rate of the request packet. It is difficult for these methods similar to the ECN mechanism in the IP network to avoid global synchronization of traffic. Moreover, owing to the well-known differences between ICN and IP, including receiver-driven flow control, stateless forwarding, symmetric paths, we believe that deploying the traditional AQM algorithm in the ICN router directly and mechanically can not achieve significant performance improvement. In summary, the contribution of our work comprises: Electronics 2021, 10, 806 3 of 23
• We analyzed how additional end attributes in ICN router contributes to congestion through probability theory. Afterwards, we proposed a novel active queue manage- ment algorithm YELLOW based on bandwidth competition prediction and limitation for ICN content routers. YELLOW provides a new idea for the design of ICN conges- tion control algorithm and cache service module in router. • In order to analyze the correlation between the input rate of request packets and congestion, we modeled the packets’ dynamics of bandwidth competition in the YELLOW algorithm through the classic totally asymmetric simple exclusion process (TASEP) model, and deduced the approximate solution of the existence condition for each stationary phase. • We performed a large number of comparative experiments with several widespread used AMQ algorithms under the ICN environment simulating by NS-3. Experimental results demonstrated the queue of YELLOW can be stable at the expected value, and the significant gains of a router with low packet loss rate, robustness and high throughput. Moreover, we conducted extensive experiments to verify the accuracy of our analysis model for the YELLOW algorithm. The remainder of this paper is organized as follows. Section2 provides related research of our work. Section3 presents the cause and solution analysis of congestion in ICN and the design of YELLOW. The TASEP model analysis of the traffic behavior pattern in YELLOW is presented in Section4. Our experimental results are shown in Section5. Finally, we conclude the paper and describe our future work in Section6.
2. Related Work 2.1. Active Queue Management Since the change of internal state of the network can not be detected accurately in the end system, it is more effective and timely to detect and adjust congestion in a router than the window-based TCP congestion control strategy. The simplest drop-tail algorithm is widely used at the earliest, but the long-term full queue will lead to TCP global syn- chronization, queue deadlock and other network performance problems. Floyd et al. [23] proposed the random early detection (RED) algorithm in 1993 to overcome the shortcom- ings of drop-tail, which is the earliest standard AQM scheme recommended by the Internet Engineering Task Force (IETF). RED estimates congestion and calculates the marking prob- ability according to the queue length. In the past 20 years, many AQM algorithms have been proposed, which can be divided into two types: one is the optimization algorithm based on RED, the other is designed based on control theory. The performance of the RED algorithm is closely related to the fluctuation of network traffic and the different settings of parameter configuration. Meanwhile, the lack of fairness of RED is neatly illustrated by the fact that the burst flow will quickly occupy the queue resources, which leads to the abnormal transmission of other flow. Therefore, many improved algorithms are proposed, especially GRED [24], ARED [25], SRED [26] and BLUE [27]. SRED algorithm is so complex that it consumes abundant router memory resources, resulting in low scalability. ARED and GRED make the algorithm adaptive and keep the queue length convergent by dynamically adjusting the packet loss probability, although the problem of parameter sensitivity has not been solved perfectly. Compared with the above algorithms, BLUE achieves the lowest packet loss rate with the lowest memory overhead while including a scheduling algorithm based on the Bloom filter to ensure the fairness of each flow. Misra [28] et al. first proposed a feedback control model based on TCP to optimize the AQM algorithm while they gave the exact solution. The adaptive virtual queue algorithm (AVQ) [29] achieves a proper balance between high utilization and low delay through using linear differential equations to adjust the virtual capacity of the router. However, due to the lack of explicit control to queue length, the performance of AVQ is not ideal. Ünal [30] et al. introduced the proportional integral (PI) controller to maintain the stability of the queue, but it has the defects of slow response speed and overdependence on buffer size. With the improvement of artificial neural network and fuzzy logic control theory, some Electronics 2021, 10, 806 4 of 23
researchers tried to apply intelligent control theory to design an AQM algorithm based on a proportion integral differential (PID) controller. The self-learning ability of a neuron can adjust the three parameters of PID online, so that these algorithms [31,32] can obtain stable performance under the fluctuating network environment. Not only can control theory be used to model the congestion caused by limited bandwidth and buffer resource of content routers, the well-assessed queuing theory is a common method to analyze and improve the performance of resource-constrained networks. For example, to eliminate the coupling effect between multiple flows in the router on the packet forwarding rate, [33] deployed multiple decoupled queues on a single node and calculated the ideal transmission rate of packets through the M/D/1 queuing model. Besides, [34,35] utilized queuing theory model called Jackson networks (M/M/k open queueing networks) [36] to analyze the dependence between service response time and node capacity constraints, and deduces the optimal cache allocation to meet the required cost/resource tradeoff. Nowadays, there are few research works that apply the AQM algorithm on ICN. In an ICN-5G network scenario, to satisfy the strict delay constraint from the perspective of transmission control, Shahin et al. proposed a centralized AQM algorithm including load balancing and rerouting [37]. Moreover, Wang et al. [38]. proposed an AQM algorithm in which congestion is detected by monitoring the queuing time of packets. Although this method could achieve high link utilization, the simulation experiment was limited bandwidth to 100 Mbps. We believe that the high complexity of this algorithm may make it difficult for ICN routers to maintain line speed forwarding in actual deployment.
2.2. Congestion Control in Information-Centric Network (ICN) Although ubiquitous cache nodes in ICN reduce redundant transmission traffic on the network and achieve efficient content distribution, congestion may still occur. ICN has yet to determine its approach to congestion control, including whether window-based or rate-based congestion control would be the best. Since the window-based congestion control has been studied and deployed widely in the IP network, the majority of research on ICN congestion control focuses on it as well. ICP [18] and ICTP [19] detected retransmission timeout (RTO) as congestion signal and adjust congestion window through additive increase multiplicative decrease (AIMD). Since the segments of one content chunk may be scattered around the network, the response delay from different sources varies greatly. Unfortunately, both these two protocols do not consider the influence of multi-source content on RTO value. CCTCP [20] attempted to solve the above problem by maintaining an independent RTO timer for each content source, but the huge cost makes it difficult to extend with a large scale. However, the error of RTO estimation cannot be avoided when the RTT detection is not accurate or the network link is unreliable. M. Amadeo [39] proposed an improved protocol to reduce the error of RTO estimation in the wireless environment of Named Data Networking (NDN) through adjusting the sending gap of interest packets according to the arrival rate of data packets. The “pull” request mode in ICN turn the transmission protocol from the sender-driven to the receiver-driven, which offloads the state management and transmission control to the user. The cache module in the router does not need to save the state of each service flow, which reduces the memory overhead and improves its robustness and performance. Moreover, routers can directly par- ticipate in congestion control by shaping the forwarding rate of interest packets, and report congestion information to the requester through NDN acknowledge character (NACK), especially HOBHIS [21] that is a hop by hop congestion control algorithm. [22] considered that the shaping rate should refer to the predicted value of content popularity, which is essentially to reallocate the router bandwidth resources in term of the popularity. However, how to determine and maintain the content popularity for a long time is still an outstanding problem. Karami et al. [40] considered using neural network to predict which link may be congested in the whole network. However, how to design a reasonable neural network model with low training complexity is an urgent problem for this kind of study. The design Electronics 2021, 10, 806 5 of 23
purpose of a loss-based transport protocol is one of the main factor of queue overflow. Therefore, Liu [41] proposed and implemented a delay-based transmission protocol in a wireless environment, which calculates the transmission rate and the maximum trans- mission window of the request according to the real-time predictive network bandwidth. Experimental results showed that this method improves the flow fairness and robustness, and can effectively reduce the congestion in the network.
3. The Design of Active Queue Management (AQM) Algorithm for ICN Router It is still an unsolved problem whether the traditional active queue management algorithm in a TCP network (such as RED, BLUE) is suitable for ICN or not. Firstly, we analyze how the end system added in ICN routers contribute to congestion. Secondly, we present the main ideas on how to relieve congestion caused by this problem. Eventually, we propose a lightweight active queue management algorithm YELLOW for ICN.
3.1. Problem Description Above all, we attempt to explain the cause of congestion from the perspective of the traffic direction into the router. Figure1 is a simple architecture diagram, which depicts an ICN content router with two ports. The character i represents the request packets. Suppose a request packet arrives at port 0 at a certain time, the ICN router will check whether the requested content has been cached. If not, the packet will be forwarded from port 1 to the next node according to the flow tables. When the requested data have been stored in the router, chunk will be fetched from cache memory and then put on the ICN protocol stack for transmission. The character d represents the data packets that arrive at port 0, which will be stored and forwarded by the router at the same time. Without the support of specific network strategy, the higher the cache-hit ratio in router, the higher the query per second (QPS) will be, which means that the throughput of internal service traffic will try its best to encroach on the router bandwidth. The ICN router at the edge of the network may often encounter bursting flow. For example, users watch a new popular movie at the same time. Although ICN can
Electronics 2021, 10, x FOR PEER REVIEWreduce the transmission traffic in the network, it is difficult to avoid6 of 24 congestion and packet loss in the router caused by the bandwidth competition of flow in different directions.
d i Forward
port 0
lookup
i port Forward Store Content d 1 Store d Send flow table Routing decision bandwidth competition ICN Content Router Figure 1. Information 1. Information-centric-centric network (ICN network) router (ICN)with content router store with. content store.
Specifically, for 푝표푟푡 1 with bandwidth 퐵푝, bandwidth competition always occurs betweenSpecifically, external traffic forforwardedport 1 fromwith 푝표푟푡 bandwidth 0 and internal Btrafficp, bandwidth generated from competition CS in always occurs responsebetween to request external traffic traffic. We believe forwarded that the main from factorport of 0congestionand internal and packet traffic loss generated from CS in inresponse ICN router to cannot request be explained traffic. by We buffer believe overflow that simply, themain but excessive factor bandwidth of congestion and packet loss competition at a more practical level. As shown in Figure 2, with the increase of the re- in ICN router cannot be explained by buffer overflow simply, but excessive bandwidth quest arrival rate, the throughput of response traffic 휏푐 increases while the available bandwidthcompetition of forwarding at a more traffic practical 휏푓 decreases. level. At As the shownright side in of Figurethe figure2, with(gray area) the, increase of the request the bandwidth suffers conflict (i.e. 휏 + 휏 > 퐵 ). arrival rate, the throughput푓 of response푐 푝 traffic τc increases while the available bandwidth of forwarding traffic τf decreases. At the right side of the figure (gray area), the bandwidth suffers conflict (i.e. τf + τc > Bp). conflict area
port capacity /
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Throughput Throughput
available bandwidth available
Response
cache hit arrive rate Figure 2. Bandwidth competition.
3.2. The Priority of Flow in Bandwidth Allocation With the increase of router cache capacity, cache hit rate and task concurrency will be improved greatly [11]. Therefore, the real-time bandwidth requirement of cache ser- vice traffic cannot be ignored and the conflict may occur at any time. Considering that some classic AQM that drop packets entering the buffer indiscriminately (such as RED Electronics 2021, 10, x FOR PEER REVIEW 6 of 24
d i Forward
port 0
lookup
i port Forward Store Content d 1 Store d Send flow table Routing decision bandwidth competition ICN Content Router Figure 1. Information-centric network (ICN) router with content store.
Specifically, for 푝표푟푡 1 with bandwidth 퐵푝, bandwidth competition always occurs between external traffic forwarded from 푝표푟푡 0 and internal traffic generated from CS in response to request traffic. We believe that the main factor of congestion and packet loss in ICN router cannot be explained by buffer overflow simply, but excessive bandwidth competition at a more practical level. As shown in Figure 2, with the increase of the re- Electronics 2021, 10, 806 quest arrival rate, the throughput of response traffic 휏푐 increases while the available6 of 23 bandwidth of forwarding traffic 휏푓 decreases. At the right side of the figure (gray area), the bandwidth suffers conflict (i.e. 휏푓 + 휏푐 > 퐵푝).
conflict area
port capacity /
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Throughput Throughput
available bandwidth available
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cache hit arrive rate Figure 2. 2. BandwidthBandwidth competition competition..
33.2..2. The The Priority Priority of of Flow Flow in in Bandwidth Bandwidth Allocation Allocation WithWith the the increase increase of of router router cache cache capacity, capacity, cache cache hit hit rate rate and and task task concurrency concurrency will will be beimproved improved greatly greatly [11 [1].1]. Therefore, Therefore, the the real-time real-time bandwidthbandwidth requirement of of cache cache ser- service Electronics 2021, 10, x FOR PEER REVIEW 7 of 24 vicetraffic traffic cannot cannot be ignored be ignored and and the the conflict conflict may may occur occur at anyat any time. time. Considering Considering that that some someclassic classic AQM AQM that that drop drop packets packets entering entering the the buffer buffer indiscriminately indiscriminately (such (such asas REDRED and BLUE), we figure that designing an AQM algorithm that can operate differently to the and BLUE), we figure that designing an AQM algorithm that can operate differently to trafficsthe traffics of of two two directions directions can can improve improve the QoS the QoSof the ofICN the network ICN networkmore effectively. more effectively. Now theNow question the question is, whichis, which direction direction traffictraffic should should have have higher higher priority priority in bandwidth in bandwidth allocation andallocation how and to take how careto take of care it carefully of it carefully when whenτf +휏푓 +τc휏>푐 >B퐵p푝. Figure 33 constructs constructs a a simple linear networksimple linear being network used being to used answer to answer the abovethe above question question from the the perspective perspective of of probability probability theory. We allocate port bandwidth by weighting, i.e., 휆1휏푓 + 휆2휏푐 = 퐵푝, theory. We allocate port bandwidth by weighting, i.e., λ1τf + λ2τc = Bp, where λ1, λ2 ≤ 1. where 휆1, 휆2 ≤ 1.
chunk m
User 1 content store
p p R3 R2 R1 chunk k
User 2 Pull NDO (chunk) by request content source
FigureFigure 3. 3. A Alinear linear topology topology using to using indicate to that indicate forward thating traffic forwarding should have traffic highershould priority have higher priority whenwhen bandwidth bandwidth competition competition happen happen..
In Figure 3, 푅1, 푅2, 푅3 are three adjacent ICN content routers with CS (dark red In Figure3, R , R , R are three adjacent ICN content routers with CS (dark red square). square). 푅1 is the closest1 to2 the3 content source server and the most upstream of the con- Rtent1 is transmission the closest path. to the R3 content is the closest source to the server user,and so it theis located most downstream. upstream of The the data content transmission path.chunk R3푚 requested is the closest by User1 to the is locateduser, so in it router is located 푅1 while downstream. User2 request The data data chunk chunk m requested 푘 from the content source server. Many studies indicate that the large size of chunk can by User1 is located in router R1 while User2 request data chunk k from the content source improve the link utilization, such as 4K in CCN [3] or even up to few MBs [13]. Owing to server.the limitation Many of studies the maximum indicate transmission that the largeunit (MTU), size of these chunk large can chunks improve will be the link utilization, suchsegmented as 4K into in CCNa certain [3 ]number or even of uppackets to few and MBsbe transmitted [13]. Owing on the to network the limitation then. As of the maximum transmissionshown in Figure unit 3, chunk (MTU), 푘 and these 푚 are large segmented chunks into will4 packets. be segmented The router will into collect a certain number of packetsthese packets and andbetransmitted then assemble on them the into network a complete then. chunk Asshown for caching in Figure in CS. 3It, ischunk k and m are supposed that routers adopting traditional AQM will drop the packets indiscriminately with probability 푝1 when congestion occurs. In addition, we analyze two ideal cases of the bandwidth allocation with different priorities under the condition of 휆1휏푓 + 휆2휏푐 = 퐵푝. One is 휆1 = 1. In other word, the router tries its best to allocate sufficient bandwidth for external traffic while the cache service traffic is dropped with probability 푝2. The other is 휆2 = 1, which is the opposite of the above. The router tries its best to ensure the caching service bandwidth while the external forwarding traffic is dropped with probability 푝2. Noted that we can easily deduce that 푝2 > 푝1. Therefore, a single segment of chunk dropped in a router can be regarded as a random independent event and follows the binomial distribution with probability 푝1/푝2. We supposed that once there is a packet loss in any node, the chunk that loss packet belongs to will be unable to cache in all the subsequent nodes on the transmission path. The reason is that in a realis- tic environment, RTT and the queuing delay are enough to release the assembling space allocated from the router memory for this chunk before all the retransmission packets arrive. Tables 1 and 2 summarize the probability and expectation of the number of cache nodes and retransmission for chunk 푚 and 푘, respectively. As the expectation analyses summarized in Tables 1 and 2 show, we can draw a conclusion that the forwarding traffic from upstream deserves more bandwidth, which can bring better benefit to QoS of cache Electronics 2021, 10, 806 7 of 23
segmented into 4 packets. The router will collect these packets and then assemble them into a complete chunk for caching in CS. It is supposed that routers adopting traditional AQM will drop the packets indiscriminately with probability p1 when congestion occurs. In addition, we analyze two ideal cases of the bandwidth allocation with different priorities under the condition of λ1τf + λ2τc = Bp. One is λ1 = 1. In other word, the router tries its best to allocate sufficient bandwidth for external traffic while the cache service traffic is dropped with probability p2. The other is λ2 = 1, which is the opposite of the above. The router tries its best to ensure the caching service bandwidth while the external forwarding traffic is dropped with probability p2. Noted that we can easily deduce that p2 > p1. Therefore, a single segment of chunk dropped in a router can be regarded as a random independent event and follows the binomial distribution with probability p1/p2. We supposed that once there is a packet loss in any node, the chunk that loss packet belongs to will be unable to cache in all the subsequent nodes on the transmission path. The reason is that in a realistic environment, RTT and the queuing delay are enough to release the assembling space allocated from the router memory for this chunk before all the retransmission packets arrive. Tables1 and2 summarize the probability and expectation of the number of cache nodes and retransmission for chunk m and k, respectively. As the expectation analyses summarized in Tables1 and2 show, we can draw a conclusion that the forwarding traffic from upstream deserves more bandwidth, which can bring better benefit to QoS of cache and transmission efficiency when congestion occurs. Note that the linear topology is an important part of complex networks, so this conclusion can be easily extended to any network node.
Table 1. The probability and expectation of the number of cache nodes for chunk m and k.
Strategy Chunk Cache in 3 Nodes Cache in 2 Nodes Cache in 1 Node Expectation 4 4 3 m (1 − p )8 3 i 8−i 3 i 4−i 1 ∑ C4 p1(1 − p1) ∑ C4 p1(1 − p1) ∑ xk pk i=1 i=1 k=1 Forwarding without distinction 4 4 3 k (1 − p )12 3 i 12−i 3 i 8−i 1 ∑ C4 p1(1 − p1) ∑ C4 p1(1 − p1) ∑ xk pk i=1 i=1 k=1 3 4 x p Forwarding internal traffic from CS m (1 − p )8 3 i 8−i 0 ∑ k k 2 ∑ C4 p2(1 − p2) k=2 with high priority i=1 ( = ) λ2 1 k 0 0 1 1 Forwarding external traffic from port m 0 0 1 1 with high priority (λ1 = 1) k 1 0 0 3
Table 2. The probability and expectation of retransmission for chunk m and k.
Strategy Chunk Retransmission Hop Expectation 12 h 12i m 1 − (1 − p1) 3 3 1 − (1 − p1) Forwarding without distinction 12 h 12i k 1 − (1 − p1) >3 >3 1 − (1 − p1) Forwarding internal traffic from 8 h 8i m 1 − (1 − p2) 3 3 1 − (1 − p2) CS with high priority (λ2 = 1) k 1 >3 >3 Forwarding external traffic from m 1 3 3 port with high priority (λ1 = 1) k 0 >3 0
3.3. The Design of YELLOW Algorithm In light of the above analysis, we consider that designing an active queue manage- ment algorithm for ICN should assign bandwidth with higher priority to the traffic from upstream nodes. Therefore, we propose a novel AQM algorithm called YELLOW, which employs dual queue and real-time requests arrive to monitor congestion caused by band- width competition between forwarding and caching. Algorithm 1 shows the details of Electronics 2021, 10, 806 8 of 23
YELLOW, which differs from lots of known AQM algorithms that only use the instanta- neous occupancy of a single queue to identify congestion [23–27]. Without increasing the memory overhead, YELLOW sets two queues Q f and Qc in which the forwarding traffic from external and the cache response traffic from internal content stores are queued. Yellow maintains two probabilities p f and pc to drop (mark) packets before they enter the queue. The instantaneous queue length is still a significant monitoring parameter. YELLOW will always firstly increase pc when the packet loss or instantaneous queue length exceed the threshold (L1 or L2), while the change of p f depends on the more restrictions. In ICN, every data packet segmented from one chunk needs to be pulled to user by one request packet [20]. Therefore, the throughput τc required by the cache service can be well pre- dicted by the arrival rate of request γ (γ ≤ τc). If γ ≥ B − τf at a certain time, it means that the packet loss rate will rise sharply because of the rapid queue overflow. YELLOW will limit the rate of request packets entering the router by token bucket algorithm, which allows YELLOW to respond quickly to excessive bandwidth competition. Note that by contrast with some AQM algorithms who shape the rate of the request forwarding outward, YELLOW adjusts the rate of the request entering CS. If the explicit congestion notification (ECN) mechanism is allowed, router will set the ECN field in packet header to 1 to inform the requester. On the contrary, if the queue length is lower than the threshold or the link is idle, YELLOW will reduce the marking probability. δ1, δ2, δ3 are the values with which the marking probability increases or decreases when an abnormal condition is detected. Moreover, they are set to provide the link ability to effectively adapt to macroscopic changes in load across the link. The value of δ1 should be several orders of magnitude greater than that of δ2, δ3, which also reflects our biased treatment on cache response traffic and p f should be set to 0 at the beginning. freeze_time is the minimum interval of each update to the marking probability. The value of freeze_time should be set with reference to the effective RTT of the cache service flow in router, so as to allow the changes to be adequately fed back to the requester at the time interval. Over typical links, using freeze_time values between 10 and 200 millisecond (ms) will allow the marking probability to range from 0 to 1 on the order of 5 to 15 s.
Algorithm 1: YELLOW (Len > L Len > L 1. Upon Packet loss or Qf 1 or Qc 2) event: 2. If (( now − last _update) > freeze _time) then 3. pc = pc + δ1 4. if γ × M ≥ B − τf then 5. Limiting the rate of the hit request to B − τf 6. if ECN_PERMIT then 7. set ECN_FLAG in response packet 8. end 9. end Len > L 10. if Qf 1 then 11. pf = pf + δ2 12. if ECN_PERMIT then 13. set ECN_FLAG in response packet 14. end 15. end 16. last_update = now 17. End 18. Upon link idle event: 19. If (( now − last _update) > freeze _time) then 20. pc = pc − δ3 21. pf = pf − δ3 22. last_update = now 23. End Electronics 2021, 10, 806 9 of 23
4. Modeling Electronics 2021, 10, x FOR PEER REVIEW In this chapter, we model the forwarding behavior of packets of the YELLOW10 algo-of 24
rithm through TASEP [42]. We first introduce TASEP model briefly, and then deduce the existence conditions for each stable phase of YELLOW. 4.1. Totally Asymmetric Simple Exclusion Process (TASEP) 4.1. Totally Asymmetric Simple Exclusion Process (TASEP) TASEP is the most studied model, which is often used to analyze the dynamics and TASEP is the most studied model, which is often used to analyze the dynamics and phase transition process of moving objects. The rules of particle motion in the TASEP phase transition process of moving objects. The rules of particle motion in the TASEP model are simple, which makes the mathematical analysis easy to deduce. TASEP and its model are simple, which makes the mathematical analysis easy to deduce. TASEP and itsrelated related models models can can be be used used to to effectively effectively analyze analyze many many common statistical physical physical phenomena, such such as as simulating simulating road road traffic traffic flow flow and transport and transport process process of biological of biological protein molecules.protein molecules. In some In relatively some relatively simple scenes simple where scenes the where TASEP the model TASEP is applied,model is theapplied, exact solutionthe exact can solution be obtained can be easilyobtained by theeasily Bethe by the ansatz Bethe method ansatz [43 method]. [43]. To facilitatefacilitate understanding,understanding, we we introduce introduce TASEP TASEP through through modeling modeling traffic traffic flow flow on theon road.the road. Figure Figure4 depicts 4 depicts a scene a scene in which in which many many vehicles vehicles are drivingare driving on aon road a road that that can can be regardedbe regarded as aas one-dimensional a one-dimensional queue queue with with L lattices. L lattices. As a As particle a particle occupying occupying the lattice the lat- of thetice queue,of the queue, vehicle vehicle can only can move only forward move forward one step one when step the when next the lattice next in lattice the forward in the directionforward direction is empty. is (The empty. model (The turns model to anturn asymmetrics to an asymmetric simple exclusion simple exclusion process p (ASEP)rocess when(ASEP) a particle when a in particle the queue in the may queue move forwardmay move or backward forward or with backward different with probability different at theprobability same time at the [44 ].)same The time vehicle [44].) enters The thevehicle first latticeenters ofthe the first queue lattice with of probabilitythe queue withα if thereprobability is no occupation α if there byis no any occupation particle. Similarly, by any particle. the vehicles Similarly, at the the end vehicles of the queue at the jump end outof the of queue the system jump with out probabilityof the systemβ atwith each probability time step. β Each at each lattice time in thestep. system Each lattice is either in emptythe system or occupied is either byempty vehicles. or occupied by vehicles.
p = 1
Road L FigureFigure 4. The totally asymmetric simple exclusion process (TASEP)(TASEP) modelmodel ofof traffictraffic flowflow onon road.road.
System may be in in the the following following three three different different stationary stationary phases phases when when αα,,ββ taketake different values. 1. αα<<ββ andand α <<00.5.5.. The The system system is is in in l low-densityow-density (LD) phase, which can bebe regarded asas an an unblocked unblocked road. road. In In LD, LD, the the volume volume of of flow flow JJ and the the particle particle density density ρ ofof thethe modelmodel are determined determined by by the the entering entering probability probabilityα. Namely,α. Namely,J =Jα=(1α−(1α−),훼ρ)1,휌=1 α=, α α 훼ρ,L휌퐿== α(1(1−−α훼)/)⁄β훽, ρ, bulk휌푏푢푙푘==,α where, where the the subscripts subscripts 1, L1, and L and bulk bulk denote denote the head,the head, tail tailand and the the middle middle lattice lattice of TASEP of TASEP queue, queue respectively., respectively. 2. α > β and β < 0.5. The system is in high-density (HD) phase, which can be seen 2. α > β and β < 0.5. The system is in high-density (HD) phase, which can be seen as a as a congested road. In HD, the volume of flow J and the particle density ρ of congested road. In HD, the volume of flow J and the particle density ρ of the the model are determined by the ejecting probability β. Namely, J = β/(1 − β), model are determined by the ejecting probability β. Namely, J = 훽⁄(1 − 훽), 휌 = ρ = 1 − β(1 − β)/α, ρ = 1 − β, ρ = β. 1 1 1− β (1 − 훽)⁄훼, 휌 = 1L− 훽, 휌 =bulkβ. 3. α > 0.5 and β > 0.5퐿 . The system푏푢푙푘 is in maximum-current (MC) phase in which the 3. α > 0.5 and β > 0.5. The system is in maximum-current (MC) phase in which the1 maximum number of vehicles running on the road. And J = 0.25, ρ1 = 1 − 14 α, maximumβ number of vehicles running on the road. And J = 0.25, 휌 = 1 − 훼, ρ = , ρ = 0.5. 1 4 L 훽4 bulk 휌 = , 휌 = 0.5. Moreover,퐿 4 푏푢푙푘 when α = β < 0.5, the system is in a coexistence phase between LD and HD, whichMoreover is divided, when byα = a shock.β < 0.5 From, the system this example, is in a wecoexistence can easily phase point between out that αLDand andβ canHD, be which understood is divided as theby normalizeda shock. From relative this example, value between we can the easily entrance point (exit) out that rate α of and the particleβ can be and understood the capacity as the of intersectionnormalized inrelative TASEP value queue. between the entrance (exit) rate of the particle and the capacity of intersection in TASEP queue.
4.2. Modeling the Dynamics of YELLOW Algorithm through TASEP Similarly, we can use TASEP to model the forwarding behavior of packet of YEL- LOW algorithm in ICN router. Queuing packets in buffer can be regarded as identical particles that move along the lattice. The system consists of three queues with a junction Electronics 2021, 10, 806 10 of 23
Electronics 2021, 10, x FOR PEER REVIEW 11 of 24 4.2. Modeling the Dynamics of YELLOW Algorithm through TASEP Similarly, we can use TASEP to model the forwarding behavior of packet of YELLOW algorithm in ICN router. Queuing packets in buffer can be regarded as identical particles positionedthat move alongin the the middle lattice. of Thethe system system as consists shown of in three Figure queues 5. Each with queue a junction contains positioned L sites. qinueue the 1 middle and queue of the 2 me systemrge together as shown at insite Figure 2L +5 1.. EachThe external queue contains forwardingL sites. traffic/internalqueue 1 and cachequeue 2 service merge togethertraffic enters at site queue 2L + 1.1/ Thequeue external 2 for buffering, forwarding and traffic/internal then converges cache into service the porttraffic’s forwarding enters queue queue1/queue queue2 for 3 buffering,for actual andforwarding. then converges Packets into enter the the port’s queue forwarding 1/queue 2 withqueue thequeue rate3 for훼1/ actual훼2 (such forwarding. as arriving Packets following enter Poisson the queue distribution)1/queue 2 with. The the packets rate α1 /canα2 leave(such the as arriving queue 1/queue following 2/system Poisson with distribution). the rate 훽1/훽 The2/훽 packets3. Obviously, can leave in some the queuecases,1/ queuequeue 3 will2/system enter the with HD the phase rate βbecause1/β2/β 3of. Obviously,too much packets in some entering cases, queue from 3queue will 1 enter and thequeue HD 2, whichphase becausecan be used of too to much simulate packets congestion entering on from thequeue router1 and duequeue to bandwidth2, which can conflict. be used The to dynamicssimulate congestion of this system on the modeling router due is to similar bandwidth to the conflict. traffic flow The dynamics in crossing of thiswhere system two branchmodeling roads is similar merge to into the traffic one primary flow in crossing road. In where particular, two branch the primary roads merge road into is often one blockedprimary as road. well In in particular, real life. the primary road is often blocked as well in real life.
1 1 queue 1 L 훽1
external 2L+1 queue 3 3L forward flow
L+1 queue 2 2L 2 훼푒푓푓 훽3 훽2 internal response flow
Figure 5. Modeling YELLOW through three TASEP queue with one conjunction.conjunction. Since only three stationary phases can be found in each queue, there are possible Since only three stationary phases can be found in each queue, there are possi- 33 = 27 stationary phases in our system adopting YELLOW algorithm theoretically. How- ble 33 = 27 stationary phases in our system adopting YELLOW algorithm theoretically. ever, the number of possible stationary phases decreases dramatically due to many con- However, the number of possible stationary phases decreases dramatically due to many straints. For example: constraints. For example: 1. Since β3 can be regarded as the normalization of forwarding capacity of router port, 1. Since 훽3 can be regarded as the normalization of forwarding capacity of router port, following inequalities are universal: α < β , α < β , β >0.5. Therefore, queue 3 can following inequalities are universal: 훼 1< 훽 ,3훼 2< 훽 3, 훽 3> 0.5. Therefore, queue 3 can only present maximal-current phase1 or low-density3 2 3 3 phase. This conclusion can be only present maximal-current phase or low-density phase. This conclusion can be easily understood, because the purpose of YELLOW algorithm is to avoid keeping easily understood, because the purpose of YELLOW algorithm is to avoid keeping the the congestion state (HD phase) in the router forwarding queue for a period. congestion state (HD phase) in the router forwarding queue for a period. 2. According to the principle of flow conservation, the total current passing through the 2. According to the principle of flow conservation, the total current passing through system is equal to: the system is equal to:
Joverall퐽표푣푒푟푎푙푙==J3퐽=3 =J1퐽+1 +J2퐽2 (1)(1)
where J퐽1 isis thethe volumevolume ofof flowflow ofof queuequeue 1 and J퐽22 isis that that of ofqueue queue2. 2. ItIt suggestssuggests thatthat queue 3 cannot have the low-densitylow-density phase when either queue 1 or queue 2 is in maximal-currentmaximal-current phase or High High-density-density phase. Similarly, queue 1 and queue 2 can not be in m maximal-currentaximal-current phase at the same time whenwhen queue 3 is suffering bandwidth competitioncompetition (namely at HD phase)phase).. Thus, wewe infer infer that that there there are only are six only stationary six stationary phases in the phases system: in (LD the, LD system, LD):, (퐿퐷LD,,퐿퐷LD, 퐿퐷, MC), ()퐿퐷, (LD, 퐿퐷,,HD푀퐶,)MC, (퐿퐷), (,LD퐻퐷,,MC푀퐶),,MC(퐿퐷),,푀(퐶HD, 푀퐶, LD), (,퐻퐷MC, 퐿퐷) and, 푀퐶()MC and, LD (푀퐶, MC, 퐿퐷), where, 푀퐶) , whereX/Y/Z X/Y/Z in the in expression the expression (X,Y,Z) (X,Y,Z) describes describes the phase the inphase the queuein the 1/2/3queue respectively.1/2/3 respectively. After- Afterwardswards, we attempt, we attempt to deduce to deduce the approximate the approximate solution solution of existence of existence conditions conditions for these for thesesix stationary six stationary phases phases through thr mean-fieldough mean- theoryfield theory [45] that [45 neglects] that neglects the occupation the occupation corre- correlationslations of the of sites the beforesites before and afterand theafter junction. the junction. Mean-field Mean-field approximation approximation decomposes decom- posesmany-body many- problembody problem into multiple into multiple one-body one problem,-body problem, which is which a common is a common method tomethod study tothe study coupling the coupling of multiple of TASEPmultiple queues. TASEP Jonathan queues. CJonathan et al. [46 C] haveet al. proved[46] have that proved the power that thespectrum power characteristicsspectrum characteristics of three queues of three with queues one junction with one is junction the same is as the that same of a as single that of a single TASEP queue. Hence, our system can be analyzed form the perspective of simple coupling of three separate TASEP queues, as the known conclusions introduced in Section 4.1 can be easily utilized such as phase diagram, particle currents and density Electronics 2021, 10, 806 11 of 23
TASEP queue. Hence, our system can be analyzed form the perspective of simple coupling of three separate TASEP queues, as the known conclusions introduced in Section 4.1 can be easily utilized such as phase diagram, particle currents and density profiles. In order to facilitate the analysis, we introduce the intermediate variable αe f f as the equivalent entry rate of queue 3. Firstly, we analyze the simplest stationary phase (LD, LD, LD), which exists when the following inequality is fulfilled:
1 1 1 α < , α < β , α < , α < β , α < , α < β (2) 1 2 1 1 2 2 2 2 e f f 2 e f f 3 According to Equation (1), we can deduce that α1(1 − α1) + α2(1 − α2) = αe f f 1 − αe f f (3)
Thus, the possible conditions for the existence of phase (LD, LD, LD) is as follows, p 1 − 1 − 4[α (1 − α ) + α (1 − α )] 1 α = 1 1 2 2 < min β , (4) e f f 2 3 2
For phase (LD, LD, MC), it should satisfy,
1 1 1 1 α < , α < β , < , β < α , α > , β > (5) 1 2 1 1 2 2 2 e f f 2 3 2 Similarly, the possible conditions for the existence of phase (LD, LD, MC) is as follows, p 1 − 1 − 4[α (1 − α ) + α (1 − α )] 1 α = 1 1 2 2 ≥ (6) e f f 2 2 So the only solution of the equation is,
1 α (1 − α ) + α (1 − α ) = (7) 1 1 2 2 4 The (LD, HD, MC) phase is defined by the following expression:
1 1 1 1 α < , α < β , α < , α < β , α > , β > (8) 1 2 1 1 2 2 2 2 e f f 2 3 2 Taking into account Equation (1), we obtain:
1 α1(1 − α1) + β2(1 − β2) = 4 1 p 1 (9) β2 = 2 − α1(1 − α1) < 2
At this time, the current on queue 2 (J2) should be more than that of queue 1 (J1). We could obtain: J 1 J = α (1 − α ) < 3 = (10) 1 1 1 2 8 √ 2− 2 Hence, we can deduce that α1 < 4 from (10). The known conclusion of mean-filed theory for the current [] can be utilized in in our system as follows,
Joverall = hτL(1 − τ2L+1)i + hτ2L(1 − τ2L+1)i ≈ (hτLi + hτ2L+1i)(1 − hτ2L+1i) (11) = (ρL + ρ2L)(1 − ρ2L+1) Electronics 2021, 10, 806 12 of 23
where h ... i denotes a statistical average. τi = 1 (or τi = 0) indicates that the state of the ith lattice is occupied (or free). Thus the current of each queue can be written as:
J1 = β1ρL, J2 = β2ρ2L, J3 = αe f f (1 − ρ2L+1) (12)
Therefore, the αe f f can be deduced from (11) and (12) as follows:
q 1 1 α = ρ + ρ = 1 − β + ρ = α (1 − α ) − + ρ > > α (13) e f f L 2L 2 L 1 1 2 L 2 2 From (11)–(13), we find the system is in the (LD, HD, MC) phase when: √ 1 q 2 − 2 α > − α (1 − α ), α < (14) 2 2 1 1 1 4 Similarly, for phase (HD, LD, MC), it should satisfy,
1 1 1 1 β < , β < α , α < , α < β , α > , β > (15) 1 2 1 1 2 2 2 2 e f f 2 3 2 We obtain the following equations according to (1):
1 β1(1 − β1) + α2(1 − α2) = 4 1 p 1 (16) β2 = 2 − α2(1 − α2) < 2
At this time, the current on queue 2 (J2) should be less than that of queue 1 (J1). We could obtain: J 1 J = α (1 − α ) < 3 = (17) 2 2 2 2 8 q 1 1 α = ρ + ρ = 1 − β + ρ = α (1 − α ) + + ρ > > α (18) e f f L 2L 1 2L 2 2 2 2L 2 2 Hence, the Equation (15) can be rewritten as: √ 1 q 2 − 2 1 α > − α (1 − α ), α < , β > (19) 1 2 2 2 2 4 2 The (LD, MC, MC) is defined by the following expression:
1 1 1 1 1 α < , α < β , α > , β > , α > , β > (20) 1 2 1 1 2 2 2 2 e f f 2 3 2 According to the law of conservation of flow in (1), we can obtain the following 1 1 equation J3 4 = J2 4 + J1. Hence, J1 ≈ 0. For phase (MC, LD, MC), it should satisfy:
1 1 1 1 1 α > , β > , α < , α < β , α > , β > (21) 1 2 2 2 2 2 2 2 e f f 2 3 2 According to the law of conservation of flow in (1), we can obtain the following 1 1 equation J3 4 = J1 4 + J2. Hence, J2 ≈ 0.
5. Performance Evaluation In this chapter, firstly, we evaluate the performance of algorithm YELLOW in a small linear topology network. Afterwards, we use Monte Carlo simulation method to verify the accuracy of the approximate solution for the existence of conditions of each phase in YELLOW deduced by the TASEP model in the previous section. Electronics 2021, 10, 806 13 of 23
5.1. The Performance of the YELLOW Algorithm To evaluate the performance of YELLOW, we carry out packet-level simulations using the NS-3 simulator [47], which is based on a discrete event. NS-3 abstracts the topologies, Electronics 2021, 10, x FOR PEER REVIEW 14 of 24 channels, network protocols, and some commonly network element devices used in real networks, and encapsulates them into common C++ class objects. We deploy ICN packets upon the IP layer in the form of overlay, so that routing can be easily implemented through schemethe default like IPCCN routing [3]. W rathere adopt than the complex lookup- routing-by-namingby-name mechanism scheme [11,48] liketo help CCN user [3]. find We theadopt named the lookup-by-name data chunk (NDC). mechanism Specifically, [11, 48a hash] to help table user is set find to therecord named the mapping data chunk of (NDC).the name Specifically, of NDCs and a hash their table global is addresses. set to record the mapping of the name of NDCs and theirA global robust addresses. and receiver-driven transport protocol, content-centric TCP (CCTCP) [20], is implementedA robust and to receiver-drivenguarantee the transmission transport protocol, quality, content-centricwhich supports TCP the mechanism (CCTCP) [20 of], timeoutis implemented request to retransmission guarantee the based transmission on RTT quality, and retransmission which supports time the-out mechanism (RTO) esti- of matetimeouts. Besides, request retransmission CCTCP limits based the user’s on RTT send and window retransmission of NDC time-out request (RTO) in the estimates. AIMD modelBesides, like CCTCP TCP to limits avoid the congestion. user’s send We window deploy the of NDCalgorithm request YELLOW in the AIMDon the modelbottle- necklike TCP link toin avoida small congestion. linear topology We deploy network the algorithmas shown in YELLOW Figure 6 on. For the a bottleneck thorough per- link formancein a small comparison, linear topology we also network implement as shown two inother Figure classical6. For AQM a thorough algorithms performance which are REDcomparison, and BLUE. we also The implement ICN client two application other classical is AQM implemented algorithms and which installed are RED in and the nodesBLUE.(푁 The1, 푁 ICN2, 푁3) client on the application left side ofis implemented the graph, which and installed sends 10 in requests the nodes for( N new1, N 2 NDC, N3) eachon the seconds. left side of The the graph, ICN server which sends application 10 requests is implemented for new NDC each and seconds. installedThe in ICN the ( ) nodesserver( application푁4, 푁5, 푁6) on is implementedthe right side and and installed the routers in the (A, nodes B, C),N 4which, N5, N are6 on responsible the right side for respondingand the routers the (A,request B, C),s whichform client. are responsible As the most for respondingbasic component the requests in each form end client. system, As the mostICN protocol basic component stack ought in each to assemble end system, received the ICN ICN protocol packets stack to a oughtchunk tocompletely assemble andreceived sequentially. ICN packets to a chunk completely and sequentially.
N1 5ms N4 10ms
15ms 50Mbps 50Mbps N2 A B C N5 10ms 10ms 15ms
10ms 100Mbps 100Mbps 5ms N3 N6
Figure 6. Simulation topology topology..
Chunk sizesize isis setsetto to 256 256 KB KB to to allow allow enough enough time time for for the the AQM AQM algorithms algorithms to make to make the theclient-end client-end to adjust to adjust the requestthe request rate whenrate when congestion congestion occurs. occurs. The workloadThe workload extracted extracted from fromcatalog catalog of N =of1 N×=1015 ×content105 content objects objects follows follows the Zipf the distribution Zipf distribution (α = 0.8 (α).= The0.8 size). The of sizethe cacheof the store cache in store router in is router 100 (chunks). is 100 (chunks). The buffer The of buffer the queue of the and queue assembling and assembling memory memoryof cache moduleof cache accommodates module accommodates 200 packets 200 which, packets for 1500-bytewhich, for packets, 1500-byte corresponds packets, cor- to a queuingresponds delay to a queuing of 0.35 s. delay In order of 0.35 to ensure s. In order the same to ensure memory the costsame of memory YELLOW cost algorithm of YEL- LOWand comparison algorithm and algorithms, comparison thelength algorithm of cachings, the length queue of and caching forwarding queue queueand forwarding are set to 100.queue Tables are 3set and to4 100shows. Table thes configurations 3 and 4 shows used the forconfigurations RED and BLUE used respectively, for RED and which BLUE is respectively,set according which to the is experience set according of previous to the experience studies [23 of,27 previous]. studies [23,27].
Table 3. RED configuration.
Configuration Value
푚푖푛푡ℎ 20% 푚푎푥푡ℎ 80% 푚푎푥푝 1 푤푞 0.002
Electronics 2021, 10, 806 14 of 23
Table 3. RED configuration. Electronics 2021, 10, x FOR PEER REVIEW 15 of 24
Configuration Value
minth 20% max 80% Table 4. BLUE configuration. th maxp 1 Configuration wq Value 0.002 freeze_time 50 ms
Table 4. BLUE훿1 configuration. 0.02 훿2 Configuration0.002 Value L 100 freeze_time 50 ms δ1 0.02 In the following experiments, weδ2 find that even if YELLOW is set with0.002 different configurations, as long as it meets theL parameter setting restrictions introduced 100 in Section 3.3, the performance of YELLOW is not significantly different. For convenience of de- scription, we set someIn the following configuration experiments, parameters we find thatto even be the if YELLOW same is as set BLUE’s, with different con- figurations, as long as it meets the parameter setting restrictions introduced in Section 3.3, where freezetime = 50 ms, 훿1 = 0.02, 훿2 = 0.0025, 훿3 = 0.001, 퐿1 = 80 and 퐿2 = 50, mainly because the algorithmthe performance YELLOW of is YELLOW designed is not with significantly reference different. to BLUE. For The convenience simulation of description, we set some configuration parameters to be the same as BLUE’s, where freeze = 50 ms, program runs for 160 s. The first 80 s are used to warm up the cache space of routers, andtime δ1 = 0.02, δ2 = 0.0025, δ3 = 0.001, L1 = 80 and L2 = 50, mainly because the algorithm the remaining timeYELLOW is used is to designed gather withstatistic references. Specifically, to BLUE. Thethe simulationrequest rate program is doubled runs for at 160 s. The 20 s to simulate thefirst more 80 s areserious used network to warm upcongestion. the cache spaceAt 60 of s, routers,the request and therate remaining is reduced time is used by one third to simulateto gather the statistics. idle network. Specifically, The sampling the request frequency rate is doubled of statistical at 20 s to data simulate is 20 the more times per second,serious and then network the average congestion. value At 60 is s, picked. the request To ratestudy is reducedthe performance by one third of to al- simulate the gorithms under idle different network. ICN The cache sampling strategies, frequency we of also statistical build data two is network 20 times per scenario second,s and then adopting leave copythe average every value(LCE) is and picked. leave To study copy the down performance (LCD) [4 of9] algorithms, respectively. under L differentCE ICN caches chunks incache every strategies, node along we alsothe buildtransmission two network path. scenarios LCD improves adopting the leave cache copy hit every (LCE) and leave copy down (LCD) [49], respectively. LCE caches chunks in every node along the rate through storing the chunks only in the next hop of the previous cache node, which transmission path. LCD improves the cache hit rate through storing the chunks only in puts the popular thecontents next hop close of theto previoususers gradually. cache node, In order which to puts fully the understand popular contents the dif- close to users ference between gradually. YELLOW, In RED order and to fully BLUE, understand we first the observe difference the between change YELLOW, of the queue RED and BLUE, length and markingwe firstprobability observe under the change different of the loads queue and length network and marking scenarios probability as shown under in different Figures 7–9. loads and network scenarios as shown in Figures7–9.
Figure 7. Cont. Electronics 2021,, 10,, xx FORFOR PEERPEER REVIEWREVIEW 16 of 24
Electronics 2021, 10, x FORElectronics PEER REVIEW2021, 10, 806 16 of 24 15 of 23
Figure 7. Comparison of queue length and marking probability under RED between leaveleave copycopy Figureevery 7.FigureComparison ((LCE 7.) )Comparison and of lleave queue copy lengthof queue down and length marking (LCD and)).. probability ((a ))marking thethe actual under probability and RED average between under queue leave RED copy length between every of (LCE) leaveunder andcopy LCE; leave ((b copy)) downthethe (LCD).every actualactual ((aLCE) andand the) actual averageandaverage leave and queuequeue average copy downlengthlength queue ( LCD lengthofof underunder). of(a) under theLCD;LCD; actual LCE; ((c)) (thetheandb) the markingmarking average actual and queueprobabilityprobability average length queue underunder of under length LCE;LCE; LCE; of ( under(d)) ( thetheb) LCD; (c) themarking markingthe actual probability probability and average under under queue LCE; LCD. ( dlength) the marking of under probability LCD; (c) underthe marking LCD. probability under LCE; (d) the marking probability under LCD.
FigureFig 8.FigureComparisonure 8. Comparison8. Comparison of queue of of length queue queue and lengthlength length marking and and probability marking marking probabilityprobability under BLUE under between BLUEBLUE LCE between between and LCD. LCE LCE (a) the and and actual and averageLCDLCD queue.. ((a.) )( theathe length) the actualactual actual of under andand and averageaverage LCE; average (b) thequeuequeue queue actual lengthlength length and average ofof of under underunder queue LCE;LCE;LCE; length ((b)) thethe of under actualactualactual LCD; and andand (average caverageaverage) the marking queue queuequeue probability underlengthlength LCElength and ofof ofunderunder LCD. under LCD;LCD; LCD; ((c )() c thethe) the markingmarking marking probabilityprobability probability under underunder LCELCE andand LCD;LCD;
Figure 9. Comparison of queue length and marking probability under YELLOW between LCE and FigureFigure 9. Comparison 9.. Comparison of queue of length queue and lengthlength marking and probability marking under probability YELLOW under between YELLOW LCE and between LCD. (a) theLCE actual and and LCD. (a) the actual and average queue length of under LCE; (b) the actual and average queue averageLCD queue.. ((a)) thethe length actualactual of under andand averageaverage LCE; (b) thequeuequeue actual lengthlength and average ofof underunder queue LCE;LCE; length ((b)) thethe of under actualactual LCD; andand ( caverageaverage) the marking queuequeue probability length of under LCD; (c) the marking probability under LCE and LCD; underlengthlength LCE and ofof underunder LCD. LCD;LCD; ((c)) thethe markingmarking probabilityprobability underunder LCELCE andand LCD;LCD; The stability of queue length is an important index to judge the performance of an AQMThe algorithm. stability of We queue observe length that iswhether an important the network index congestion to judge the is not performance obvious (<20 of s)an AQMor the algorithm. sudden trafficWe observe change that (at 20whether s or 60 thes), thenetwork queue congestion length amplitude is not obvious of RED is(<20 the s) or largest,the sudden whic traffich means change that the(at serious20 s or 60 global s), the synchronization queue length isamplitude happening of in RED the is net- the largest,largest,work. whic whicIn theh network means thatscenarios the serious with LCE, global it is synchronization difficult for RED to is keep happening the queue in the length net- work.between In the [푚푖푛 network푡ℎ, 푚푎푥 scenarios푡ℎ] even whenwith LCE, the traffic it is difficult load is for light RED (after to keep 60 s). the Blue queue iden lengthtifies between [푚푖푛푡푡ℎ,,푚푎푥푡푡ℎ] even when the traffic load is light (after 60 s). Blue identifiestifies Electronics 2021, 10, 806 16 of 23
The stability of queue length is an important index to judge the performance of an AQM algorithm. We observe that whether the network congestion is not obvious (<20 s) or the sudden traffic change (at 20 s or 60 s), the queue length amplitude of RED is the largest, which means that the serious global synchronization is happening in the network. In the network scenarios with LCE, it is difficult for RED to keep the queue length between [minth, maxth] even when the traffic load is light (after 60 s). Blue identifies whether congestion occurs through events of packet loss or link idle. BLUE performs better than RED because its marking probability is adjusted dynamically by increment. Although the memory utilization of the router has been improved, the queue length amplitude of BLUE is still large than YELLOW. Figure9c shows that even if the network is busy, the oscillation amplitude of both forwarding queue (up) and caching service queue (down) in YELLOW can be maintained at a small level. Since the monitoring mechanism of bandwidth competition make a good prediction of the burst flow from the router, YELLOW also performs well in dealing with the burst traffic. Marking probability is another important index to judge the algorithm performance, which allows us to explore the effectiveness of AQM in preventing global synchronization and in removing biases against burst sources. For RED, marking probability p is equal to pb/1 − count × pb, where pb = maxp × Qavg − minth /(maxth − minth) . We can find that pb is linear function of Qavg. The large shock of the average queue length will result in the marked probability changing significantly in a very short time (see Figure7c,d), which makes RED cannot relieve the synchronization phenomenon between content sources. By contrast, the marking probability of BLUE is relatively stable, which marks packets evenly even when the traffic is constantly fluctuating. The marking probability of YELLOW cache queue fluctuates while the marking probability of the forwarding queue can also keep a uniform value for a period of time. This is because YELLOW is self-adaptive, so it will adjust the send window of each cache service flow when router detects the change of forwarding throughput. Moreover, the ICN protocol stack in router enables YELLOW to ensure the fairness of each burst response traffic easily. In general, YELLOW can perform better than BLUE/RED and obtain better robustness while eliminating the negative effects of global synchroniza- tion. Meanwhile, we find that different caching strategies also affect the performance of AQM algorithm. Compared with LCE, the LCD strategy improves cache-hit ratio and reduces the transmission traffic on the link greatly [49]. Therefore, no matter which AQM algorithm is adopted in the network with LCD, the fluctuation amplitude of the queue length is lower than that of LCE. Figures7d,8c and9c prove that the mark probability of AQM changes more smoothly in the network with LCD. In order to better compare the performance of the three algorithms, Tables5 and6 list the bottleneck link utilization, throughput, download latency, average packet loss rate and the mean square error of queue length of the three algorithms under different network loads. We find that algorithm YELLOW can achieve the highest bottleneck link utilization and router throughput. Since low packet loss rate will increase the queuing delay, YELLOW with the lowest packet loss rate has the highest content download delay, followed by BLUE and RED. In terms of packet loss rate, YELLOW is also the best, Comparing the mean square error of queue length of three algorithms, we can obtain the same conclusion as the previous analysis about queue stability.
Table 5. Measurement data for light load network in time interval [0, 20].
RED BLUE YELLOW bottleneck link utilization 91.18% 91.46% 91.75% Throughput (Mbps) 48.13 48.52 48.75 average packet loss rate 13.34% 12.29% 11.45% Download latency (ms) 148.73 160.82 169.1 forward 17.48 mean square error of queue length 43.71 36.73 cache 13.12 Electronics 2021, 10, 806 17 of 23
Table 6. Measurement data for heavy load network in time interval [20, 40].
RED BLUE YELLOW bottleneck link utilization 94.08% 94.18% 94.32% Throughput (Mbps) 48.12 48.57 48.77 average packet loss rate 21.78% 19.48% 18.51% Download latency (ms) 155.81 163.34 172.6 forward 19.64 mean square error of queue length 50.05 42.86 cache 14.33
5.2. Verifying the Accuracy of the Model of YELLOW through Monte Carlo Simulation We build a simulation system that is same as the model shown in Figure5, which contains three queues (queue 1, queue 2 and queue 3) by the Monte Carlo method. queue 1 simulates buffer situation of forwarding traffic that comes from the external network while queue 2 simulates the situation of the cache traffic generated internally. The site scope of queue 1/queue 2/queue 3 with capacity L ranges from 1/L + 1/2L + 1 to L/2L/3L. In each Monte Carlo step (MCS), the system employing the random update mechanism updates 3L times according to the following rules: 1. Selecting a site i(1 ≤ i ≤ 3L) randomly; 2. If i = 1/(L + 1), it means that the first site of queue 1/queue 2 is selected. If there is no particle in this site, a new particle will be injected to system with probability α1/α2. 3. If i = 3L, it means that the output site of queue 3 is selected. A particle locating in this site will leaves the system with probability β3 when the site is occupied 4. If the selected site is occupied by particle and the adjacent site on the right is empty, the particle will move to the adjacent site. 5. In addition to the above cases, we need to add some rules of YELLOW algorithm. L 6. When the number of particles whether in queue 1 or queue 2 exceeds the threshold ( 2 in this experiment), α2 will be decreased by a fixed value δ1 firstly. α1 will be reduced by δ2 only if the queue occupancy of queue 1 exceeds 50%. Noted that the value of δ1 is setting more than one order of magnitude larger than δ2. 7. If α1 + α2 > β3, α2 will also be decreased by δ1. 8. System increase the value of α1 and α2 by δ3 when the stationary phase (LD, LD, LD) exists for a period of time. To simplify the parameter of the existence condition of the stationary phase, we consider indicating α2 by nα1(0 < n ≤ 1). Therefore, Equations (4), (6) and (18) can be rewritten by (LD, LD, LD): √ < n+1− 2n > 1 α1 2(1+n2) , β3 2 q (22) 1+n− (1+n)2−4(1+n2)β(1−β) < < 1 α1 2(1+n2) , β3 2
(LD, LD, MC): q 2 1 + n − (1 + n) − 4(1 + n2)β(1 − β) 1 α < , β > (23) 1 2(1 + n2) 3 2
(HD, LD, MC): √ √ n + 1 − 2n 2 − 2 1 < α < , β > (24) 2(1 + n2) 1 4n 3 2
Figure 10 presents the phase diagram of model system on α1 − β3 axis when n is fixed at 0.5. Points and lines correspond to the results of simulation and analysis respectively. We find that there are symbiotic stationary phases in some phases. For example, there are un- usual (LD, LD, MC) in (MC, LD, MC), (LD, HD, MC) in (LD, MC, MC), (LD, LD, MC) Electronics 2021, 10, x FOR PEER REVIEW 19 of 24
tively. We find that there are symbiotic stationary phases in some phases. For example, Electronics 2021, 10, 806 18 of 23 there are unusual (퐿퐷, 퐿퐷, 푀퐶) in (푀퐶, 퐿퐷, 푀퐶) , (퐿퐷, 퐻퐷, 푀퐶) in (퐿퐷, 푀퐶, 푀퐶),(LD, LD, MC) in (HD, LD, MC). The symbiotic phase exists because the sys- tem is simulating the YELLOW algorithm to relieve congestion so that probability 훼1, 훼2 will change in a small range over a period of time. However, due to the phase transition ( ) inoccurringHD, LD in ,theMC time. Thedomain, symbiotic the shock phase can not exists be seen because in this the coordinate system s isystem. simulating The the YEL- LOWreasonalgorithm why there is to no relieve stationary congestion coexistence so thatphase probability in (퐿퐷, 푀퐶,α푀퐶1, α) 2iswill thatchange the marking in a small range overprobability a period of queue of time. 2 changes However, dramatically, due to which the phase makes transition jumping phases occurring only exist in the in timea domain, thevery shock short time. can not By contrast be seen, the inthis marking coordinate probability system. of queue The 1 changes reason whyslowly there and uni- is no stationary coexistenceformly making phase it easy in to (stabilizeLD, MC for, MC jumping) is that phases the (see marking experiment probability Figure 9c).of queue 2 changes dramatically,Besides, as which shown makesin Figure jumping 11, withphases the decrease only (increase) exist in a of very n, the short areas time. occupied Bycontrast, the (퐿퐷, 퐿퐷, 푀퐶), (퐿퐷, 퐿퐷, 퐿퐷) (퐻퐷, 퐿퐷, 푀퐶)&(퐿퐷, 퐿퐷, 푀퐶) markingby probability of queue and1 changes slowly and uniformlygradually making expands it easy to stabilize (shrinks). (퐿퐷, 푀퐶, 푀퐶)&(퐿퐷, 퐻퐷, 푀퐶) is the opposite. When the value of n is equal to 1, forthe jumpingphase (퐻퐷 phases, 퐿퐷, 푀퐶 (see)&(퐿퐷 experiment, 퐿퐷, 푀퐶) disappears. Figure9 c).
FigureFigure 10. 10. SysteSystemm phase phase diagram diagram when when n is fixed n is at fixed 0.5. at 0.5.
Besides, as shown in Figure 11, with the decrease (increase) of n, the areas occupied by (LD, LD, MC), (LD, LD, LD) and (HD, LD, MC)&(LD, LD, MC) gradually expands Electronics 2021, 10, x FOR PEER REVIEW(shrinks). (LD, MC, MC)&(LD, HD, MC) is the opposite. When the value20 of of24 n is equal to
1, the phase (HD, LD, MC)&(LD, LD, MC) disappears.
. FigureFigure 11. 11. SystemSystem phase phase diagram diagram with variable with variable n. n.
Figure 12 presents the particle density distribution of six stationary phase running under specific parameters. The coordinate-axis X is the sequential site in the queue 1/2/3. Points and lines correspond to the results of simulation and analysis respectively. The simulation results are in good agreement with the analytical results. For the LD phase in the system, the density distribution is flat except near the queue boundary. Due to the adaptive adjustment of the YELLOW algorithm, the density distribution of queue 3 can converge to a fixed value around 0.5 regardless of the existence of shock at the queue boundary. Because the yellow algorithm reduces the packet loss rate of queue 1 in order to ensure the forwarding bandwidth, even if both queue 2 and queue 1 are in the LD phase at the same time, the particle density of queue 1 is significantly higher than that of queue 2. The shock appears at the head and tail of queue 3 at the same time, which is caused by the oscillation of the YELLOW algorithm in the time domain. Due to the coexistence phase existing in YELLOW modeling by TASEP, it is difficult to analyze the particle density distribution on each phase boundary by traditional domain-wall theory [50]. Therefore, we will not carry out the experimental analysis here, and will continue to study in the future.
Electronics 2021, 10, x FOR PEER REVIEW 20 of 24
. Figure 11. System phase diagram with variable n.
Figure 12 presents the particle density distribution of six stationary phase running
Electronicsunder2021 ,specific10, 806 parameters. The coordinate-axis X is the sequential site in the queue 1/2/319. of 23 Points and lines correspond to the results of simulation and analysis respectively. The simulation results are in good agreement with the analytical results. For the LD phase in the system, the density distributionFigure 12 presents is flat the particleexcept density near the distribution queue ofboundary. six stationary Due phase to runningthe adaptive adjustmentunder of the specific YELLOW parameters. algorithm, The coordinate-axis the density X is thedistribution sequential site of in queue the queue 3 can 1/2/3. Points and lines correspond to the results of simulation and analysis respectively. The converge to a fixed valuesimulation around results 0.5 are inregardless good agreement of the with existence the analytical of shock results. Forat the the LDqueue phase in boundary. Because thethe yellow system, algorithm the density distributionreduces the is flatpacket except los nears rate the queueof queue boundary. 1 in order Due to the ensure the forwardingadaptive bandwidth, adjustment even of theif both YELLOW queue algorithm, 2 and queue the density 1 are distributionin the LD ofphasequeue at3 can the same time, the particleconverge density to a fixed of value queue around 1 is significantly 0.5 regardless of higher the existence than that of shock of queue at the queue2. boundary. Because the yellow algorithm reduces the packet loss rate of queue 1 in order The shock appears atto the ensure head the and forwarding tail of bandwidth,queue 3 at eventhe ifsame both queuetime,2 which and queue is 1caused are in the by LD the phase oscillation of the YELLOWat the same algorithm time, the particlein the densitytime domain. of queue 1 isDue significantly to the coexistence higher than that phase of queue existing in YELLOW2. modeling The shock appearsby TASEP, at the headit is anddifficult tail of queueto analyze3 at the samethe particle time, which density is caused distribution on each byphase the oscillation boundary of the by YELLOW traditional algorithm domain in the-wall time domain.theory Due[50]. to Therefore, the coexistence phase existing in YELLOW modeling by TASEP, it is difficult to analyze the particle density we will not carry outdistribution the experimental on each phase analysis boundary here, by traditional and will domain-wall continue theory to study [50]. Therefore, in the we future. will not carry out the experimental analysis here, and will continue to study in the future.
Figure 12. Cont. Electronics 2021, 10, x FOR PEER REVIEW 21 of 24 Electronics 2021, 10, 806 20 of 23
( )( ) = = = ( )( ) = = = FigureFigure 12. (a퐚) (LD퐿퐷, LD, 퐿퐷, MC, 푀퐶, )α, 1훼1 =0.2,0.2,α훼2 2 =0.1,0.1,β훽 = 00.8.8;; b(퐛) LD(퐿퐷, HD, 퐻퐷, MC, 푀퐶, )α,1훼1 =0.5,0.5α,2훼2 =0.1,0.1β, 훽 =0.8; (c)(LD, MC, MC), α = 0.1, α = 0.55, β = 0.8; (d)(MC, LD, MC), α = 0.55, α = 0.1, β = 0.8; (e)(LD, LD, LD), 0.8; (퐜) (퐿퐷, 푀퐶, 푀퐶1 ), 훼1 = 20.1, 훼2 = 0.55, 훽 = 0.8; (퐝) (푀퐶, 퐿퐷1 , 푀퐶), 훼21 = 0.55, 훼2 = 0.1, 훽 = 0.8; α1 = 0.2, α2 = 0.1, β = 0.4; (f)(HD, LD, MC), α1 = 0.25, α2 = 0.5, β = 0.7. (퐞) (퐿퐷, 퐿퐷, 퐿퐷), 훼1 = 0.2, 훼2 = 0.1, 훽 = 0.4; (퐟) (퐻퐷, 퐿퐷, 푀퐶), 훼1 = 0.25, 훼2 = 0.5, 훽 = 0.7. 6. Discussion 6. Discussion In this paper, we consider that one of the main factors for congestion and packet loss in In this paper, weICN consider routers withthat an one additional of the endmain system factor cans befor further congestion summarized and as packet the competition loss between the external forwarding traffic and the internal cache response traffic for limited in ICN routers with anbandwidth additional resources. end Wesystem propose can an adaptivebe further active summarized queue management as the algorithm compe- with tition between the externaldual queues forwarding for ICN routers, traffic which and predictsthe internal and limits cache the throughputresponse traffic of the response for limited bandwidth resources.flow of burst We request propose while guaranteeingan adaptive the active throughput queue of forwardingmanagement flow. algo- We prove rithm with dual queuesthat for ensuring ICN the routers, priority which of forwarding predicts traffic and when limits allocating the thethroughput bandwidth canof t achievehe better benefits mathematically through probability theory. In addition, when bandwidth response flow of burstcompetition request is while predicted, guaranteeing YELLOW will the limit throughput the rate of request of packetsforwarding to enter flow. the cache We prove that ensuringmodule the ofpriority the router of throughforwarding a token traffic bucket when algorithm. allocating In order the to study bandwidth the effect of can achieve better benefitspacket arrivalmathematically rate on the performance through probability of the YELLOW theory. algorithm, In additi we modelon, when YELLOW through the widely studied TASEP model, and give the approximate solution of each bandwidth competitionstationary is predicted, phase and theYELLO particleW density. will limit the rate of request packets to enter the cache module ofCompared the router with through the other twoa token classical bucket AQM algorithmsalgorithm. (RED In andorder BLUE) to study in network the effect of packet arrivalscenarios rate with on different the performance ICN cache strategies of the and YELLOW load, the simulationalgorithm, results we showedmodel that YELLOW through thethe widely queue of studied YELLOW TASEP can be stablemodel, at the and expected give the value, approximate and the significant solution gains of of each stationary phase and the particle density. Compared with the other two classical AQM algorithms (RED and BLUE) in net- work scenarios with different ICN cache strategies and load, the simulation results showed that the queue of YELLOW can be stable at the expected value, and the signifi- cant gains of router with low packet loss rate, robustness and high throughput. We verify the accuracy of the module results of YELLOW through Monte Carlo approximation while we find an interesting phenomenon that there are some symbiotic phases appear- ing in the system phase diagram. This is because the input/output rate of TASEP queues are adjusted adaptively in time domain when the YELLOW algorithm detects congestion. We hope that this paper can provide ideas for more research on optimizing the ex- isting ICN transport protocol and congestion control. Moreover, we will continue to Electronics 2021, 10, 806 21 of 23
router with low packet loss rate, robustness and high throughput. We verify the accuracy of the module results of YELLOW through Monte Carlo approximation while we find an interesting phenomenon that there are some symbiotic phases appearing in the system phase diagram. This is because the input/output rate of TASEP queues are adjusted adaptively in time domain when the YELLOW algorithm detects congestion. We hope that this paper can provide ideas for more research on optimizing the existing ICN transport protocol and congestion control. Moreover, we will continue to study how to analyze and deduce the approximate solution of the existence condition of the symbiotic phase more accurately. In the future, we are interested in further research on how to ensure the fairness of each burst response flow in the router, and how to analyze the particle density distribution on the phase boundary.
Author Contributions: Conceptualization, L.Z., H.N., and R.H.; methodology, L.Z., H.N.; software, L.Z.; writing—original draft preparation, L.Z.; writing—review and editing, L.Z., H.N., and R.H.; supervision, H.N.; project administration, R.H.; funding acquisition, H.N. All authors have read and agreed to the published version of the manuscript. Funding: This work was funded by Strategic Leadership Project of Chinese Academy of Sciences: SEANET Technology Standardization Research System Development (Project No. XDC02070100). Acknowledgments: We would like to express our gratitude to Hong Ni, Rui Han, Yuanhang Li for their meaningful support for this work. Conflicts of Interest: The authors declare no conflict of interest.
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